Abstract:
A lever is supported by a lever supporting portion. The lever is urged by a first spring and a second spring. The urging force of the first spring varies over the entire operational range of the lever. The second spring and a third spring are provided serially through a movable supporting member. The displacement of the movable supporting member is restricted by a fixed supporting member. If the urging force of the second spring exceeds the urging force of the third spring, the restriction on the displacement of the movable supporting member is removed. Therefore, the present configuration provides a player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano.

Description:
This is a continuation of application Ser. No. 12/408,904 filed 23 Mar. 2009, which claims foreign priority to JP 2009-4450 and JP2009-4455 both filed 13 Jan. 2009, and JP 2008-75126 and JP 2008-75121 both filed 24 Mar. 2008, the disclosures of which are all incorporated herein by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a pedal apparatus of an electronic musical instrument, the pedal apparatus controlling the manner in which a musical tone is generated. 
     2. Description of the Related Art 
     Conventionally, it is known that a pedal apparatus of an electronic musical instrument is designed to provide a player with a feeling similar to that perceived by a player on manipulation of a pedal of an acoustic piano. For example, Japanese Unexamined Patent Publication No. 2004-334008 discloses a pedal apparatus which has a lever that pivots in response to a depression of a pedal and a first spring and a second spring provided in parallel in order to urge the lever. The disclosed pedal apparatus is designed such that only the first spring urges the lever if the lever is shallowly depressed, whereas the first spring and the second spring urge the lever if the lever is depressed by a certain amount or more. Therefore, the disclosed pedal apparatus provides a player with a feeling as if the pedal became heavier at a certain point of a depression of the pedal. By such a structure, the disclosed pedal apparatus imitates the feeling perceived by the player when he manipulates a half pedal on a damper pedal of an acoustic piano. 
     SUMMARY OF THE INVENTION 
     As for an acoustic piano, if a player depresses a damper pedal, the player recognizes stepwise changes in the rate of change in the reaction force of the pedal according to the amount of displacement of the pedal. The stepwise change will be explained, referring to  FIG. 34 .  FIG. 34  shows characteristics of the reaction force of a pedal lever of a damper pedal of an acoustic piano, the reaction force being exerted when the damper pedal is depressed, not when the damper pedal is released. The damper pedal of the acoustic piano is connected with dampers through some connecting portions. These connecting portions are provided with play. In a range of A 0  of  FIG. 34  where the damper pedal is depressed shallowly, therefore, the manipulation of the pedal will not be conveyed to the dampers, resulting in a small rate of change in the reaction force of the pedal. If the amount of displacement of the damper pedal increases to move into a range of A 1  of  FIG. 34 , the conveyance of the force of depression to the dampers through the connecting portions starts, resulting in the increase in the rate of change in the reaction force of the pedal because of the increase in the reaction force caused by elastic constituents of the connecting portions and the weight and frictions of the dampers which start being partially lifted from strings. If the amount of displacement increases further to move into a range of A 2  of  FIG. 34 , the dampers fully leave the strings, resulting in no increase in the reaction force caused by the elastic constituents of the connecting portions. Therefore, the rate of change in the reaction force of the pedal reduces again. A range (a range AH in the figure) which extends from a later point in the range A 1  across the border between the ranges A 1 , A 2  to enter the range A 2  is commonly referred to as a half pedal range. In the range AH, skilled players subtly change the depth of the depression of the damper pedal to delicately vary the timbre, resonance and the like of musical tones to be generated. Depending on models and manufacturers, furthermore, the respective structures of the damper pedal, the connecting portions and the dampers vary, and so do the respective widths of the ranges A 0 , A 1 , AH and A 2  of  FIG. 34 . As shown in a dashed line in  FIG. 34 , in addition, there is no difference in the rate of change in the reaction force of the pedal between the ranges A 0 , A 1  in some cases. However, the conventional pedal apparatus of an electronic musical instrument as described above fails to provide the player with the feeling that the player of an acoustic piano perceives at the range of A 2  of  FIG. 34  (the state where the rate of change in the reaction force reduces again) which follows the range A 1  of  FIG. 34 . 
     The present invention was accomplished to solve the above-described problem, and an object thereof is to provide a pedal apparatus of an electronic musical instrument, the pedal apparatus achieving light weight and allowing a player to feel as if the player were manipulating a damper pedal of an acoustic piano. 
     In order to achieve the above-described object, it is a feature of the present invention to provide a pedal apparatus of an electronic musical instrument, the pedal apparatus including, a lever ( 40 ) which is supported by a fixed supporting member (FR) and pivots by a player&#39;s depression of the lever; a plurality of springs ( 45 ,  45 A,  56 ,  56 A,  82 ,  145 ,  152 ,  166 ;  46 ,  46 A,  57 ,  57 A,  83 ,  148 ,  158 ,  167 ;  47 ,  47 A,  61 ,  61 A,  90 ) which exert spring force on the lever ( 40 ); and a movable supporting member ( 48 ,  48 A,  53 ,  53 A,  58 ,  58 A,  84 ,  85 ,  146 ,  153 ,  157 ,  161 ,  163 ,  165 ) which supports any of the plurality of springs ( 45 ,  45 A,  56 ,  56 A,  82 ,  145 ,  152 ,  166 ;  46 ,  46 A,  57 ,  57 A,  83 ,  148 ,  158 ,  167 ;  47 ,  47 A,  61 ,  61 A,  90 ) and is displaced in response to pivoting of the lever ( 40 ), and the displacement of the movable supporting member being restricted by the fixed supporting member (FR); and when an amount of depression of the lever ( 40 ) increases from an initial state to reach a first predetermined amount of depression, a rate of change in reaction force with respect to the depression is reduced because of collaboration of the plurality of springs ( 45 ,  45 A,  56 ,  56 A,  82 ,  145 ,  152 ,  166 ;  46 ,  46 A,  57 ,  57 A,  83 ,  148 ,  158 ,  167 ;  47 ,  47 A,  61 ,  61 A,  90 ) and the movable supporting member ( 48 ,  48 A,  53 ,  53 A,  58 ,  58 A,  84 ,  85 ,  146 ,  153 ,  157 ,  161 ,  163 ,  165 ). 
     The present invention configured as described above can make the rate of change in the reaction force of the lever ( 40 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 40 ). Therefore, the present invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano shown by the dashed line in  FIG. 34 . 
     It is another feature of the present invention to provide a pedal apparatus of an electronic musical instrument, the pedal apparatus including, a lever ( 40 ) which is supported by a fixed supporting member (FR) and pivots by a player&#39;s depression of the lever; first to third springs ( 45 ,  45 A,  56 ,  56 A,  82 ;  46 ,  46 A,  57 ,  57 A,  83 ;  47 ,  47 A,  61 ,  61 A,  90 ) which exert spring force on the lever ( 40 ); and a movable supporting member ( 48 ,  48 A,  53 ,  53 A,  58 ,  58 A,  84 ,  85 ) which supports any of the first to third springs ( 45 ,  45 A,  56 ,  56 A,  82 ;  46 ,  46 A,  57 ,  57 A,  83 ;  47 ,  47 A,  61 ,  61 A,  90 ) and is displaced in response to pivoting of the lever ( 40 ), and the displacement of the movable supporting member being restricted by the fixed supporting member (FR), wherein the first spring ( 45 ,  45 A,  56 ,  56 A,  82 ) exerts spring force on the lever ( 40 ) at all times in a direction resisting the depression of the lever ( 40 ); and if an amount of depression of the lever ( 40 ) increases from an initial state to reach a first predetermined amount of depression, a rate of change in reaction force with respect to the depression is reduced because of collaboration of the second spring, the third spring ( 46 ,  46 A,  57 ,  57 A,  83 ;  47 ,  47 A,  61 ,  61 A,  90 ) and the movable supporting member ( 48 ,  48 A,  53 ,  53 A,  58 ,  58 A,  84 ,  85 ). 
     The present invention configured as described above can make the rate of change in the reaction force of the lever ( 40 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 40 ). Therefore, the present invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano shown by the dashed line in  FIG. 34 . Because the first spring ( 45 ,  45 A,  56 ,  56 A,  82 ) exerts spring force on the lever ( 40 ) at all times in the direction resisting the depression of the lever ( 40 ), furthermore, the present invention can stabilize the reaction force of the lever ( 40 ) even at the time of change in the reaction force in the first predetermined amount of depression. 
     More specifically, as shown in  FIGS. 2A ,  6 ,  7 , for example, the present invention may be configured such that the displacement of the movable supporting member ( 48 ,  48 A) from a predetermined position toward a first predetermined direction is restricted by the fixed supporting member (FR), while the displacement toward a second direction opposite to the first direction is allowed; the first spring ( 45 ,  45 A) is provided between the fixed supporting member (FR) and the lever ( 40 ) to exert spring force on the lever ( 40 ) at all times in the direction resisting the depression of the lever ( 40 ); the second spring ( 46 ,  46 A) is provided between the movable supporting member ( 48 ,  48 A) and the lever ( 40 ) so that both ends of the second spring ( 46 ,  46 A) are in contact with the movable supporting member ( 48 ,  48 A) and the lever ( 40 ) in a state where the lever ( 40 ) is not depressed and that the second spring ( 46 ,  46 A) exerts spring force on the lever ( 40 ) in the direction resisting the depression during depression of the lever ( 40 ); and the third spring ( 47 ,  47 A) is provided between the fixed supporting member (FR) and the movable supporting member ( 48 ,  48 A) so that the third spring ( 47 ,  47 A) exerts spring force on the lever ( 40 ) in the direction resisting the depression during the displacement of the movable supporting member ( 48 ,  48 A) from the predetermined position toward the second direction. 
     According to the specific invention configured as described above, if the amount of depression of the lever ( 40 ) is small, the movable supporting member ( 48 ,  48 A) stands still at the predetermined position until the force exerted by the lever ( 40 ) through the second spring ( 46 ,  46 A) to urge the movable supporting member ( 48 ,  48 A) toward the second direction reaches the spring force exerted by the third spring ( 47 ,  47 A) to urge the movable supporting member ( 48 ,  48 A) toward the first direction. As for this configuration, the movable supporting member ( 48 ,  48 A) may be either so light that the weight of the movable supporting member ( 48 ,  48 A) can be ignored or so heavy that the weight cannot be ignored. In this description, however, it is considered that an influence caused by the weight of the movable supporting member ( 48 ,  48 A) can be ignored. Hereinafter, the weight of the movable supporting member is similarly considered in the other specific inventions. In this state, therefore, not only the spring force exerted by the first spring ( 45 ,  45 A) but also the spring force exerted by the second spring ( 46 ,  46 A) is exerted on the lever ( 40 ) in parallel. Then, if the amount of depression of the lever ( 40 ) increases further, so that the force exerted by the lever ( 40 ) through the second spring ( 46 ,  46 A) to urge the movable supporting member ( 48 ,  48 A) toward the second direction exceeds the force exerted by the third spring ( 47 ,  47 A) to urge the movable supporting member ( 48 ,  48 A) toward the first direction, the movable supporting member ( 48 ,  48 A) starts being displaced. The amount of depression of the lever ( 40 ) at the start of the displacement of the movable supporting member ( 48 ,  48 A) corresponds to the first amount of depression. 
     Then, if the amount of depression of the lever ( 40 ) increases further from this state, the movable supporting member ( 48 ,  48 A) is displaced toward the second direction, with the third spring ( 47 ,  47 A) starting acting. In this state, it is considered that the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A) are connected serially, so that the spring constant of the serial springs is smaller than that of the second spring ( 46 ,  46 A). In this state, therefore, not only the spring force exerted by the first spring ( 45 ,  45 A) but also the spring force exerted by the serial springs formed of the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A) is applied to the lever ( 40 ) in parallel. As a result, the present invention can make the rate of change in the reaction force of the lever ( 40 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 40 ). Therefore, the present invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano. 
     As described above, the movable supporting member ( 48 ,  48 A) may be either so light that the weight of the movable supporting member ( 48 ,  48 A) can be ignored or so heavy that the weight cannot be ignored. In a case where an influence caused by the weight of the movable supporting member ( 48 ,  48 A) cannot be ignored, however, it is necessary to take the inertial force acting on the movable supporting member ( 48 ,  48 A) into account. More specifically, in a case where the player deeply depresses the lever ( 40 ) and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever ( 40 ), the movable supporting member ( 48 ,  48 A) can temporarily oscillate due to collaboration of the inertial force and spring force applied to the movable supporting member ( 48 ,  48 A). Furthermore, the movable supporting member ( 48 ,  48 A) can collide with the fixed supporting member (FR) to cause oscillation of the movable supporting member ( 48 ,  48 A). The oscillation of the movable supporting member ( 48 ,  48 A) is conveyed to the lever ( 40 ) through the second spring ( 46 ,  46 A) to be perceived by the player as unnatural reaction force. As for the present invention configured as described above, however, the respective spring forces of the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A) act on the movable supporting member ( 48 ,  48 A) in the directions opposite to each other. Therefore, the present invention is able to suppress or quickly cease the oscillation. Furthermore, because the force of the springs acting on the lever ( 40 ) can be divided into the spring force exerted by the first spring ( 45 ,  45 A), and the spring force exerted by the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A), the spring force (spring constant) exerted by the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A) can be reduced. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the present invention can stabilize the reaction force of the lever ( 40 ). 
     In a case where the influence caused by the weight of the movable supporting member ( 48 ,  48 A) can be ignored, it can be considered that the inertial force acting on the movable supporting member ( 48 ,  48 A) can be also ignored. Therefore, the present invention can prevent the unnatural reaction force, also achieving reduction in weight of the pedal apparatus. 
     As shown in  FIG. 8  and  FIG. 9 , in addition, the present invention may be configured such that the movable supporting member is formed of a first movable supporting member ( 53 ,  53 A) whose displacement from a first predetermined position toward a first predetermined direction is restricted by the fixed supporting member (FR), and whose displacement toward a second direction opposite to the first direction is allowed, the first movable supporting member being connected to the lever ( 40 ) so that the first movable supporting member ( 53 ,  53 A) conveys force to the lever ( 40 ), and a second movable supporting member ( 58 ,  58 A) whose displacement toward the first direction from a second predetermined position which is apart from the first predetermined position toward the second direction is restricted by the fixed supporting member (FR) and whose displacement toward the second direction is allowed; the first spring ( 56 ,  56 A) is provided between the fixed supporting member (FR) and the first movable supporting member ( 53 ,  53 A) to exert spring force through the first movable supporting member ( 53 ,  53 A) on the lever ( 40 ) at all times in the direction resisting the depression; the second spring ( 57 ,  57 A) is provided between the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A) so that in a state where the lever ( 40 ) is not depressed, both ends of the second spring ( 57 ,  57 A) are in contact with the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A), while the second spring ( 57 ,  57 A) exerts spring force on the lever ( 40 ) in the direction resisting the depression of the lever ( 40 ) during depression of the lever ( 40 ); and the third spring ( 61 ,  61 A) is provided between the fixed supporting member (FR) and the second movable supporting member ( 58 ,  58 A) to exert spring force on the lever ( 40 ) in the direction resisting the depression during the displacement of the second movable supporting member ( 58 ,  58 A) from the second predetermined position toward the second direction. 
     According to another specific invention configured as described above, if the amount of depression of the lever ( 40 ) is small, the second movable supporting member ( 58 ,  58 A) stands still at the predetermined position until the force exerted by the lever ( 40 ) through the second spring ( 57 ,  57 A) to urge the second movable supporting member ( 58 ,  58 A) toward the second direction reaches the spring force exerted by the third spring ( 61 ,  61 A) to urge the second movable supporting member ( 58 ,  58 A) toward the first direction. In this state, therefore, not only the spring force exerted by the first spring ( 56 ,  56 A) but also the spring force exerted by the second spring ( 57 ,  57 A) is exerted on the lever ( 40 ) in parallel. Then, if the amount of depression of the lever ( 40 ) increases further, so that the force exerted by the lever ( 40 ) through the second spring ( 57 ,  57 A) to urge the second movable supporting member ( 58 ,  58 A) toward the second direction exceeds the force exerted by the third spring ( 61 ,  61 A) to urge the second movable supporting member ( 58 ,  58 A) toward the first direction, the second movable supporting member ( 58 ,  58 A) starts being displaced toward the second direction. The amount of depression of the lever ( 40 ) at the start of the displacement of the second movable supporting member ( 58 ,  58 A) corresponds to the first amount of depression. 
     Then, if the amount of depression of the lever ( 40 ) increases further from this state, the second movable supporting member ( 58 ,  58 A) is displaced toward the second direction, with the third spring ( 61 ,  61 A) starting acting. In this state, it is considered that the second spring ( 57 ,  57 A) and the third spring ( 61 ,  61 A) are connected serially, so that the spring constant of the serial springs is smaller than that of the second spring ( 57 ,  57 A). In this state, therefore, not only the spring force exerted by the first spring ( 56 ,  56 A) but also the spring force exerted by the serial springs formed of the second spring ( 57 ,  57 A) and the third spring ( 61 ,  61 A) is applied to the lever ( 40 ) in parallel. As a result, the another specific invention can make the rate of change in the reaction force of the lever ( 40 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 40 ). Therefore, the another specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano. 
     As for the another specific invention as well, similarly to the specific invention described with reference to  FIGS. 2A ,  6 ,  7 , if the influence caused by the weight of the second movable supporting member ( 58 ,  58 A) is taken into account, in a case where the player deeply depresses the lever ( 40 ) and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever ( 40 ), the second movable supporting member ( 58 ,  58 A) can temporarily oscillate due to collaboration of the inertial force and spring force applied to the second movable supporting member ( 58 ,  58 A). Furthermore, the second movable supporting member ( 58 ,  58 A) can collide with the fixed supporting member (FR) to cause oscillation of the second movable supporting member ( 58 ,  58 A). As for the another specific invention as well, however, the respective spring forces of the second spring ( 57 ,  57 A) and the third spring ( 61 ,  61 A) act on the second movable supporting member ( 58 ,  58 A) in the directions opposite to each other. Therefore, the another specific invention is able to suppress or quickly cease the oscillation. Furthermore, because the force of the springs acting on the lever ( 40 ) is divided into the spring force exerted by the first spring ( 56 ,  56 A), and the spring force exerted by the second spring ( 57 ,  57 A) and the third spring ( 61 ,  61 A), the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the another specific invention can stabilize the reaction force of the lever ( 40 ). In a case where the influence caused by the weight of the second movable supporting member ( 58 ,  58 A) can be ignored, it can be considered that the inertial force acting on the second movable supporting member ( 58 ,  58 A) can be also ignored. Therefore, the another specific invention can prevent the unnatural reaction force, also achieving reduction in weight of the pedal apparatus. 
     As shown in  FIG. 10  for example, furthermore, the present invention may be configured such that the movable supporting member is formed of a first movable supporting member ( 85 ) whose displacement between a first predetermined position and a second predetermined position which is away from the first predetermined position toward a first predetermined direction is allowed by the fixed supporting member (FR) and, a second movable supporting member ( 84 ) which is in contact with the lever ( 40 ), and whose displacement toward a second direction opposite to the first direction from a third predetermined position which is away from the first predetermined position toward the second direction is restricted by the fixed supporting member (FR), and which is in contact with the first movable supporting member ( 85 ) at all times to restrict displacement toward the first direction with respect to the first movable supporting member ( 85 ); the first spring ( 82 ) is provided between the fixed supporting member (FR) and the lever ( 40 ) to exert spring force on the lever ( 40 ) at all times in the direction resisting the depression; the second spring ( 83 ) is provided between the fixed supporting member (FR) and the second movable supporting member ( 84 ) to exert spring force on the lever ( 40 ) in a direction facilitating the depression until the displacement of the first movable supporting member ( 85 ) from the second predetermined position toward the first direction is restricted; and the third spring ( 90 ) is provided between the fixed supporting member (FR) and the first movable supporting member ( 85 ) to exert, during the displacement of the first movable supporting member ( 85 ) from the first predetermined position to the second predetermined position, spring force on the lever ( 40 ) in the direction resisting the depression. 
     According to still another specific invention configured as described above, if the amount of depression of the lever ( 40 ) is small, the first movable supporting member ( 85 ) is displaced from the first predetermined position toward the first direction along with the second movable supporting member ( 84 ). The first spring ( 82 ) and the third spring ( 90 ) exert spring force in the direction resisting depression of the lever ( 40 ), whereas the second spring ( 83 ) exerts spring force in the direction facilitating depression of the lever ( 40 ). In this state, it can be considered that the first through third springs ( 82 ,  83 ,  90 ) are connected in parallel, so that the spring constant of the combined springs of the three springs is larger than the spring constant of the first spring ( 82 ). Then, if the amount of depression of the lever ( 40 ) increases further, the displacement of the first and second movable supporting members ( 84 ,  85 ) toward the first direction is restricted at the second predetermined position by the fixed supporting member (FR). The amount of depression of the lever ( 40 ) when the displacement of the first and second movable supporting members ( 84 ,  85 ) is restricted corresponds to the first amount of depression. 
     If the amount of depression of the lever ( 40 ) increases further from this state, the spring forces of the second and third springs ( 83 ,  90 ) will not affect the depression of the lever ( 40 ), with only the first spring ( 82 ) acting on the depression of the lever ( 40 ). As a result, the still another specific invention can make the rate of change in the reaction force of the lever ( 40 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 40 ). Therefore, the invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano. 
     As for this case as well, in a case where the player deeply depresses the lever ( 40 ) and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever ( 40 ), the lever ( 40 ) collides with the second movable supporting member ( 84 ). The impact caused by the collision of the lever ( 40 ) with the second movable supporting member ( 84 ) is absorbed by the first spring ( 82 ) and the second spring ( 83 ) to be reduced. Therefore, the still another specific invention can lessen the impact on the lever ( 40 ) caused by the collision to stabilize the reaction force of the lever ( 40 ). 
     Another feature of the present invention is that in a range of the amount of depression which is smaller than the first amount of depression, when the amount of depression of the lever ( 40 ) increases from the initial state to reach a second predetermined amount of depression, the rate of change in reaction force with respect to the depression increases because of collaboration of the second spring the third spring ( 46 ,  46 A,  57 ,  57 A,  83 ;  47 ,  47 A,  61 ,  61 A,  90 ) and the movable supporting member ( 48 ,  48 A,  53 ,  53 A,  58 ,  58 A,  84 ,  85 ). 
     According to the another feature of the present invention configured as above, the rate of change in the reaction force of the lever ( 40 ) can increase and decrease stepwise according to the amount of depression of the lever ( 40 ) to start with a low rate of change to increase to a high rate to be followed by a medium rate, for example. Therefore, the another feature can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano shown by a solid line in  FIG. 34 . In this case as well, because the first spring ( 45 ,  45 A,  56 ,  56 A,  82 ) exerts spring force at all times in the direction resisting depression of the lever ( 40 ), the another feature can stabilize the reaction force of the lever ( 40 ) at the time of the change in the reaction force at the first and second amounts of depression as well. 
     As shown in  FIGS. 12 ,  16 ,  17 , more specifically, the present invention may be configured such that the displacement of the movable supporting member ( 48 ,  48 A) from a predetermined position toward a first predetermined direction is restricted by the fixed supporting member (FR), while the displacement toward a second direction opposite to the first direction is allowed; the first spring ( 45 ,  45 A) is provided between the fixed supporting member (FR) and the lever ( 40 ) to exert spring force on the lever ( 40 ) at all times in the direction resisting the depression of the lever ( 40 ); the second spring ( 46 ,  46 A) is provided between the movable supporting member ( 48 ,  48 A) and the lever ( 40 ) so that in a state where the lever ( 40 ) is not depressed, one end of the second spring ( 46 ,  46 A) is away from the movable supporting member ( 48 ,  48 A) or the lever ( 40 ), whereas a depression of the lever ( 40 ) causes both ends of the second spring ( 46 ,  46 A) to come into contact with the movable supporting member ( 48 ,  48 A) and the lever ( 40 ) to exert spring force on the lever ( 40 ) in the direction resisting the depression of the lever ( 40 ); and the third spring ( 47 ,  47 A) is provided between the fixed supporting member (FR) and the movable supporting member ( 48 ,  48 A) so that the third spring ( 47 ,  47 A) exerts spring force on the lever ( 40 ) in the direction resisting the depression during the displacement of the movable supporting member ( 48 ,  48 A) from the predetermined position toward the second direction. 
     According to a further specific invention configured as described above, if the amount of depression of the lever ( 40 ) is small, the both ends of the second spring ( 46 ,  46 A) are not in contact with the movable supporting member ( 48 ,  48 A) and the lever ( 40 ), so that the spring force of only the first spring ( 45 ,  45 A) is exerted on the lever ( 40 ). If the amount of depression of the lever ( 40 ) increases from this state, the both ends of the second spring ( 46 ,  46 A) come into contact with the movable supporting member ( 48 ,  48 A) and the lever ( 40 ). The amount of depression of the lever ( 40 ) at the time of contact of the both ends of the second spring ( 46 ,  46 A) with the movable supporting member ( 48 ,  48 A) and the lever ( 40 ) corresponds to the second amount of depression. Even if the amount of depression of the lever ( 40 ) increases further from this state, the movable supporting member ( 48 ,  48 A) stands still at the predetermined position until the force exerted by the lever ( 40 ) through the second spring ( 46 ,  46 A) to urge the movable supporting member ( 48 ,  48 A) toward the second direction reaches the force exerted by the third spring ( 47 ,  47 A) to urge the movable supporting member ( 48 ,  48 A) toward the first direction. In this state, therefore, not only the spring force of the first spring ( 45 ,  45 A) but also the spring force of the second spring ( 46 ,  46 A) is exerted on the lever ( 40 ) in parallel. 
     Then, if the amount of depression of the lever ( 40 ) increases further, so that the force exerted by the lever ( 40 ) through the second spring ( 46 ,  46 A) to urge the movable supporting member ( 48 ,  48 A) toward the second direction exceeds the force exerted by the third spring ( 47 ,  47 A) to urge the movable supporting member ( 48 ,  48 A) toward the first direction, the movable supporting member ( 48 ,  48 A) starts being displaced toward the second direction. The amount of depression of the lever ( 40 ) at the start of the displacement of the movable supporting member ( 48 ,  48 A) toward the second direction corresponds to the first amount of depression. Then, if the amount of depression of the lever ( 40 ) increases further from this state, the movable supporting member ( 48 ,  48 A) is displaced toward the second direction, with the third spring ( 47 ,  47 A) starting acting. In this state, it is considered that the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A) are connected serially, so that the spring constant of the serial springs is smaller than that of the second spring ( 46 ,  46 A). In this state, therefore, not only the spring force exerted by the first spring ( 45 ,  45 A) but also the spring force exerted by the serial springs formed of the second spring ( 46 ,  46 A) and the third spring ( 47 ,  47 A) is applied to the lever ( 40 ) in parallel. As a result, the further specific invention can make the rate of change in the reaction force of the lever ( 40 ) increase and decrease stepwise according to the amount of depression of the lever ( 40 ) to start with a low rate of change to increase to a high rate to be followed by a medium rate. Therefore, the further specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano. Similarly to the specific invention described with reference to  FIGS. 2A ,  6 ,  7 , in addition, the further specific invention can stabilize the reaction force of the lever ( 40 ). 
     Furthermore, as shown in  FIGS. 18 ,  19 , for example, the present invention may be configured such that the movable supporting member is formed of a first movable supporting member ( 53 ,  53 A) whose displacement from a first predetermined position toward a first predetermined direction is restricted by the fixed supporting member (FR), and whose displacement toward a second direction opposite to the first direction is allowed, the first movable supporting member ( 53 ,  53 A) being connected to the lever ( 40 ) so that the first movable supporting member ( 53 ,  53 A) conveys force to the lever ( 40 ), and a second movable supporting member ( 58 ,  58 A) whose displacement toward the first direction from a second predetermined position which is away from the first predetermined position toward the second direction is restricted by the fixed supporting member (FR) and whose displacement toward the second direction is allowed; the first spring ( 56 ,  56 A) is provided between the fixed supporting member (FR) and the first movable supporting member ( 53 ,  53 A) to exert spring force through the first movable supporting member ( 53 ,  53 A) on the lever ( 40 ) at all times in the direction resisting the depression; the second spring ( 57 ,  57 A) is provided between the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A) so that in a state where the lever ( 40 ) is not depressed, one end of the second spring ( 57 ,  57 A) is away from the first movable supporting member ( 53 ,  53 A) or the second movable supporting member ( 58 ,  58 A), whereas a depression of the lever ( 40 ) causes both ends of the second spring ( 57 ,  57 A) to come into contact with the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A) to exert spring force on the lever ( 40 ) in the direction resisting the depression of the lever ( 40 ); and the third spring ( 61 ,  61 A) is provided between the fixed supporting member (FR) and the second movable supporting member ( 58 ,  58 A) to exert spring force on the lever ( 40 ) in the direction resisting the depression during the displacement of the second movable supporting member ( 58 ,  58 A) from the second predetermined position toward the second direction. 
     According to a still further specific invention configured as described above, if the amount of depression of the lever ( 40 ) is small, the spring force of the first spring ( 56 ,  56 A) is exerted on the lever ( 40 ) through the first movable supporting member ( 53 ,  53 A), with the first movable supporting member ( 53 ,  53 A) being displaced from the first predetermined position toward the second direction. In this state, the both ends of the second spring ( 57 ,  57 A) are not in contact with the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A), resulting in the spring force of only the first spring ( 56 ,  56 A) being exerted on the lever ( 40 ). If the amount of depression of the lever ( 40 ) increases from this state, the both ends of the second spring ( 57 ,  57 A) come into contact with the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A). The amount of depression of the lever ( 40 ) at the time of contact of the both ends of the second spring ( 57 ,  57 A) with the first movable supporting member ( 53 ,  53 A) and the second movable supporting member ( 58 ,  58 A) corresponds to the second amount of depression. Even if the amount of depression of the lever ( 40 ) increases further from this state, the second movable supporting member ( 58 ,  58 A) stands still at the predetermined position until the force exerted by the lever ( 40 ) through the second spring ( 57 ,  57 A) to urge the second movable supporting member ( 58 ,  58 A) toward the second direction reaches the force exerted by the third spring ( 61 ,  61 A) to urge the second movable supporting member ( 58 ,  58 A) toward the first direction. In this state, therefore, not only the spring force of the first spring ( 56 ,  56 A) but also the spring force of the second spring ( 57 ,  57 A) is exerted on the lever ( 40 ) in parallel. 
     Then, if the amount of depression of the lever ( 40 ) increases further, so that the force exerted by the lever ( 40 ) through the second spring ( 57 ,  57 A) to urge the second movable supporting member ( 58 ,  58 A) toward the second direction exceeds the force exerted by the third spring ( 61 ,  61 A) to urge the second movable supporting member ( 58 ,  58 A) toward the first direction, the second movable supporting member ( 58 ,  58 A) starts being displaced toward the second direction. The amount of depression of the lever ( 40 ) at the start of the displacement of the second movable supporting member ( 58 ,  58 A) corresponds to the first amount of depression. Then, if the amount of depression of the lever ( 40 ) increases further from this state, the second movable supporting member ( 58 ,  58 A) is displaced toward the second direction, with the third spring ( 61 ,  61 A) starting acting. In this state, it is considered that the second spring ( 57 ,  57 A) and the third spring ( 61 ,  61 A) are connected serially, so that the spring constant of the serial springs is smaller than that of the second spring ( 57 ,  57 A). In this state, therefore, not only the spring force exerted by the first spring ( 56 ,  56 A) but also the spring force exerted by the serial springs formed of the second spring ( 57 ,  57 A) and the third spring ( 61 ,  61 A) is applied to the lever ( 40 ). As a result, the still further specific invention can make the rate of change in the reaction force of the lever ( 40 ) increase and decrease stepwise according to the amount of depression of the lever ( 40 ) to start with a low rate of change to increase to a high rate to be followed by a medium rate. Therefore, the still further specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano. Similarly to the another specific invention described with reference to  FIGS. 8 ,  9 , in addition, the still further specific invention can stabilize the reaction force of the lever ( 40 ). 
     Furthermore, as shown in  FIG. 20 , for example, the present invention may be configured such that the movable supporting member is formed of a first movable supporting member ( 85 ) whose displacement between a first predetermined position and a second predetermined position which is away from the first predetermined position toward a first predetermined direction is allowed by the fixed supporting member (FR), and a second movable supporting member ( 84 ) which is in contact with the lever ( 40 ), and whose displacement toward a second direction opposite to the first direction from a third predetermined position which is away from the first predetermined position toward the second direction is restricted by the fixed supporting member (FR), and whose displacement toward the first direction with respect to the first movable supporting member ( 85 ) is restricted by contact with the first movable supporting member ( 85 ); the first spring ( 82 ) is provided between the fixed supporting member (FR) and the lever ( 40 ) to exert spring force on the lever ( 40 ) at all times in the direction resisting the depression; the second spring ( 83 ) is provided between the fixed supporting member (FR) and the second movable supporting member ( 84 ) to exert spring force on the lever ( 40 ) in a direction facilitating the depression until the displacement of the first movable supporting member ( 85 ) from the second predetermined position toward the first direction is restricted with the displacement of the second movable supporting member ( 84 ) with respect to the first movable supporting member ( 85 ) being restricted; and the third spring ( 90 ) is provided between the fixed supporting member (FR) and the first movable supporting member ( 85 ) to exert spring force on the lever ( 40 ) in the direction resisting the depression during the displacement of the first movable supporting member ( 85 ) from the first predetermined position to the second predetermined position caused by the contact of the second movable supporting member ( 84 ) with the first movable supporting member ( 85 ). 
     According to another specific invention configured as described above, if the amount of depression of the lever ( 40 ) is small, the spring forces of the first and second springs ( 82 ,  83 ) are exerted on the lever ( 40 ), with the second movable supporting member ( 84 ) being displaced toward the first direction. More specifically, the first spring ( 82 ) exerts the spring force in the direction resisting the depression of the lever ( 40 ) whereas the second spring ( 83 ) exerts the spring force which is smaller than that of the first spring ( 82 ) in the direction facilitating the depression of the lever ( 40 ). Therefore, the reaction force resisting the depression of the lever ( 40 ) is the spring force of the combined springs obtained by subtracting the spring force of the second spring ( 83 ) from the spring force of the first spring ( 82 ). Consequently, the spring constant of the combined springs is smaller than the spring constant of the first spring ( 82 ). If the amount of depression of the lever ( 40 ) increases from this state, the second movable supporting member ( 84 ) comes into contact with the first movable supporting member ( 85 ). The amount of depression of the lever ( 40 ) at the time of contact of the second movable supporting member ( 84 ) with the first movable supporting member ( 85 ) corresponds to the second amount of depression. If the amount of depression of the lever ( 40 ) increases further from this state, the first movable supporting member ( 85 ) starts being displaced along with the second movable supporting member ( 84 ) from the first predetermined position toward the first direction. This displacement causes the spring force of the third spring ( 90 ) in addition to the spring force of the combined springs to be exerted on the lever ( 40 ) in the direction resisting the depression of the lever ( 40 ). 
     Then, if the amount of depression of the lever ( 40 ) further increases, the displacement of the first and second movable supporting members ( 84 ,  85 ) toward the first direction is restricted at the second predetermined position by the fixed supporting member (FR). The amount of depression of the lever ( 40 ) at the time of restriction of the displacement of the first and second movable supporting members ( 84 ,  85 ) at the second predetermined position by the fixed supporting member (FR) corresponds to the first amount of depression. If the amount of depression of the lever ( 40 ) increases further from this state, the spring forces of the second and third springs ( 82 ,  83 ) will not affect the depression of the lever ( 40 ) with only the first spring ( 82 ) starting acting on the depression of the lever ( 40 ). As a result, the another specific invention can make the rate of change in the reaction force of the lever ( 40 ) increase and decrease stepwise according to the amount of depression of the lever ( 40 ) to start with a low rate of change to increase to a high rate to be followed by a medium rate. Therefore, the another specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano. 
     Similarly to the still another specific invention described with reference to  FIG. 10 , in addition, the another specific invention can stabilize the reaction force of the lever ( 40 ). 
     It is still another feature of the present invention to provide a pedal apparatus of an electronic musical instrument, the pedal apparatus including a lever ( 140 ) which is supported by a fixed supporting member (FR) and pivots by a player&#39;s depression of the lever ( 140 ); first and second springs ( 145 ,  152 ,  166 ;  148 ,  158 ,  167 ) which exert spring force on the lever ( 140 ); and a movable supporting member ( 146 ,  153 ,  157 ,  161 ,  163 ,  165 ) which supports the second spring ( 148 ,  158 ,  167 ) and is displaced in response to pivoting of the lever ( 140 ), and the displacement of the movable supporting member being restricted by the fixed supporting member (FR), wherein the first spring ( 145 ,  152 ,  166 ) exerts spring force on the lever ( 140 ) at all times in a direction resisting the depression of the lever ( 140 ); and if an amount of depression of the lever ( 140 ) increases from an initial state to reach a first predetermined amount of depression, a rate of change in reaction force with respect to the depression is reduced because of collaboration of the second spring ( 148 ,  158 ,  167 ) and the movable supporting member ( 146 ,  153 ,  157 ,  163 ,  165 ). 
     The present invention configured as described above can make the rate of change in the reaction force of the lever ( 140 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 140 ). Therefore, the present invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano shown by the dashed line in  FIG. 34 . In addition, the present invention can realize desired capabilities with a simple structure. Because the first spring ( 145 ,  152 ,  166 ) exerts spring force on the lever ( 140 ) at all times in the direction resisting the depression of the lever ( 140 ), furthermore, the present invention can stabilize the reaction force of the lever ( 140 ) even at the time of change in the reaction force in the first amount of depression. 
     More specifically, as shown in  FIGS. 22A ,  26 , for example, the present invention may be configured such that the downward displacement of the movable supporting member ( 146 ,  153 ,  157 ) from a predetermined position is restricted by the fixed supporting member (FR), while the upward displacement is allowed; the first spring ( 145 ,  152 ) is provided between the fixed supporting member (FR) and the lever ( 140 ) to exert spring force on the lever ( 140 ) at all times in the direction resisting the depression of the lever ( 140 ); and the second spring ( 148 ,  158 ) is provided between the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ) so that both ends of the second spring ( 148 ,  158 ) are in contact with the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ) in a state where the lever ( 140 ) is not depressed and that the second spring ( 148 ,  158 ) exerts spring force on the lever ( 140 ) in the direction resisting the depression during depression of the lever ( 140 ). In this case, the movable supporting member ( 146 ,  153 ,  157 ) may be a weight whose displacement is restricted by itself from the initial state of the amount of depression of the lever ( 140 ) until the first amount of depression. 
     According to a specific invention configured as described above, if the amount of depression of the lever ( 140 ) is small, the movable supporting member ( 146 ,  153 ,  157 ) stands still at the predetermined position until the force exerted by the lever ( 140 ) through the second spring ( 148 ,  158 ) to lift the movable supporting member ( 146 ,  153 ,  157 ) reaches the weight of the movable supporting member ( 146 ,  153 ,  157 ). In this state, therefore, not only the spring force exerted by the first spring ( 145 ,  152 ) but also the spring force exerted by the second spring ( 148 ,  158 ) is exerted on the lever ( 140 ) in parallel. Then, if the amount of depression of the lever ( 140 ) increases further, so that the force exerted by the lever ( 140 ) through the second spring ( 148 ,  158 ) to lift the movable supporting member ( 146 ,  153 ,  157 ) exceeds the weight of the movable supporting member ( 146 ,  153 ,  157 ), the movable supporting member ( 146 ,  153 ,  157 ) starts being displaced upward. The amount of depression of the lever ( 140 ) at the start of the upward displacement of the movable supporting member ( 146 ,  153 ,  157 ) corresponds to the first amount of depression. 
     Then, if the amount of depression of the lever ( 140 ) increases further from this state, the movable supporting member ( 146 ,  153 ,  157 ) is displaced upward. In this state, the second spring ( 148 ,  158 ) will not be compressed any further. In this state, therefore, although the spring force exerted by the first spring ( 145 ,  152 ) and the spring force exerted by the second spring ( 148 ,  158 ) are applied to the lever ( 140 ) in parallel, the spring force of the second spring ( 148 ,  158 ) will not change, with the spring force of only the first spring ( 145 ,  152 ) increasing. As a result, the specific invention can make the rate of change in the reaction force of the lever ( 140 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 140 ). Therefore, the specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano as shown by the dashed line in  FIG. 34 . 
     Furthermore, in a case where the player deeply depresses the lever ( 140 ) and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever ( 140 ), the movable supporting member ( 146 ,  153 ,  157 ) can temporarily oscillate due to collaboration of the inertial force and spring force. Furthermore, the movable supporting member ( 146 ,  153 ,  157 ) can collide with the fixed supporting member (FR) to cause oscillation of the movable supporting member ( 146 ,  153 ,  157 ). The oscillation of the movable supporting member ( 146 ,  153 ,  157 ) is conveyed to the lever ( 140 ) through the second spring ( 148 ,  158 ) to be perceived by the player as unnatural reaction force. As for the invention configured as described above, however, because the force of the springs acting on the lever ( 140 ) can be divided into the spring force exerted by the first spring ( 145 ,  152 ) and the spring force exerted by the second spring ( 148 ,  158 ), the spring force (spring constant) exerted by the second spring ( 148 ,  158 ) can be reduced. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the specific invention can stabilize the reaction force of the lever ( 140 ). In addition, the specific invention can realize the desired capabilities with the simple structure formed of the two springs ( 145 ,  152 ;  148 ,  158 ) and the movable supporting member ( 146 ,  153 ,  157 ). 
     In addition, as shown in  FIG. 27 , for example, the present invention may be configured such that the movable supporting member is formed of a first movable supporting member ( 161 ) whose downward displacement from a first predetermined position is restricted by the fixed supporting member (FR), and whose upward displacement is allowed, the first movable supporting member ( 161 ) being connected to the lever ( 140 ) so that the first movable supporting member ( 161 ) conveys force to the lever ( 140 ), and a second movable supporting member ( 163 ,  165 ) whose downward displacement from a second predetermined position which is apart upward from the first predetermined position is restricted by the fixed supporting member (FR) and whose upward displacement is allowed; the first spring ( 166 ) is provided between the fixed supporting member (FR) and the first movable supporting member ( 161 ) to exert spring force through the first movable supporting member ( 161 ) on the lever ( 140 ) at all times in the direction resisting the depression; and the second spring ( 167 ) is provided between the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ) so that in a state where the lever ( 140 ) is not depressed, both ends of the second spring ( 167 ) are in contact with the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ), while the second spring ( 167 ) exerts spring force on the lever ( 140 ) in the direction resisting the depression of the lever ( 140 ) during depression of the lever ( 140 ). In this case, the second movable supporting member ( 163 ,  165 ) may be a weight whose displacement is restricted by itself from the initial state of the amount of depression of the lever ( 140 ) until the first amount of depression. 
     According to another specific invention configured as described above, if the amount of depression of the lever ( 140 ) is small, the second movable supporting member ( 163 ,  165 ) stands still at the predetermined position until the force exerted by the lever ( 140 ) through the second spring ( 167 ) to lift the second movable supporting member ( 163 ,  165 ) reaches the weight of the second movable supporting member ( 163 ,  165 ). In this state, therefore, not only the spring force exerted by the first spring ( 166 ) but also the spring force exerted by the second spring ( 167 ) is exerted on the lever ( 140 ) in parallel. Then, if the amount of depression of the lever ( 140 ) increases further, so that the force exerted by the lever ( 140 ) through the second spring ( 167 ) to lift the second movable supporting member ( 163 ,  165 ) exceeds the weight of the second movable supporting member ( 163 ,  165 ), the second movable supporting member ( 163 ,  165 ) starts being displaced upward. The amount of depression of the lever ( 140 ) at the start of the upward displacement of the second movable supporting member ( 163 ,  165 ) corresponds to the first amount of depression. 
     Then, if the amount of depression of the lever ( 140 ) increases further from this state, the second movable supporting member ( 163 ,  165 ) is displaced upward. In this state, the second spring ( 167 ) will not be compressed any further. In this state, therefore, although the spring force exerted by the first spring ( 166 ) and the spring force exerted by the second spring ( 167 ) are applied to the lever ( 140 ) in parallel, the spring force of the second spring ( 167 ) will not change, with the spring force of only the first spring ( 166 ) increasing. As a result, the another specific invention can make the rate of change in the reaction force of the lever ( 140 ) vary from a greater rate of change to a smaller rate of change according to the amount of depression of the lever ( 140 ). Therefore, the another specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano as shown by the dashed line in  FIG. 34 . 
     As for the another specific invention, similarly to the specific invention described with reference to  FIGS. 22A ,  26 , in a case where the player deeply depresses the lever ( 140 ) and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever ( 140 ), the second movable supporting member ( 163 ,  165 ) can temporarily oscillate due to collaboration of the inertial force and spring force. Furthermore, the second movable supporting member ( 163 ,  165 ) can collide with the fixed supporting member (FR) to cause oscillation of the second movable supporting member ( 163 ,  165 ). As for the another specific invention as well, however, because the force of the springs acting on the lever ( 140 ) can be divided into the spring force exerted by the first spring ( 166 ) and the spring force exerted by the second spring ( 167 ), the spring force exerted by the second spring ( 167 ) can be reduced. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the another specific invention can stabilize the displacement of the first movable supporting member ( 161 ), resulting in the stable reaction force of the lever ( 140 ) connected with the first movable supporting member ( 161 ) so that the first movable supporting member ( 161 ) conveys force to the lever ( 140 ). In addition, the another specific invention can realize the desired capabilities with the simple structure. 
     It is a further feature of the present invention that in a range of the amount of depression which is smaller than the first amount of depression, when the amount of depression of the lever ( 140 ) increases from the initial state to reach a second predetermined amount of depression, the rate of change in reaction force with respect to the depression increases because of collaboration of the second spring ( 148 ,  158 ,  167 ) and the movable supporting member ( 146 ,  153 ,  157 ,  161 ,  163 ,  165 ). 
     According to the further feature of the present invention configured as above, the rate of change in the reaction force of the lever ( 140 ) can increase and decrease stepwise according to the amount of depression of the lever ( 140 ) to start with a low rate of change to increase to a high rate to be followed by a low rate, for example. Therefore, the further feature can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano shown by the solid line in  FIG. 34 . In addition, the further feature can realize the desired capabilities with the simple structure. In this case as well, because the first spring ( 145 ,  152 ,  166 ) exerts spring force at all times in the direction resisting depression of the lever ( 140 ), the further feature can stabilize the reaction force of the lever ( 140 ) at the time of the change in the reaction force at the first and second amounts of depression as well. 
     More specifically, as shown in  FIGS. 28 ,  32 , for example, the present invention may be configured such that the downward displacement of the movable supporting member ( 146 ,  153 ,  157 ) from a predetermined position is restricted by the fixed supporting member (FR), while the upward displacement is allowed; the first spring ( 145 ,  152 ) is provided between the fixed supporting member (FR) and the lever ( 140 ) to exert spring force on the lever ( 140 ) at all times in the direction resisting the depression of the lever ( 140 ); and the second spring ( 148 ,  158 ) is provided between the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ) so that in a state where the lever ( 140 ) is not depressed, one end of the second spring ( 148 ,  158 ) is away from the movable supporting member ( 146 ,  153 ,  157 ) or the lever ( 140 ), whereas a depression of the lever ( 140 ) causes both ends of the second spring ( 148 ,  158 ) to come into contact with the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ) to exert spring force on the lever ( 140 ) in the direction resisting the depression of the lever ( 140 ). In this case, the movable supporting member ( 146 ,  153 ,  157 ) may be a weight whose displacement is restricted by itself from the initial state of the amount of depression of the lever ( 140 ) until the first amount of depression. 
     According to still another specific invention configured as described above, if the amount of depression of the lever ( 140 ) is small, the both ends of the second spring ( 148 ,  158 ) are not in contact with the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ), so that the spring force of only the first spring ( 145 ,  152 ) is exerted on the lever ( 140 ). If the amount of depression of the lever ( 140 ) increases from this state, the both ends of the second spring ( 148 ,  158 ) come into contact with the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ). The amount of depression of the lever ( 140 ) at the time of contact of the both ends of the second spring ( 148 ,  158 ) with the movable supporting member ( 146 ,  153 ,  157 ) and the lever ( 140 ) corresponds to the second amount of depression. 
     Even if the amount of depression of the lever ( 140 ) increases further from this state, the movable supporting member ( 146 ,  153 ,  157 ) stands still at the predetermined position until the force exerted by the lever ( 140 ) through the second spring ( 148 ,  158 ) to lift the movable supporting member ( 146 ,  153 ,  157 ) reaches the weight of the movable supporting member ( 146 ,  153 ,  157 ). In this state, therefore, not only the spring force of the first spring ( 145 ,  152 ) but also the spring force of the second spring ( 148 ,  158 ) is exerted on the lever ( 140 ) in parallel. Then, if the amount of depression of the lever ( 140 ) increases further, so that the force exerted by the lever ( 140 ) through the second spring ( 148 ,  158 ) to lift the movable supporting member ( 146 ,  153 ,  157 ) exceeds the weight of the movable supporting member ( 146 ,  153 ,  157 ), the movable supporting member ( 146 ,  153 ,  157 ) starts being displaced upward. The amount of depression of the lever ( 140 ) at the start of the upward displacement of the movable supporting member ( 146 ,  153 ,  157 ) corresponds to the first amount of depression. 
     Then, if the amount of depression of the lever ( 140 ) increases further from this state, the movable supporting member ( 146 ,  153 ,  157 ) is displaced upward. In this state, the second spring ( 148 ,  158 ) will not be compressed any further. In this state, therefore, although the spring force exerted by the first spring ( 145 ,  152 ) and the spring force exerted by the second spring ( 148 ,  158 ) are applied to the lever ( 140 ) in parallel, the spring force of the second spring ( 148 ,  158 ) will not change, with the spring force of only the first spring ( 145 ,  152 ) increasing. As a result, the still another specific invention can make the rate of change in the reaction force of the lever ( 140 ) increase and decrease stepwise according to the amount of depression of the lever ( 140 ) to start with a low rate of change to increase to a high rate to be followed by a low rate. Therefore, the still another specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano as shown by the solid line in  FIG. 34 . Similarly to the specific invention described with reference to FIGS.  22 A,  26 , in addition, the still another specific invention can stabilize the reaction force of the lever ( 140 ). Furthermore, the still another specific invention can realize the desired capabilities with the simple structure. 
     Furthermore, as shown in  FIG. 33 , for example, the present invention may be configured such that the movable supporting member is formed of a first movable supporting member ( 161 ) whose downward displacement from a first predetermined position is restricted by the fixed supporting member (FR), and whose upward displacement is allowed, the first movable supporting member ( 161 ) being connected to the lever ( 140 ) so that the first movable supporting member ( 161 ) conveys force to the lever ( 140 ), and a second movable supporting member ( 163 ,  165 ) whose downward displacement from a second predetermined position which is away upward from the first predetermined position is restricted by the fixed supporting member (FR) and whose upward displacement is allowed; the first spring ( 166 ) is provided between the fixed supporting member (FR) and the first movable supporting member ( 161 ) to exert spring force through the first movable supporting member ( 161 ) on the lever ( 140 ) at all times in the direction resisting the depression; and the second spring ( 167 ) is provided between the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ) so that in a state where the lever ( 140 ) is not depressed, one end of the second spring ( 167 ) is away from the first movable supporting member ( 161 ) or the second movable supporting member ( 163 ,  165 ), whereas a depression of the lever ( 140 ) causes both ends of the second spring ( 167 ) to come into contact with the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ) to exert spring force on the lever ( 140 ) in the direction resisting the depression of the lever ( 140 ). In this case, the second movable supporting member ( 163 ,  165 ) may be a weight whose displacement is restricted by itself from the initial state of the amount of depression of the lever ( 140 ) until the first amount of depression. 
     According to a further specific invention configured as described above, if the amount of depression of the lever ( 140 ) is small, the spring force of the first spring ( 166 ) is exerted on the lever ( 140 ) through the first movable supporting member ( 161 ), with the first movable supporting member ( 161 ) being displaced upward from the first predetermined position. In this state, the both ends of the second spring ( 167 ) are not in contact with the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ), resulting in the spring force of only the first spring ( 166 ) being exerted on the lever ( 140 ). If the amount of depression of the lever ( 140 ) increases from this state, the both ends of the second spring ( 167 ) come into contact with the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ). The amount of depression of the lever ( 140 ) at the time of contact of the both ends of the second spring ( 167 ) with the first movable supporting member ( 161 ) and the second movable supporting member ( 163 ,  165 ) corresponds to the second amount of depression. Even if the amount of depression of the lever ( 140 ) increases further from this state, the second movable supporting member ( 163 ,  165 ) stands still at the predetermined position until the force exerted by the lever ( 140 ) through the second spring ( 167 ) to lift the second movable supporting member ( 163 ,  165 ) reaches the weight of the second movable supporting member ( 163 ,  165 ). In this state, therefore, not only the spring force of the first spring ( 166 ) but also the spring force of the second spring ( 167 ) is exerted on the lever ( 140 ) in parallel. 
     Then, if the amount of depression of the lever ( 140 ) increases further, so that the force exerted by the lever ( 140 ) through the second spring ( 167 ) to lift the second movable supporting member ( 163 ,  165 ) exceeds the weight of the second movable supporting member ( 163 ,  165 ), the second movable supporting member ( 163 ,  165 ) starts being displaced upward. The amount of depression of the lever ( 140 ) at the start of the upward displacement of the second movable supporting member ( 163 ,  165 ) corresponds to the first amount of depression. Then, if the amount of depression of the lever ( 140 ) increases further from this state, the second movable supporting member ( 163 ,  165 ) is displaced upward. In this state, the second spring ( 167 ) will not be compressed any further. In this state, therefore, although the spring force of the first spring ( 166 ) and the spring force of the second spring ( 167 ) are exerted on the lever ( 140 ) in parallel, the spring force of the second spring ( 167 ) will not change, with the spring force of only the first spring ( 166 ) increasing. As a result, the further specific invention can make the rate of change in the reaction force of the lever ( 140 ) increase and decrease stepwise according to the amount of depression of the lever ( 140 ) to start with a low rate of change to increase to a high rate to be followed by a low rate. Therefore, the further specific invention can provide the player with feeling similar to that the player perceives when he manipulates a damper pedal of an acoustic piano as shown by the solid line in  FIG. 34 . Similarly to the another specific invention described with reference to  FIG. 27 , in addition, the further specific invention can stabilize the reaction force of the lever ( 140 ). Furthermore, the further specific invention can realize the desired capabilities with the simple structure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram showing an example general configuration of an electronic musical instrument to which a pedal apparatus according to first to six embodiments of the present invention is applied; 
         FIG. 2A  is a side view of the pedal apparatus according to the first embodiment of the present invention; 
         FIG. 2B  is an enlarged view of a portion on which a capstan is mounted according to a modification of the first embodiment; 
         FIG. 3A  is a diagram showing the position of a lever and the state where a first spring, a second spring and a third spring are compressed in a state where the lever is not depressed according to the first embodiment; 
         FIG. 3B  is a diagram showing the position of the lever and the state where the first spring, the second spring and the third spring are compressed in a state where a movable supporting member starts being displaced according to the first embodiment; 
         FIG. 3C  is a diagram showing the position of the lever and the state where the first spring, the second spring and the third spring are compressed in a state where the amount of depression of the lever is at the maximum according to the first embodiment; 
         FIG. 4A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the first embodiment; 
         FIG. 4B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the first embodiment; 
         FIG. 4C  is a graph showing characteristics of changes in the urging force of the third spring with respect to the amount of displacement of the lever according to the first embodiment; 
         FIG. 4D  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the first embodiment; 
         FIG. 5A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the modification of the first embodiment; 
         FIG. 5B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the modification of the first embodiment; 
         FIG. 5C  is a graph showing characteristics of changes in the urging force of the third spring with respect to the amount of displacement of the lever according to the modification of the first embodiment; 
         FIG. 5D  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the modification of the first embodiment; 
         FIG. 6  is a side view of the pedal apparatus according to a modification of the first embodiment; 
         FIG. 7  is a side view of the pedal apparatus according to the other modification of the first embodiment; 
         FIG. 8  is a side view of the pedal apparatus according to the second embodiment; 
         FIG. 9  is a side view of the pedal apparatus according to a modification of the second embodiment; 
         FIG. 10  is a side view of the pedal apparatus according to the third embodiment; 
         FIG. 11A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the third embodiment; 
         FIG. 11B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the third embodiment; 
         FIG. 11C  is a graph showing characteristics of changes in the urging force of the third spring with respect to the amount of displacement of the lever according to the third embodiment; 
         FIG. 11D  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the third embodiment; 
         FIG. 12  is a side view of the pedal apparatus according to the fourth embodiment; 
         FIG. 13A  is a diagram showing the position of the lever and the state where the first spring, the second spring and the third spring are compressed in a state where the lever is not depressed according to the fourth embodiment; 
         FIG. 13B  is a diagram showing the position of the lever and the state where the first spring, the second spring and the third spring are compressed in a state where the lever comes into contact with the second spring according to the fourth embodiment; 
         FIG. 13C  is a diagram showing the position of the lever and the state where the first spring, the second spring and the third spring are compressed in a state where the movable supporting member starts being displaced according to the fourth embodiment; 
         FIG. 13D  is a diagram showing the position of the lever and the state where the first spring, the second spring and the third spring are compressed in a state where the amount of depression of the lever is at the maximum according to the fourth embodiment; 
         FIG. 14A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the fourth embodiment; 
         FIG. 14B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the fourth embodiment; 
         FIG. 14C  is a graph showing characteristics of changes in the urging force of the third spring with respect to the amount of displacement of the lever according to the fourth embodiment; 
         FIG. 14D  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the fourth embodiment; 
         FIG. 15A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to a modification of the fourth embodiment; 
         FIG. 15B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the modification of the fourth embodiment; 
         FIG. 15C  is a graph showing characteristics of changes in the urging force of the third spring with respect to the amount of displacement of the lever according to the modification of the fourth embodiment; 
         FIG. 15D  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the modification of the fourth embodiment; 
         FIG. 16  is a side view of the pedal apparatus according to a modification of the fourth embodiment; 
         FIG. 17  is a side view of the pedal apparatus according to the other modification of the fourth embodiment; 
         FIG. 18  is a side view of the pedal apparatus according to the fifth embodiment; 
         FIG. 19  is a side view of the pedal apparatus according to a modification of the fifth embodiment; 
         FIG. 20  is a side view of the pedal apparatus according to the sixth embodiment; 
         FIG. 21A  is a graph showing characteristics of changes in the urging force of a first spring with respect to the amount of displacement of the lever according to the sixth embodiment; 
         FIG. 21B  is a graph showing characteristics of changes in the urging force of a second spring with respect to the amount of displacement of the lever according to the sixth embodiment; 
         FIG. 21C  is a graph showing characteristics of changes in the urging force of a third spring with respect to the amount of displacement of the lever according to the sixth embodiment; 
         FIG. 21D  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the sixth embodiment; 
         FIG. 22A  is a side view of the pedal apparatus according to a seventh embodiment of the present invention; 
         FIG. 22B  is an enlarged view of a portion on which a capstan is mounted according to a modification of the seventh embodiment; 
         FIG. 23A  is a diagram showing the position of a lever and a weight, and the state where a first spring and a second spring are compressed in a state where the lever is not depressed according to the seventh embodiment; 
         FIG. 23B  is a diagram showing the position of the lever and the weight, and the state where the first spring and the second spring are compressed in a state where the weight starts being displaced according to the seventh embodiment; 
         FIG. 23C  is a diagram showing the position of the lever and the weight, and the state where the first spring and the second spring are compressed in a state where the amount of depression of the lever is at the maximum according to the seventh embodiment; 
         FIG. 24A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the seventh embodiment; 
         FIG. 24B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the seventh embodiment; 
         FIG. 24C  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the seventh embodiment; 
         FIG. 25A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the modification of the seventh embodiment; 
         FIG. 25B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the modification of the seventh embodiment; 
         FIG. 25C  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the modification of the seventh embodiment; 
         FIG. 26  is a side view of the pedal apparatus according to a modification of the seventh embodiment; 
         FIG. 27  is a side view of the pedal apparatus according to an eighth embodiment; 
         FIG. 28  is a side view of the pedal apparatus according to a ninth embodiment; 
         FIG. 29A  is a diagram showing the position of the lever and the weight, and the state where the first spring and the second spring are compressed in a state where the lever is not depressed according to the ninth embodiment; 
         FIG. 29B  is a diagram showing the position of the lever and the weight, and the state where the first spring and the second spring are compressed in a state where the lever comes into contact with the second spring according to the ninth embodiment; 
         FIG. 29C  is a diagram showing the position of the lever and the weight, and the state where the first spring and the second spring are compressed in a state where the weight starts being displaced according to the ninth embodiment; 
         FIG. 29D  is a diagram showing the position of the lever and the weight, and the state where the first spring and the second spring are compressed in a state where the amount of depression of the lever is at the maximum according to the ninth embodiment; 
         FIG. 30A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to the ninth embodiment; 
         FIG. 30B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the ninth embodiment; 
         FIG. 30C  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the ninth embodiment; 
         FIG. 31A  is a graph showing characteristics of changes in the urging force of the first spring with respect to the amount of displacement of the lever according to a modification of the ninth embodiment; 
         FIG. 31B  is a graph showing characteristics of changes in the urging force of the second spring with respect to the amount of displacement of the lever according to the modification of the ninth embodiment; 
         FIG. 31C  is a graph showing characteristics of changes in the reaction force of the lever with respect to the amount of displacement of the lever according to the modification of the ninth embodiment; 
         FIG. 32  is a side view of the pedal apparatus according to a modification of the ninth embodiment; 
         FIG. 33  is a side view of the pedal apparatus according to a tenth embodiment; and 
         FIG. 34  is a graph showing characteristics of changes in the reaction force of the lever of an acoustic piano with respect to the amount of displacement of the lever. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     a. General Configuration of Electronic Musical Instrument 
     Before a pedal apparatus according to respective embodiments of the present invention is described, a general configuration of an electronic musical instrument to which the pedal apparatus according to the embodiments is applied will now be described.  FIG. 1  is a block diagram showing an example general configuration of an electronic musical instrument to which the pedal apparatus of the respective embodiments is applied. An electronic musical instrument  10  has a keyboard  11 , a pedal apparatus  12 , a plurality of panel operators  13 , a display unit  14 , a tone generator  15 , a computer portion  16 , a clock circuit  17  and an external storage device  18 . 
     The keyboard  11  is manipulated by a player with his hands to specify the tone pitch of respective musical tones to be generated. The manipulation of the keyboard  11  is detected by a detection circuit  22  connected to a bus  21 , so that data (e.g., note data, key-on data, key-off data, etc.) indicative of the player&#39;s manipulation is supplied to the computer portion  16  through the bus  21 . The pedal apparatus  12  is manipulated by the player with his foot to control the manner in which musical tones are generated by the electronic musical instrument. In the respective embodiments which will be described later, the pedal apparatus  12  is a damper pedal which adds a damper effect to a musical tone to be generated by a depression of the damper pedal by the player&#39;s foot. The manipulation of the pedal apparatus  12  is detected by a detection circuit  23  connected to the bus  21 , as described in detail later, so that data indicative of the manipulation is supplied to the computer portion  16  through the bus  21 . The plurality of panel operators  13  are used in order to specify the operation of the electronic musical instrument. The manipulation of the panel operators  13  is detected by a detection circuit  24  connected to the bus  21 , so that data indicative of the manipulation is supplied to the computer portion  16  through the bus  21 . The display unit  14  is configured by a liquid crystal display, a CRT or the like to display characters, numerals, graphics and the like on a screen. The display unit  14  is controlled by a display circuit  25  connected to the bus  21 . More specifically, what is to be displayed on the screen is specified on the basis of display instruction signals and display data supplied to the display circuit  25  through the bus  21 . 
     The tone generator  15 , which is connected to the bus  21 , generates digital musical tone signals on the basis of musical tone control data (note data, key-on data, key-off data, tone color control data, tone volume control data, etc.) supplied from the computer portion  16  through the bus  21  and then supplies the generated digital musical tone signals to an effect circuit  26 . The effect circuit  26 , which is connected to the bus  21 , adds an effect to the supplied digital musical tone signals on the basis of effect control data supplied from the computer portion  16  through the bus  21 , and then supplies the digital musical tone signals to which the effect has been added to a sound system  27 . The above-described damper effect is added to the digital musical tone signals in the tone generator  15  or in the effect circuit  26 . The sound system  27 , which is configured by a D/A converter, amplifiers, speakers and the like, converts the supplied digital musical tone signals having the effect to analog musical tone signals, and then emits musical tones corresponding to the analog musical tone signals. 
     The computer portion  16 , which is formed of a CPU  16   a , a RAM  16   b  and a ROM  16   c  connected to the bus  21 . The computer portion  16  also includes a timer  16   d  which is connected to the CPU  16   a . By execution of programs, the computer portion  16  controls the electronic musical instrument  10 . The clock circuit  17  continuously measures date and time. The external storage device  18  includes various kinds of storage media such as a hard disk and a flash memory incorporated into the electronic musical instrument  10 , and a compact disk which can be connected to the electronic musical instrument  10 . The external storage device  18  also includes drive units provided for the various storage media, so that the external storage device  18  can store and read out large amounts of data and programs. 
     The electronic musical instrument  10  also has a network interface circuit  28  and a MIDI interface circuit  29 . The network interface circuit  28  connects the electronic musical instrument  10  to a server apparatus  30  through a communications network NW so that the electronic musical instrument  10  can communicate with the server apparatus  30 . The MIDI interface circuit  29  connects the electronic musical instrument  10  to an external MIDI apparatus  31  such as the other electronic musical instrument or a sequencer so that the electronic musical instrument  10  can communicate with the external MIDI apparatus  31 . 
     b. First Embodiment 
     Next, a first embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 2A  shows a side view of the pedal apparatus of the electronic musical instrument according to the present embodiment. A lever  40  is a long plate-shaped member. The forward part (left side in  FIG. 2A ) of the lever  40  is a wide depression part on which a player steps. The lever  40  is supported at a middle part thereof by a lever supporting portion  41  provided on a frame FR which serves as a fixed supporting member so that the front end of the lever  40  can pivot upward and downward about a rotary shaft  42 . Below the middle part of the lever  40 , a long lower limit stopper  43  made of a shock-absorbing member such as felt extends in a lateral direction to be fixed to the frame FR. The lower limit stopper  43  restricts downward displacement of the forward part of the lever  40 . The frame FR is a structural body for supporting various parts of the pedal apparatus  12  and a housing itself of the pedal apparatus  12 . Below the rear part of the lever  40 , an upper limit stopper  44  which is similar to the lower limit stopper  43  is fixed to the frame FR to restrict upward displacement of the forward part of the lever  40 . 
     Behind the rotary shaft  42  of the lever  40 , the top end of a first spring  45  is fixed to the frame FR so that the top end of the first spring  45  is situated above the rear part of the lever  40 . The lower end of the first spring  45  is inserted into a concave portion  40   a  provided on the top surface of the rear part of the lever  40  to be in contact with the bottom surface of the concave portion  40   a , so that the first spring  45  urges the rear part of the lever  40  downward. The first spring  45  is a compression spring. Behind the rotary shaft  42  of the lever  40 , furthermore, a second spring  46 , a third spring  47  and a movable supporting member  48  are provided so that the second and third springs  46 ,  47  and the movable supporting member  48  are situated above the rear part of the lever  40 . The movable supporting member  48  is shaped like a cylinder having concave portions  48   a ,  48   b  on its upper surface and lower surface. The top end of the third spring  47  is fixed to the frame FR situated above the rear part of the lever  40 . The lower end of the third spring  47  is inserted into the concave portion  48   a  of the movable supporting member  48  to be fixed to the bottom surface of the concave portion  48   a  to be supported by the movable supporting member  48 . The top end of the second spring  46  is inserted into the concave portion  48   b  of the movable supporting member  48  to be fixed to the upper bottom surface of the concave portion  48   b  to be supported by the movable supporting member  48 . The lower end of the second spring  46  is in contact with the top surface of the lever  40 . 
     The second spring  46  and the third spring  47  are compression springs. If comparisons of spring constant are made among the first spring  45 , the second spring  46  and the third spring  47 , the first spring  45  has the largest spring constant. The spring constant of the third spring  47  is sufficiently small when compared with the spring constant of the first spring  45  and the second spring  46 . The relationship of the magnitude of the spring constant among the first to third springs  45 ,  46 ,  47  is not limited to that of the present embodiment, but can vary according to desired characteristics of reaction force of the lever  40 . In a case where the difference of the rate of change in the reaction force is small between range A 1  and range A 2  shown in  FIG. 34 , for instance, the third spring  47  may have a larger spring constant than the second spring  46 . The movable supporting member  48 , which is a plate-shaped member, is allowed to move only upward and downward by a guide member which is not shown. By a movable supporting member lower limit stopper  49  fixed to the frame FR, furthermore, the downward displacement of the movable supporting member  48  is restricted. The movable supporting member lower limit stopper  49 , which is made of a shock-absorbing member such as felt, prevents shock noise that would be generated when the movable supporting member  48  collides with the frame FR. 
     Into the concave portion  48   b  of the movable supporting member  48 , a load sensor  50  for sensing the urging force of the second spring  46  (load applied to the lever  40  which is the pedal apparatus  12 ) is incorporated. By electrically sensing elastic deformation caused by the urging force of the second spring  46  (e.g., with a strain gauge), the load sensor  50  obtains the urging force of the second spring  46 . Above the middle part of the lever  40 , furthermore, a displacement sensor  51  for sensing the amount of displacement of the lever  40  is provided. By electrically or optically sensing the distance to the top surface of the lever  40  (e.g., by reflection of laser light), the displacement sensor  51  obtains the amount of displacement of the lever  40 . The displacement sensor  51  may be replaced with a sensor for mechanically and electrically sensing the amount of upward and downward displacement of the lever  40  (e.g., variable resistance). 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained.  FIG. 3A  through  FIG. 3C  show various states in which the lever  40  is displaced, with the first spring  45 , the second spring  46  and the third spring  47  being compressed.  FIG. 4A ,  FIG. 4B  and  FIG. 4C  show the urging force of the first spring  45 , the second spring  46  and the third spring  47  with respect to the amount of displacement of the lever  40 .  FIG. 4D  shows the reaction force generated by the lever  40  according to the displacement of the lever  40 . In a state where the lever  40  is not depressed, the rear part of the lever  40  is urged downward by the first spring  45 . As a result, the undersurface of the rear part of the lever  40  is in contact with the upper limit stopper  44 , so that the lever  40  stands still to be in a state shown in  FIG. 3A . In this state, the second spring  46  is in its natural length, resulting in the urging force exerted on the lever  40  of “0”. In this state, furthermore, the movable supporting member  48  is in contact with the movable supporting member lower limit stopper  49  by the urging force of the third spring  47  and the weight of the movable supporting member  48 , so that the movable supporting member  48  stands still. In this state, although the second spring  46  may be slightly compressed to urge the lever  40 , the urging force of the second spring  46  is designed to be smaller than a combined force in which the urging force of the third spring  47  and the weight of the movable supporting member  48  are combined so that the movable supporting member  48  is in contact with the movable supporting member lower limit stopper  49 . 
     If the player depresses the lever  40  in spite of the urging force exerted by the first spring  45 , the lever  40  starts pivoting counterclockwise about the rotary shaft  42  in  FIG. 3A , so that the rear part of the lever  40  is displaced upward. This displacement causes compression of the first spring  45  to increase the urging force exerted by the first spring  45  (A 1  of  FIG. 4A ). If the urging force exerted by the second spring  46  is smaller than the combined force formed of the urging force exerted by the third spring  47  to urge the movable supporting member  48  downward and the weight of the movable supporting member  48 , furthermore, the movable supporting member  48  remains to be in contact with the movable supporting member lower limit stopper  49 . By the pivoting of the lever  40 , as a result, the second spring  46  also starts compressing to increase the urging force exerted by the second spring  46  as well (A 1  of  FIG. 4B ). In this operational range (from  FIG. 3A  to  FIG. 3B ), therefore, the reaction force of the lever  40  and the change in the reaction force are brought about by the first spring  45  and the second spring  46  (A 1  of  FIG. 4D ). 
     Then, if the urging force exerted by the second spring  46  exceeds the combined force formed of the urging force exerted by the third spring  47  to urge the movable supporting member  48  downward and the weight of the movable supporting member  48 , the movable supporting member  48  leaves the movable supporting member lower limit stopper  49  to move upward. The amount of depression of the lever  40  at the time of the start of upward move of the movable supporting member  48  is referred to as a first amount of depression. As described above, the spring constant of the third spring  47  is sufficiently small, compared with the second spring  46 . If the amount of displacement of the lever  40  increases, therefore, the third spring  47  is compressed to increase the urging force of the third spring  47 . However, the second spring  46  will be hardly compressed any further with little increase in the urging force of the second spring  46  (A 2  of  FIG. 4B  and A 2  of  FIG. 4C ). In this operational range (from  FIG. 3B  to  FIG. 3C ), therefore, the reaction force of the lever  40  is brought about by the first spring  45 , the second spring  46  and the third spring  47 . Strictly speaking, the change in the reaction force is brought about by the first spring  45 , the second spring  46  and the third spring  47 . However, the spring constant of the third spring  47  is sufficiently smaller than that of the second spring  46 , resulting in little compression of the second spring  46  and little increase in the urging force exerted by the second spring  46 . Therefore, it can be considered that the change in the reaction force is brought about by the first spring  45  and the third spring  47  (A 2  of  FIG. 4D ). 
     Then, the undersurface of the middle part of the lever  40  comes into contact with the lower limit stopper  43  to restrict downward displacement of the forward part of the lever  40 . If the depression of the lever  40  is released, the urging forces exerted by the first spring  45 , the second spring  46  and the third spring  47  cause the lever  40  to operate in the order opposite to that in which the lever  40  has operated on the depression of the lever  40 . More specifically, the lever  40  pivots clockwise about the rotary shaft  42  in  FIG. 3C , so that the undersurface of the rear part of the lever  40  comes into contact with the upper limit stopper  44  to recover to the original state ( FIG. 3A ). In the above-described explanation, the weight of the movable supporting member  48  is taken into account. In a case where the movable supporting member  48  is made of a light material such as resin, however, the weight of the movable supporting member  48  can be ignored. 
     The detection circuit  23  detects a point where the rate of change in the reaction force of the lever  40  changes on the basis of the change in the urging force exerted by the second spring  46  detected by the load sensor  50 . Furthermore, the displacement sensor  51  detects the amount of displacement of the lever  40 . In accordance with the changing point of the rate of change of the reaction force and the information on the amount of displacement of the lever  40 , the electronic musical instrument  10  adds a damper effect to a musical tone to be generated, also controlling musical tone elements such as timbre and resonance (acoustic effect) of the musical tone to be generated. In a range AH of  FIG. 4D  corresponding to the above-described half pedal range AH of  FIG. 34 , particularly, on the basis of the load detected by the load sensor  50  and the amount of displacement detected by the displacement sensor  51 , the tone generator  15  and the effect circuit  26  subtly change the musical tone elements such as timbre and resonance (acoustic effect) of musical tones to be generated in accordance with pedal manipulation of the player. The above-described control of the musical tone elements may be done on the basis of either of the load detected by the load sensor  50  or the amount of displacement detected by the displacement sensor  51 . 
     The pedal apparatus according to the present embodiment configured as described above can achieve the characteristics ( FIG. 4D ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the dashed line in  FIG. 34 . In the operational range (A 1  of  FIG. 4D ) equivalent to A 0  and A 1  of  FIG. 34 , more specifically, the urging force exerted by the first spring  45  and the second spring  46  to urge the lever  40  changes, whereas in the operational range (A 2  of  FIG. 4D ) equivalent to A 2  of  FIG. 34 , the urging force exerted by the third spring  47  changes in addition to the urging force of the first spring  45 . Because the spring constant of the third spring  47  is sufficiently smaller than that of the second spring  46 , the rate of change in the reaction force in the operational range (A 2  of  FIG. 4D ) equivalent to the range of A 2  of  FIG. 34  can be reduced, compared with the operational range (A 1  of  FIG. 4D ) equivalent to the range of A 0  and A 1  of  FIG. 34 . Even if the spring constant of the third spring  47  is not sufficiently smaller than that of the second spring  46 , or is larger than that of the second spring  46 , in the operational range (A 2  of  FIG. 4D ) equivalent to the range of A 2  of  FIG. 34 , the serial connection of the second spring  46  and the third spring  47  results in the spring constant of the combined springs of the second spring  46  and the third spring  47  being smaller than the spring constant of the second spring  46 . In this case as well, therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 4D ) can be reduced, compared with the rate of change in the reaction force of the operational range of A 1  of  FIG. 4D . 
     As for the acoustic piano, the range of A 3  of  FIG. 34  indicates a relationship between the amount of displacement of the lever caused by the lever and a linkage mechanism coming into contact with various stopper members to slightly compress the stopper members and the reaction force. This range is equivalent to a state of the pedal apparatus  12  of the present embodiment where the undersurface of the forward part of the lever  40  is in contact with the lower limit stopper  43 . Therefore, the pedal apparatus  12  of the embodiment can realize the characteristics of the acoustic piano as shown by the dashed line in  FIG. 34 . 
     In a case where the player deeply depresses the lever  40  and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever  40 , the movable supporting member  48  can temporarily oscillate due to collaboration of inertial force and spring force applied to the movable supporting member  48 . Furthermore, the movable supporting member  48  can collide with the movable supporting member lower limit stopper  49  to cause oscillation of the movable supporting member  48 . In a case where the player periodically changes the amount of depression of the lever  40  in the neighborhood of the range AH of  FIG. 4 , particularly, if the frequency of the periodic changes is close to the natural frequency of the second spring  46  or the third spring  47 , the amplitude of the movable supporting member  48  can grow to cause periodic collision of the movable supporting member  48  with the movable supporting member lower limit stopper  49 . The oscillation of the movable supporting member  48  is conveyed to the lever  40  through the second spring  46  to be perceived by the player as unnatural reaction force. As for the pedal apparatus  12  configured as described above, however, the respective spring forces of the second spring  46  and the third spring  47  act on the movable supporting member  48  in the directions opposite to each other. Therefore, the pedal apparatus  12  is able to suppress or quickly cease the oscillation. Furthermore, because the force of the springs acting on the lever  40  is divided into the spring force exerted by the first spring  45 , and the spring force exerted by the second spring  46  and the third spring  47 , the spring force exerted by the second spring  46  and the third spring  47  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  configured as described above can stabilize the reaction force of the lever  40 . 
     In the above description, the weight of the movable supporting member  48  is taken into account. However, if the movable supporting member  48  is made of a light material such as resin, the weight of the movable supporting member  48  can be ignored. In this case, because the inertial force acting on the movable supporting member  48  can be also ignored, such a light movable supporting member  48  prevents the unnatural reaction force, also achieving reduction in weight of the pedal apparatus  12 . 
     Due to variations in the spring constant of the first spring  45 , the second spring  46  and the third spring  47 , and depending on assembling accuracy of various parts, variations occur in the relationship between the amount of displacement of the lever  40  and the reaction force. As for the pedal apparatus  12  of the present embodiment, however, the load sensor  50  detects the reaction force of the lever  40  to find out a point where the rate of change in the reaction force changes. Therefore, the pedal apparatus  12  of the embodiment can reliably distinguish a range equivalent to the current amount of displacement of the lever  40  from among the ranges of  FIG. 34 . As a result, the pedal apparatus  12  of the embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  40  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated and timbre, resonance (acoustic effect) and the like of musical tones to be generated. 
     As shown in  FIG. 2B , furthermore, a capstan CS may be added. The capstan CS has a cylindrical head portion CSa. Downward from the undersurface of the head portion CSa, a screw portion CSb whose diameter is slightly smaller than that of the head portion CSa extends. With a screw hole being provided on the top surface of the lever  40 , the screw portion CSb is screwed into the screw hole to fix the capstan CS to the lever  40 . The capstan CS is designed to have an outer diameter smaller than the interior diameter of the second spring  46  so that the central axis of the second spring  46  is overlaid with the central axis of the capstan CS. In other words, the capstan CS is situated inside the second spring  46 . In a state where the lever  40  is not depressed, the top end of the head portion CSa is apart from the movable supporting member  48  to oppose to the undersurface of the movable supporting member  48 . The length of the capstan CS is adjusted such that when the lever  40  is depressed to balance between the combined force formed of the urging force of the third spring  47  and the weight of the movable supporting member  48  and the urging force of the second spring  46 , the capstan CS comes into contact with the undersurface of the movable supporting member  48 . 
     In the case where the pedal apparatus  12  is configured as described above, while the movable supporting member  48  is apart from the movable supporting member lower limit stopper  49  to be displaced upward, the movable supporting member  48  is supported by the capstan CS to prevent further compression of the second spring  46 . Therefore, the movable supporting member  48  can stably move upward and downward, resulting in stable reaction force exerted by the lever  40 . 
     The length of the capstan CS may be adjusted such that before the urging force of the second spring  46  exceeds the combined force formed of the urging force of the third spring  47  and the weight of the movable supporting member  48  after the depression of the lever  40 , the capstan CS comes into contact with the undersurface of the movable supporting member  48 . The respective urging forces of the first spring  45 , the second spring  46  and the third spring  47  with respect to the amount of displacement of the lever  40  configured as described above are shown in  FIG. 5A ,  FIG. 5B  and  FIG. 5C . The reaction force exerted by the lever  40  according to the displacement of the lever  40  is shown in  FIG. 5D . For comparison, the respective urging forces of the respective springs and the reaction force of the lever  40  without the capstan CS are shown by dashed lines in  FIG. 5A  through  FIG. 5D . In this case, from the start of a depression of the lever  40  until the contact of the capstan CS with the movable supporting member  48 , the urging forces of the first spring  45  and the second spring  46  increase (A 1  of  FIG. 5A  and  FIG. 5B ). Once the capstan CS comes into contact with the movable supporting member  48 , the second spring  46  will not be compressed any further with no increase in the urging force any more (A 2  of  FIG. 5B ). As a result, as long as the combined force formed of the force exerted by the lever  40  to urge the movable supporting member  48  upward through the capstan CS and the urging force of the second spring  46  is smaller than the combined force formed of the urging force of the third spring  47  and the weight of the movable supporting member  48 , the movable supporting member  48  is in contact with the movable supporting member lower limit stopper  49  to stand still. If the combined force formed of the force exerted by the lever  40  to urge the movable supporting member  48  upward through the capstan CS and the urging force of the second spring  46  exceeds the combined force formed of the urging force of the third spring  47  and the weight of the movable supporting member  48 , the movable supporting member  48  starts being displaced upward. Then, the third spring  47  is compressed to increase the urging force of the third spring  47  (A 2  of  FIG. 5C ). In addition, the urging force of the first spring  45  also increases with the increase in the amount of depression of the lever  40  (A 2  of  FIG. 5A ). Therefore, the reaction force of the lever  40  increases stepwise when the capstan CS comes into contact with the movable supporting member  48 . Compared with the rate of change in the reaction force before the contact of the capstan CS with the movable supporting member  48 , the rate of change in the reaction force after the contact is small ( FIG. 5D ). 
     As for this modification, on the boundary between the range where the rate of change in the reaction force is great and the range where the rate of change is small, the reaction force of the lever  40  changes stepwise. The stepwise change in the reaction force facilitates player&#39;s perception of the boundary. Compared with the pedal apparatus  12  without the capstan CS, furthermore, the pedal apparatus  12  having the capstan CS can narrow the range where the rate of change in the reaction force is great (A 1  of  FIG. 5D ) and widen the range where the rate of change in the reaction force is small (A 2  of  FIG. 5D ). 
     Although this modification is designed such that the capstan CS is situated inside the second spring  46 , the capstan CS may be placed anywhere as long as the top end of the capstan CS opposes to the undersurface of the movable supporting member  48 . Alternatively, the capstan CS may be placed on the movable supporting member  48  side so that the head portion CSa of the capstan CS opposes to the top surface of the lever  40 . 
     The above-described first embodiment is designed such that the top end of the first spring  45  is fixed to the frame FR situated above the rear part of the lever  40 , with the lower end of the first spring  45  being in contact with the top surface of the rear part of the lever  40 . However, the first embodiment may be modified such that the lower end of the first spring  45  is fixed to the frame FR situated below the forward part of the lever  40 , with the top end of the first spring  45  being contact with the undersurface of the forward part of the lever  40 . Furthermore, the first embodiment is designed such that the top end of the third spring  47  is fixed to the frame FR situated above the rear part of the lever  40 , with the lower end of the third spring  47  being inserted into the concave portion  48   a  of the movable supporting member  48  to be fixed to the bottom surface of the concave portion  48   a  so that the third spring  47  is supported by the movable supporting member  48 . However, the first embodiment may be modified such that the movable supporting member  48  has a spring supporting portion so that the spring supporting portion supports the top end of an extension spring with the lower end of the spring being fixed to the frame FR situated below the movable supporting member  48 . 
     In the first embodiment, furthermore, the mechanism which urges the lever  40  is provided behind the rotary shaft  42  of the lever  40  to be situated above the lever  40 . However, the first embodiment may be modified to turn the mechanism which urges the lever  40  upside down. More specifically, the mechanism which urges the lever  40  may be provided in front of the rotary shaft  42  of the lever  40  to be situated below the lever  40 . Unlike the first embodiment, the upward displacement of the movable supporting member  48  is restricted in this modification. In this modification as well, the first spring  45 , the second spring  46  and the third spring  47  urge upward the undersurface of the lever  40  on a point situated in front of the rotary shaft  42  to achieve the effect similar to that achieved by the first embodiment. In this modification, oppositely to the first embodiment, the weight of the movable supporting member  48  acts in a direction in which the displacement of the movable supporting member  48  is allowed. In this modification as well, in a case where the movable supporting member  48  is made of a light material, the weight of the movable supporting member  48  can be ignored. 
     The first embodiment is designed such that the movable supporting member  48  can move upward and downward. However, the embodiment may be modified to have a movable supporting member  48 A which pivots in response to the lever  40  as shown in  FIG. 6 . The movable supporting member  48 A is formed of an upper plate extending toward the front and the rear and a side plate extending downward from the left end or the right end of the upper plate. The forward part of the movable supporting member  48 A is supported by the lever supporting portion  41  so that the rear end of the movable supporting member  48 A can pivot upward and downward about the rotary shaft  42 . The downward displacement of the rear end of the movable supporting member  48 A is restricted by the movable supporting member lower limit stopper  49  fixed to the frame FR. Into the concave portion  40   a  provided on the top surface of the lever  40  behind the lever supporting portion  41 , the lower end of the first spring  45  is inserted to be fixed to the bottom surface of the concave portion  40   a  to be supported. In the middle of the upper plate of the movable supporting member  48 A, a hole penetrating from the top surface to the undersurface is provided. The first spring  45  passes through the hole so that the top end of the first spring  45  is fixed to the frame FR situated above. Although the modification is designed such that the movable supporting member  48 A is provided with the hole so that the first spring  45  passes through the hole, this configuration is not necessarily required. More specifically, the first spring  45  may be provided outside the movable supporting member  48 A. Into a concave portion  48 Aa provided on the undersurface of the rear part of the upper plate of the movable supporting member  48 A, the top end of the second spring  46  is inserted to be fixed to the upper bottom surface of the concave portion  48 Aa, with the lower end of the second spring  46  being in contact with the top surface of the rear part of the lever  40 . With the top surface of the rear part of the movable supporting member  48 A, the lower end of the third spring  47  is in contact, with the top end of the third spring  47  being fixed to the frame FR situated above. Such a modification can also achieve the effect similar to that achieved by the first embodiment. 
     In the first embodiment and its modifications, the second spring  46  and the third spring  47  are compression springs. However, the second spring  46  and the third spring  47  may be replaced with a second spring  46 A and a third spring  47 A, respectively, which are extension springs as shown in  FIG. 7 . In this modification, the second spring  46 A and the third spring  47 A are provided in front of the rotary shaft  42  of the lever  40  to be situated above the lever  40 . Into the concave portion  48   a  of the movable supporting member  48 , the lower end of the third spring  47 A is inserted to be fixed to the bottom surface of the concave portion  48   a  to be supported. The top end of the third spring  47 A is fixed to the frame FR situated above the movable supporting member  48 . The top end of the second spring  46 A is inserted into the concave portion  48   b  of the movable supporting member  48  to be fixed to the upper bottom surface of the concave portion  48   b  to be supported. The lower end of the second spring  46 A is shaped like a hook. The lever  40  is provided with a spring supporting portion  40   b  which engages the hook provided on the lower end of the second spring  46 A. The hook provided on the lower end of the second spring  46 A is in contact with the spring supporting portion  40   b  at all times. The upward displacement of the movable supporting member  48  is restricted by a movable supporting member upper limit stopper  49 A fixed to the frame FR. Such a modification can also achieve the effect similar to that achieved by the first embodiment. In this modification as well, oppositely to the first embodiment, the weight of the movable supporting member  48  acts in the direction in which the displacement of the movable supporting member  48  is allowed. Therefore, this modification is designed such that the extension spring force exerted by the second spring  46 A is smaller than the extension spring force exerted by the third spring  47 A so that the movable supporting member  48  will not be displaced downward in a state where the amount of displacement of the lever  40  is small (A 1  of  FIG. 4D ). In this modification as well, in a case where the movable supporting member  48  is made of a light material, the weight of the movable supporting member  48  can be ignored. 
     c. Second Embodiment 
     Next, a second embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 8  is a side view of the pedal apparatus  12  according to the present embodiment. The lever  40 , the lever supporting portion  41 , the lower limit stopper  43  and the upper limit stopper  44  are similar to those of the first embodiment. Into a concave portion  40   c  provided on the top surface of the rear part of the lever  40  to be situated behind the rotary shaft  42  of the lever  40 , the lower end of a drive rod  52  is inserted to be in contact with the bottom surface of the concave portion  40   c . The drive rod  52 , which is a long member, extends upward from the rear part of the lever  40 . The top end of the drive rod  52  is inserted into a concave portion  53   a  provided on the undersurface of a first movable supporting member  53  to be in contact with the upper bottom surface of the concave portion  53   a . By a guide member which is not shown, the drive rod  52  is allowed to move only upward and downward. 
     The first movable supporting member  53 , which is a plate-shaped member, is allowed to move only upward and downward by a guide member which is not shown. The downward displacement of the first movable supporting member  53  is restricted by a first movable supporting member lower limit stopper  54  fixed to the frame FR. The first movable supporting member lower limit stopper  54  is also made of a shock-absorbing member such as felt in order to prevent shock noise. On the undersurface of the first movable supporting member  53 , a spring supporting portion  55  is provided so that the top end of a first spring  56  is fixed to the spring supporting portion  55  to be supported by the spring supporting portion  55 . The lower end of the first spring  56  is fixed to the frame FR situated below the first movable supporting member  53 . The first spring  56  is an extension spring. Into a concave portion  53   b  provided on the top surface of the first movable supporting member  53 , the lower end of a second spring  57  is inserted to be fixed to the concave portion  53   b  to be supported. The second spring  57  is a compression spring. 
     Above the second spring  57 , a second movable supporting member  58  is provided. The second movable supporting member  58 , which is a plate-shaped member, is allowed to move only upward and downward by a guide member which is not shown. The downward displacement of the second movable supporting member  58  is restricted by a second movable supporting member lower limit stopper  59  fixed to the frame FR. The second movable supporting member lower limit stopper  59  is also made of a shock-absorbing member such as felt in order to prevent shock noise. The top end of the second spring  57  is in contact with the undersurface of the second movable supporting member  58 . On the undersurface of the second movable supporting member  58 , a spring supporting portion  60  is provided so that the top end of a third spring  61  is fixed to the spring supporting portion  60  to be supported. The lower end of the third spring  61  is fixed to the frame FR situated below the second movable supporting member  58 . The third spring  61  is an extension spring. If comparisons of spring constant are made among the first spring  56 , the second spring  57  and the third spring  61 , the first spring  56  has the largest spring constant. The spring constant of the third spring  61  is sufficiently small when compared with the spring constant of the first spring  56  and the second spring  57 . In this embodiment, similarly to the first embodiment, the relationship of the magnitude of the spring constant among the first to third springs  56 ,  57 ,  61  is not limited to that of the present embodiment, but can vary according to desired characteristics of reaction force of the lever  40 . In a case where the difference of rate of change in the reaction force is small between range A 1  and range A 2  shown in  FIG. 34 , for instance, the third spring  61  may have a larger spring constant than the second spring  57 . Similarly to the first embodiment, the load sensor  50  is provided on the undersurface of the second movable supporting member  58 , while the displacement sensor  51  is provided on the frame FR. 
     Next, the operation of the pedal apparatus  12  configured as described above will be described. In a state where the lever  40  is not depressed, the first movable supporting member  53  is urged downward by the first spring  56  to be in contact with the first movable supporting member lower limit stopper  54 . As a result, the rear part of the lever  40  is urged downward through the drive rod  52 . Resultantly, the undersurface of the rear part of the lever  40  is in contact with the upper limit stopper  44 , so that the lever  40  stands still to be in the state shown in  FIG. 8 . In this state, the second spring  57  is in its natural length, resulting in the urging force exerted on the lever  40  of “0”. In this state, furthermore, the second movable supporting member  58  is in contact with the second movable supporting member lower limit stopper  59  by the urging force of the third spring  61  and the weight of the second movable supporting member  58 . In this state, although the second spring  57  may be slightly compressed to urge the lever  40  through the drive rod  52 , the urging force of the second spring  57  is designed to be smaller than a combined force in which the urging force of the third spring  61  and the weight of the second movable supporting member  58  are combined so that the second movable supporting member  58  is in contact with the second movable supporting member lower limit stopper  59 . 
     If the player depresses the lever  40  in spite of the urging force exerted by the first spring  56 , the lever  40  starts pivoting counterclockwise about the rotary shaft  42  in  FIG. 8 , so that the rear part of the lever  40  is displaced upward. By this displacement, the drive rod  52  causes the first movable supporting member  53  to be displaced upward. As a result, the first spring  56  is extended to increase the urging force exerted on the lever  40  by the first spring  56  (A 1  of  FIG. 4A ). If the urging force exerted by the second spring  57  is smaller than the combined force formed of the urging force exerted by the third spring  61  to urge the second movable supporting member  58  downward and the weight of the second movable supporting member  58 , furthermore, the second movable supporting member  58  remains to be in contact with the second movable supporting member lower limit stopper  59 . By the upward displacement of the first movable supporting member  53 , as a result, the second spring  57  also starts compressing to increase the urging force exerted by the second spring  57  (A 1  of  FIG. 4B ). In this operational range, therefore, the reaction force of the lever  40  and the change in the reaction force are brought about by the first spring  56  and the second spring  57  (A 1  of  FIG. 4D ). 
     Then, if the urging force exerted by the second spring  57  exceeds the combined force formed of the urging force exerted by the third spring  61  to urge the second movable supporting member  58  downward and the weight of the second movable supporting member  58 , the second movable supporting member  58  moves upward. The amount of depression of the lever  40  at the time of the start of upward move of the second movable supporting member  58  is referred to as the first amount of depression. As described above, the spring constant of the third spring  61  is sufficiently small, compared with the second spring  57 . If the amount of displacement of the lever  40  increases, therefore, the third spring  61  is extended to increase the urging force of the third spring  61 . However, the second spring  57  will be hardly compressed any further with little increase in the urging force of the second spring  57  (A 2  of  FIG. 4B  and A 2  of  FIG. 4C ). In this operational range, therefore, the reaction force of the lever  40  is brought about by the first spring  56 , the second spring  57  and the third spring  61 . Strictly speaking, the change in the reaction force is brought about by the first spring  56 , the second spring  57  and the third spring  61 . However, the spring constant of the third spring  61  is sufficiently smaller than that of the second spring  57 , resulting in little compression of the second spring  57  and little increase in the urging force exerted by the second spring  57 . Therefore, it can be considered that the change in the reaction force is brought about by the first spring  56  and the third spring  61  (A 2  of  FIG. 4D ). 
     Then, the undersurface of the middle part of the lever  40  comes into contact with the lower limit stopper  43  to restrict downward displacement of the forward part of the lever  40 . If the depression of the lever  40  is released, the urging forces exerted by the first spring  56 , the second spring  57  and the third spring  61  cause the lever  40  to operate in the order opposite to that in which the lever  40  has operated on the depression of the lever  40 . More specifically, the lever  40  pivots clockwise about the rotary shaft  42  in  FIG. 8 , so that the undersurface of the rear part of the lever  40  comes into contact with the upper limit stopper  44  to recover to the original state ( FIG. 8 ). The load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment to control the damper effect and musical tone elements of musical tones to be generated as in the case of the first embodiment. In the above-described explanation, the weight of the second movable supporting member  58  is taken into account. In a case where the second movable supporting member  58  is made of a light material such as resin, however, the weight of the second movable supporting member  58  can be ignored. 
     Similarly to the first embodiment, as for the pedal apparatus according to the embodiment configured as described above, the urging forces exerted by the first spring  56 , the second spring  57  and the third spring  61  change according to the ranges equivalent to the respective operational ranges shown in  FIG. 34 . As a result, the pedal apparatus according to the present embodiment can achieve the characteristics ( FIG. 4D ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the dashed line in  FIG. 34 . 
     In the present embodiment, similarly to the first embodiment, in the case where the player deeply depresses the lever  40  and then sharply decreases the amount of depression, and in the case where the player periodically changes the amount of depression of the lever  40 , the second movable supporting member  58  can temporarily oscillate due to collaboration of inertial force and spring force. Furthermore, the second movable supporting member  58  can collide with the second movable supporting member lower limit stopper  59 . As for the present embodiment as well, however, the respective spring forces of the second spring  57  and the third spring  61  act on the second movable supporting member  58  in the directions opposite to each other. Therefore, the pedal apparatus  12  is able to suppress or quickly cease the oscillation. Furthermore, because the force of the springs acting on the lever  40  is divided into the spring force exerted by the first spring  56 , and the spring force exerted by the second spring  57  and the third spring  61 , the spring force exerted by the second spring  57  and the third spring  61  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  can stabilize the reaction force of the lever  40 . 
     In the above description, the weight of the second movable supporting member  58  is taken into account. However, if the second movable supporting member  58  is made of a light material such as resin, the weight of the second movable supporting member  58  can be ignored. In this case, because the inertial force acting on the second movable supporting member  58  can be also ignored, such a light second movable supporting member  58  prevents the unnatural reaction force, also achieving reduction in weight of the pedal apparatus  12 . 
     In addition, because the load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  40  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated, and timbre, resonance (acoustic effect) and the like of musical tones to be generated. 
     Between the first movable supporting member  53  and the second movable supporting member  58 , the capstan CS similar to that of the modification of the first embodiment may be provided. Such a modification also achieves the effect similar to the modification of the first embodiment. 
     In the second embodiment, the top end of the first spring  56  is supported by the spring supporting portion  55  provided on the first movable supporting member  53 , with the lower end of the first spring  56  being fixed to the frame FR situated below the first movable supporting member  53 . However, the second embodiment may be modified such that the top end of a compression spring is fixed to the frame FR situated above the first movable supporting member  53 , with the lower end of the compression spring being in contact with the top surface of the first movable supporting member  53 . The second embodiment is designed such that the lower end of the second spring  57  is inserted into the concave portion  53   b  of the first movable supporting member  53  to be fixed to the upper bottom surface of the concave portion  53   b  to be supported. However, the second embodiment may be modified such that a concave portion is provided on the undersurface of the second movable supporting member  58  so that the top end of the second spring  57  is fixed to the upper bottom surface of the concave portion to be supported, with the lower end of the second spring  57  being inserted into the concave portion  53   b  of the first movable supporting member  53  to be in contact with the concave portion  53   b . Furthermore, the second embodiment is designed such that the top end of the third spring  61  is supported by the spring supporting portion  60  of the second movable supporting portion  58 , with the lower end of the third spring  61  being fixed to the frame FR situated below the second movable supporting member  58 . However, the second embodiment may be modified such that the top end of a compression spring is fixed to the frame FR situated above the second movable supporting member  58 , with the lower end of the compression spring being in contact with the top surface of the second movable supporting member  58 . 
     In the second embodiment, furthermore, the mechanism which urges the lever  40  is provided behind the rotary shaft  42  of the lever  40  to be situated above the lever  40 . However, the second embodiment may be modified to turn the mechanism which urges the lever  40  upside down. More specifically, the mechanism which urges the lever  40  may be provided in front of the rotary shaft  42  of the lever  40  to be situated below the lever  40 . Unlike the second embodiment, the upward displacement of the first movable supporting member  53  and the second movable supporting member  58  is restricted in this modification. In this modification as well, the first spring  56 , the second spring  57  and the third spring  61  urge upward the undersurface of the lever  40  on a point situated in front of the rotary shaft  42  to achieve the effect similar to that achieved by the second embodiment. In this modification, oppositely to the second embodiment, the weight of the second movable supporting member  58  acts in a direction in which the displacement of the second movable supporting member  58  is allowed. In this modification as well, in a case where the second movable supporting member  58  is made of a light material, the weight of the second movable supporting member  58  can be ignored. 
     The second embodiment is designed such that the first movable supporting member  53  and the second movable supporting member  58  can move only upward and downward. However, the embodiment may be modified to have a first movable supporting member  53 A and a second movable supporting member  58 A which pivot in response to the lever  40  as shown in  FIG. 9 . Each of the first movable supporting member  53 A and the second movable supporting member  58 A is a plate-shaped member which extends from the front toward the rear of the pedal apparatus  12 . The respective first and second movable supporting members  53 A,  58 A are supported by a supporting portion  62  on their rear part so that the front end of the respective movable supporting members  53 A,  58 A can pivot upward and downward about a rotary shaft  63 . The second movable supporting member  58 A is situated above the first movable supporting member  53 A. The downward displacement of the front end of the second movable supporting member  58 A is restricted by the second movable supporting member lower limit stopper  59 A fixed to the frame FR. The top end of the drive rod  52  is in contact with a concave portion  53 Aa provided on the undersurface of the forward part of the first movable supporting member  53 A. On the top surface of the forward part of the first movable supporting member  53 A, a concave portion  53 Ab is provided so that the lower end of a first spring  56 A is inserted into the concave portion  53 Ab to be fixed to the concave portion  53 Ab to be supported, with the top end of the first spring  56 A being fixed to the frame FR situated above to be supported by the frame FR. The first spring  56 A is a compression spring. The first spring  56 A urges the front end of the lever  40  upward through the drive rod  52 . On the top surface of the middle part of the first movable supporting member  53 A, a concave portion  53 Ac is provided so that the lower end of a second spring  57 A is inserted into the concave portion  53 Ac to be fixed to the concave portion  53 Ac, with the top end of the second spring  57 A being in contact with the undersurface of the middle part of the second movable supporting member  58 A. To the top surface of the middle part of the second movable supporting member  58 A, the lower end of a third spring  61 A is fixed, with the top end of the third spring  61 A being fixed to the frame FR situated above. In this modification as well, in the operational range of A 1  of  FIG. 4D , the urging force of the third spring  61 A and the weight of the second movable supporting member  58 A cause the second movable supporting member  58 A to be in contact with a second movable supporting member lower limit stopper  59 A so that the second movable supporting member  58 A stands still. Such a modification can also achieve the effect similar to that achieved by the second embodiment. In this modification as well, the second spring  57 A is designed to have a spring force smaller than that of the third spring  61 A to prevent upward displacement of the second movable supporting member  58 A in a state where the amount of displacement of the lever  40  is small (A 1  of  FIG. 4D ). In this modification as well, in a case where the second movable supporting member  58 A is made of a light material, the weight of the second movable supporting member  58 A can be ignored. 
     Between the first movable supporting member  53 A and the second movable supporting member  58 A, the capstan CS similar to that of the modification of the first embodiment may be provided. Such a modification also achieves the effect similar to the modification of the first embodiment. 
     d. Third Embodiment 
     Next, a third embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 10  is a side view of the pedal apparatus  12  according to the present embodiment. The lever  40  and the lower limit stopper  43  are similar to those of the first embodiment. The rear end of the lever  40  is supported by a lever supporting portion  80  provided on the frame FR so that the front end of the lever  40  can pivot upward and downward about a rotary shaft  81 . Below the middle part of the lever  40 , the lower end of a first spring  82  is fixed to the frame FR, with the top end of the first spring  82  being inserted into a concave portion  40   e  provided on the undersurface of the lever  40  to be in contact with the upper bottom surface of the concave portion  40   e  to urge the forward part of the lever  40  upward. The first spring  82  is a compression spring. 
     Above the middle part of the lever  40 , the top end of a second spring  83  is fixed to the frame FR, with the lower end of the second spring  83  being inserted into a concave portion  84   a  provided on the top surface of a pressing member  84  situated above the lever  40  to be fixed to the bottom surface of the concave portion  84   a . The second spring  83  is a compression spring. The pressing member  84  is included in a movable supporting member of the present invention. The upper portion of the pressing member  84  is shaped like a circular plate, while the lower portion from the middle of the pressing member  84  is shaped like a cylinder of smaller diameter than the upper portion. The lower end of the pressing member  84  is shaped like a hemisphere. The pressing member  84  is provided on a movable supporting member  85  so that the pressing member  84  passes through a penetrating hole  85   a  which penetrates from the top surface to the undersurface of the movable supporting member  85  to be in contact with the top surface of the lever  40 . The undersurface of the upper circular plate portion of the pressing member  84  is always in contact with the top surface of the movable supporting member  85 . The pressing member  84  is allowed to move only upward and downward by a guide member which is not shown. In addition, the upward move of the pressing member  84  is restricted by a pressing member upper limit stopper  86 . Although this embodiment is designed to provide the penetrating hole  85   a  on the movable supporting member  85  so that the pressing member  84  penetrates the penetrating hole  85   a , such a configuration is not necessarily required. More specifically, the pressing member  84  may be provided outside the movable supporting member  85 . 
     The movable supporting member  85 , which is a plate-shaped member, is allowed to move only upward and downward by a guide member which is not shown. The upward and downward move of the movable supporting member  85  is restricted to a certain range by a movable supporting member upper limit stopper  87  and a movable supporting member lower limit stopper  88 . The movable supporting member upper limit stopper  87  and the movable supporting member lower limit stopper  88  are also made of a shock-absorbing member such as felt in order to prevent shock noise. On the top surface of the movable supporting member  85 , a spring supporting portion  89  is provided so that the lower end of a third spring  90  is fixed to the spring supporting portion  89  to be supported by the spring supporting portion  89 . The top end of the third spring  90  is fixed to the frame FR situated above the movable supporting member  85 . The third spring  90  is an extension spring. If comparisons of spring constant are made among the first spring  82 , the second spring  83  and the third spring  90 , the first spring  82  has the smallest spring constant. The spring constant of the second spring  83  and the third spring  90  is larger than the spring constant of the first spring  82 . The spring constant of the third spring  90  is slightly larger than the spring constant of the second spring  83 . In this embodiment, similarly to the first embodiment, the relationship of the magnitude of the spring constant among the first to third springs  82 ,  83 ,  90  is not limited to that of the present embodiment, but can vary according to desired characteristics of the reaction force of the lever  40 . In the case where the difference of rate of change in the reaction force is small between range A 1  and range A 2  shown in  FIG. 34 , for instance, the second spring  83  and the third spring  90  may have a smaller spring constant. Similarly to the first embodiment, the load sensor  50  is provided on a part of the top surface of the movable supporting member  85 , the part of the top surface coming into contact with the pressing member  84 . Similarly to the first embodiment, in addition, the displacement sensor  51  is provided on the frame FR. 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained.  FIG. 11A ,  FIG. 11B , and  FIG. 11C  show the urging force exerted by the first spring  82 , the second spring  83  and the third spring  90  with respect to the amount of displacement of the lever  40 .  FIG. 11D  shows the reaction force generated by the lever  40  according to displacement of the lever  40 . In  FIG. 11A  and  FIG. 11C , the urging force exerted in a direction resisting depression of the lever  40  is regarded as positive. In  FIG. 11B , the urging force exerted in a direction facilitating depression of the lever  40  is regarded as positive. In a state where the lever  40  is not depressed, the urging force exerted by the first spring  82  to urge the lever  40  upward causes the lever  40  to pivot clockwise about a rotary shaft  81  in  FIG. 10  to push up the pressing member  84  so that the top surface of the pressing member  84  comes into contact with the pressing member upper limit stopper  86  to make the lever  40  stand still to be in the state of  FIG. 10 . Furthermore, the movable supporting member  85  comes into contact with the movable supporting member upper limit stopper  87 , also being in contact with the pressing member  84  as well. In this state, both the first spring  82  and the second spring  83  are compressed. 
     If the player depresses the lever  40  in spite of the urging force exerted by the first spring  82 , the lever  40  starts pivoting counterclockwise about the rotary shaft  81  in  FIG. 10 , so that the forward part of the lever  40  is displaced downward. On this displacement, the first spring  82  is compressed to increase the urging force exerted by the first spring  82  (A 1  of  FIG. 11A ). Because the second spring  83  is released from compression, the urging force exerted by the second spring  83  decreases (A 1  of  FIG. 11B ). The direction in which the first spring  82  urges the lever  40  is the direction resisting the depression of the lever  40 , while the direction in which the second spring  83  urges the lever  40  is the direction facilitating the depression. 
     The second spring  83  urges the lever  40  downward, also urging the movable supporting member  85  downward. As a result, the third spring  90  is extended to increase its urging force (A 1  of  FIG. 11C ). The urging force of the second spring  83  and the third spring  90  at the start of depression of the lever  40  is adjusted such that, in this operational range (A 1  of  FIG. 11A  through  FIG. 11D ), the urging force of the third spring  90  is smaller than the urging force of the second spring  83 . The reaction force of the lever  40  is obtained by subtracting the urging force of the second spring  83  from the force in which the urging force of the third spring  90  is added to the urging force of the first spring  82 . Therefore, the change in the reaction force is brought about by the first spring  82 , the second spring  83  and the third spring  90  (A 1  of  FIG. 11D ). 
     If the amount of displacement of the lever  40  increases further, the urging force exerted by the first spring  82  also increases further (A 2  of  FIG. 11A ). The undersurface of the movable supporting member  85  comes into contact with the movable supporting member lower limit stopper  88  to restrict downward displacement of the movable supporting member  85 , so that the tip of the pressing member  84  leaves the top surface of the lever  40 . The amount of depression of the lever which triggers the restriction of downward displacement of the movable supporting member  85  is referred to as the first amount of depression. In this operational range, therefore, the reaction force which resists depression of the lever  40  is brought about only by the first spring  82 , while the change in the reaction force is also brought about only by the first spring (A 2  of  FIG. 11D ). 
     Then, the undersurface of the middle part of the lever  40  comes into contact with the lower limit stopper  43  to restrict downward displacement of the forward part of the lever  40 . If the depression of the lever  40  is released, the urging forces exerted by the first spring  82 , the second spring  83  and the third spring  90  cause the lever  40  to operate in the order opposite to that in which the lever  40  has operated on the depression of the lever  40 . More specifically, the lever  40  pivots clockwise about the rotary shaft  81  in  FIG. 10  to push up the pressing member  84 , so that the top surface of the pressing member  84  comes into contact with the pressing member upper limit stopper  86  to stand still. As a result, the pedal apparatus  12  recovers to the original state ( FIG. 10 ). The load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment. 
     The pedal apparatus according to the present embodiment configured as described above can achieve the characteristics similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the dashed line in  FIG. 34 . In the operational range (A 1  of  FIG. 11D ) equivalent to A 0  and A 1  of  FIG. 34 , more specifically, although part of the urging force exerted by the first spring  82  is canceled by the urging force exerted by the second spring  83 , part of the urging force of the second spring  83  is canceled by the third spring  90 . The parallel connection of the first to third springs  82 ,  83 ,  90  results in the spring constant of the combined springs being larger than the spring constant of the first spring  82 . 
     In the operational range (A 2  of  FIG. 11D ) equivalent to A 2  of  FIG. 34 , the urging force of the first spring  82  is designed not to be canceled by the second spring  83  and the third spring  90 . Compared with the operational range (A 1  of  FIG. 11D ) equivalent to A 0  and A 1  of  FIG. 34 , therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 11D ) equivalent to A 2  of  FIG. 34  can be reduced. As a result, the pedal apparatus  12  according to the present embodiment achieves the characteristics of the acoustic piano shown in  FIG. 34 . 
     In the case where the player sharply decreases the amount of depression of the lever  40  or in the case where the player periodically changes the amount of depression of the lever  40 , the lever  40  occasionally collides with the pressing member  84 . The impact caused by the collision of the lever  40  with the pressing member  84  is absorbed by the first spring  82  and the second spring  83 . Therefore, the present embodiment can stabilize the reaction force of the lever  40 . 
     In addition, because the load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  40  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated and timbre, resonance (acoustic effect) and the like of musical tones to be generated. 
     In the third embodiment, the lower end of the first spring  82  is fixed to the frame FR situated below the middle part of the lever  40 , with the top end of the first spring  82  being inserted into the concave portion  40   e  provided on the undersurface of the middle part of the lever  40  to be in contact with the bottom surface of the concave portion  40   e . However, the third embodiment may be modified such that a spring supporting portion is provide on the top surface of the middle part of the lever  40  so that the lower end of an extension spring is supported by the spring supporting portion, with the top end of the extension spring being fixed to the frame FR situated above the middle part of the lever  40 . In the third embodiment, furthermore, the lower end of the third spring  90  is supported by the spring supporting portion  89  of the movable supporting member  85 , with the top end of the third spring  90  being fixed to the frame FR. However, the third embodiment may be modified such that a concave portion is provided on the undersurface of the movable supporting member  85  so that the top end of a compression spring is fixed to the upper bottom surface of the concave portion to be supported by the movable supporting member  85 , with the lower end of the compression spring being fixed to the frame FR situated below the movable supporting member  85 . 
     In the third embodiment, furthermore, the mechanism which urges the lever  40  is provided in front of the rotary shaft  81  of the lever  40 . However, the third embodiment may be modified such that the lever  40  is supported on the middle part of the lever  40  as in the case of the first embodiment to provide the mechanism which urges the lever  40  behind the fulcrum. In this modification, the first spring  82  is turned upside down, compared with the third embodiment, so that the first spring  82  is provided behind and above the fulcrum of the lever  40 . The second spring  83 , the third spring  90 , the pressing member  84 , the second movable supporting member  85  and the stoppers thereof are also turned upside down, compared with the third embodiment, so that they are provided behind and below the fulcrum of the lever  40 . In this modification, unlike the third embodiment, downward displacement of the pressing member  84  is restricted, whereas upward displacement of the movable supporting member  85  is restricted. In this modification as well, the first spring  82  and the third spring  90  generate the spring force resisting depression of the lever  40 , with the second spring  83  generating the spring force facilitating depression of the lever  40  to achieve the effect similar to the third embodiment. 
     e. Fourth Embodiment 
     Next, a fourth embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 12  is a side view of a pedal apparatus of an electronic musical instrument according to the present embodiment. This embodiment is configured almost similarly to the first embodiment shown in  FIG. 2A . Unlike the first embodiment, however, in a state where the lever  40  is not depressed, the lower end of the second spring  46  is apart from the lever  40 . 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained.  FIG. 13A  through  FIG. 13D  shows various states in which the lever  40  is displaced, with the first spring  45 , the second spring  46  and the third spring  47  being compressed.  FIG. 14A ,  FIG. 14B  and  FIG. 14C  show the urging force of the first spring  45 , the second spring  46  and the third spring  47  with respect to the amount of displacement of the lever  40 .  FIG. 14D  shows the reaction force generated by the lever  40  according to the displacement of the lever  40 . In a state where the lever  40  is not depressed, the rear part of the lever  40  is urged downward by the first spring  45 . As a result, the undersurface of the rear part of the lever  40  is in contact with the upper limit stopper  44 , so that the lever  40  stands still to be in a state shown in  FIG. 13A . In this state, the movable supporting member  48  is in contact with the movable supporting member lower limit stopper  49  by the urging force of the third spring  47 , so that the movable supporting member  48  stands still. 
     If the player depresses the lever  40  in spite of the urging force exerted by the first spring  45 , the lever  40  starts pivoting counterclockwise about the rotary shaft  42  in  FIG. 13A , so that the rear part of the lever  40  is displaced upward. This displacement causes compression of the first spring  45  to increase the urging force exerted by the first spring  45  (A 0  of  FIG. 14A ). In this operational range (from  FIG. 13A  to  FIG. 13B ), the lower end of the second spring  46  is not in contact with the lever  40 . In this operational range, therefore, the reaction force of the lever  40  and the change in the reaction force are brought about by the first spring  45  (A 0  of  FIG. 14D ). 
     If the player depresses the lever  40  further to increase the amount of the displacement of the lever  40 , the urging force exerted by the first spring  45  on the lever  40  increases further (A 1  of  FIG. 14A ). The lower end of the second spring  46  comes into contact with the top surface of the lever  40 . The amount of depression of the lever  40  at the time of the contact of the lower end of the second spring  46  with the top surface of the lever  40  is referred to as a second amount of depression. If the urging force exerted by the second spring  46  is smaller than the combined force formed of the urging force exerted by the third spring  47  to urge the movable supporting member  48  downward and the weight of the movable supporting member  48 , the movable supporting member  48  remains to be in contact with the movable supporting member lower limit stopper  49 . By the pivoting of the lever  40 , as a result, the second spring  46  also starts compressing to increase the urging force exerted by the second spring  46  (A 1  of  FIG. 14B ). In this operational range (from  FIG. 13B  to  FIG. 13C ), therefore, the reaction force of the lever  40  and the change in the reaction force are brought about by the first spring  45  and the second spring  46  (A 1  of  FIG. 14D ). 
     If the amount of the displacement of the lever  40  increases further, the urging force of the first spring  45  also increases further (A 2  of  FIG. 14A ). Then, if the urging force exerted by the second spring  46  exceeds the combined force formed of the urging force exerted by the third spring  47  to urge the movable supporting member  48  downward and the weight of the movable supporting member  48 , the movable supporting member  48  leaves the movable supporting member lower limit stopper  49  to move upward. The amount of depression of the lever  40  at the time of the start of upward move of the movable supporting member  48  is referred to as the first amount of depression. Similarly to the first embodiment, the spring constant of the third spring  47  is sufficiently small, compared with the second spring  46 . If the amount of displacement of the lever  40  increases, therefore, the third spring  47  is compressed to increase the urging force of the third spring  47 . However, the second spring  46  will be hardly compressed any further with little increase in the urging force of the second spring  46  (A 2  of  FIG. 14B  and  FIG. 14C ). In this operational range (from  FIG. 13C  to  FIG. 13D ), therefore, the reaction force of the lever  40  is brought about by the first spring  45 , the second spring  46  and the third spring  47 . Strictly speaking, the change in the reaction force is brought about by the first spring  45 , the second spring  46  and the third spring  47 . However, the spring constant of the third spring  47  is sufficiently smaller than that of the second spring  46 , resulting in little compression of the second spring  46  and little increase in the urging force exerted by the second spring  46 . Therefore, it can be considered that the change in the reaction force is brought about by the first spring  45  and the third spring  47  (A 2  of  FIG. 14D ). 
     Then, the undersurface of the middle part of the lever  40  comes into contact with the lower limit stopper  43  to restrict downward displacement of the forward part of the lever  40 . If the depression of the lever  40  is released, the urging forces exerted by the first spring  45 , the second spring  46  and the third spring  47  cause the lever  40  to operate in the order opposite to that in which the lever  40  has operated on the depression of the lever  40 . More specifically, the lever  40  pivots clockwise about the rotary shaft  42  in  FIG. 13D , so that the undersurface of the rear part of the lever  40  comes into contact with the upper limit stopper  44  to recover to the original state ( FIG. 13A ). The load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment to control the damper effect and musical tone elements of musical tones to be generated as in the case of the first embodiment. In the above-described explanation, the weight of the movable supporting member  48  is taken into account. In a case where the movable supporting member  48  is made of a light material such as resin, however, the weight of the movable supporting member  48  can be ignored. 
     The pedal apparatus according to the embodiment configured as described above can achieve the characteristics ( FIG. 14D ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by a solid line in  FIG. 34 . In the operational range (A 0  of  FIG. 14D ) equivalent to A 1  of  FIG. 34 , more specifically, the urging force exerted by the first spring  45  to urge the lever  40  changes, whereas in the operational range (A 1  of  FIG. 14D ) equivalent to A 1  of  FIG. 34 , the urging force exerted by the second spring  46  also changes in addition to the urging force of the first spring  45 . Compared with the operational range (A 0  of  FIG. 14D ) equivalent to A 0  of  FIG. 34 , therefore, the rate of change in the reaction force can be increased in the operational range (A 1  of  FIG. 14D ) equivalent to A 1  of  FIG. 34 . In the operational range (A 2  of  FIG. 14D ) equivalent to A 2  of  FIG. 34 , the urging force of not only the first spring  45  but also the third spring  47  changes. Because the spring constant of the third spring  47  is sufficiently smaller than that of the second spring  46 , the rate of change in the reaction force in the operational range (A 2  of  FIG. 14D ) equivalent to the range of A 2  of  FIG. 34  can be reduced, compared with the operational range (A 1  of  FIG. 14D ) equivalent to the range of A 1  of  FIG. 34 . Even if the spring constant of the third spring  47  is not sufficiently smaller than that of the second spring  46 , or is larger than that of the second spring  46 , in the operational range (A 2  of  FIG. 14D ) equivalent to the range of A 2  of  FIG. 34 , the serial connection of the second spring  46  and the third spring  47  results in the spring constant of the combined springs of the second spring  46  and the third spring  47  being smaller than the spring constant of the second spring  46 . In this case as well, therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 14D ) can be reduced, compared with the rate of change in the reaction force of the operational range of A 1  of  FIG. 14D . Therefore, the pedal apparatus  12  of the embodiment can realize the characteristics of the acoustic piano as shown by the solid line in  FIG. 34 . 
     In the present embodiment, similarly to the first embodiment, in a case where the player deeply depresses the lever  40  and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever  40 , the movable supporting member  48  can temporarily oscillate due to collaboration of inertial force and spring force applied to the movable supporting member  48 . Furthermore, the movable supporting member  48  can collide with the movable supporting member lower limit stopper  49  to cause oscillation of the movable supporting member  48 . The oscillation of the movable supporting member  48  is conveyed to the lever  40  through the second spring  46  to be perceived by the player as unnatural reaction force. As for the pedal apparatus  12  configured as described above, however, the respective spring forces of the second spring  46  and the third spring  47  act on the movable supporting member  48  in the directions opposite to each other. Therefore, the pedal apparatus  12  is able to suppress or quickly cease the oscillation. Furthermore, because the force of the springs acting on the lever  40  is divided into the spring force exerted by the first spring  45 , and the spring force exerted by the second spring  46  and the third spring  47 , the unnatural reaction force conveyed to the lever  40  through the second spring  46  can be reduced. Therefore, the pedal apparatus  12  configured as described above can stabilize the reaction force of the lever  40 . 
     In the above description, the weight of the movable supporting member  48  is taken into account. However, if the movable supporting member  48  is made of a light material such as resin, the weight of the movable supporting member  48  can be ignored. In this case, because the inertial force acting on the movable supporting member  48  can be also ignored, such a light movable supporting member  48  prevents the unnatural reaction force, also achieving reduction in weight of the pedal apparatus  12 . 
     In addition, because the load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  40  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated and timbre, resonance (acoustic effect) and the like of musical tones to be generated. 
     Between the movable supporting member  48  and the lever  40 , the capstan CS similar to that of the modification of the first embodiment may be provided. Such a modification can stabilize reaction force of the lever  40  as in the case of the modification of the first embodiment. In addition, the modification of the fourth embodiment may be further modified such that the capstan CS comes into contact with the movable supporting member  48  before the urging force of the second spring  46  exceeds the combined force formed of the urging force of the third spring  47  and the weight of the movable supporting member  48 . The respective urging forces of the first spring  45 , the second spring  46  and the third spring  47  with respect to the amount of displacement of the lever  40  in this modification are shown in  FIG. 15A ,  FIG. 15B  and  FIG. 15C .  FIG. 15D  shows the reaction force generated by the lever  40  according to the displacement of the lever  40 . For comparison, the respective urging forces of the respective springs and the reaction force of the lever  40  without the capstan CS are shown by dashed lines in  FIG. 15A  to  FIG. 15D . From the start of a depression of the lever  40  until the contact of the second spring  46  with the lever  40 , the urging force of only the first spring  45  increases (A 0  of  FIG. 15A ). From the contact of the second spring  46  with the lever  40  until the capstan CS comes into contact with the movable supporting member  48 , the urging forces of the first spring  45  and the second spring  46  increase (A 1  of  FIG. 15A  and A 1  of  FIG. 15B ). If the contact of the capstan CS with the movable supporting member  48  is followed by the further increase in the amount of the depression of the lever  40 , the urging forces of the first spring  45  and the third spring  47  increase according to the increase in the amount of the depression, without any further increase in the urging force of the second spring  46  (A 2  of  FIG. 15A  to  FIG. 15C ). As for this modification, on the boundary between the range where the rate of change in the reaction force is great and the range where the rate of change is small, the reaction force of the lever  40  changes stepwise. The stepwise change in the reaction force facilitates player&#39;s perception of the boundary. Compared with the pedal apparatus  12  without the capstan CS, furthermore, the pedal apparatus  12  having the capstan CS can narrow the range where the rate of change in the reaction force is great (A 1  of  FIG. 15D ) and widen the range where the rate of change in the reaction force is small (A 2  of  FIG. 15D ). 
     Similarly to the modification of the first embodiment, in addition, the respective positions where the first to the third springs  45 ,  46 ,  47  are provided may be changed. As shown in  FIG. 16 , furthermore, the movable supporting member  48  may be replaced with a movable supporting member  48 A which pivots in response to the lever  40 . The modification shown in  FIG. 16  is obtained by modifying the modification of the first embodiment shown in  FIG. 6  such that the lower end of the second spring  46  in a state where the lever  40  is not depressed is apart from the top surface of the lever  40 . As shown in  FIG. 17 , furthermore, an extension spring may be employed. The modification shown in  FIG. 17  is obtained by modifying the modification of the first embodiment shown in  FIG. 7  such that the lower end of the second spring  46 A in a state where the lever  40  is not depressed is apart from the supporting portion  40   b  provided on the lever  40 . Such modifications can also achieve the effect similar to that of the fourth embodiment. 
     f. Fifth Embodiment 
     Next, a fifth embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 18  is a side view of the pedal apparatus  12  of the present embodiment. This embodiment is configured almost similarly to the second embodiment shown in  FIG. 8 . Unlike the second embodiment, however, in a state where the lever  40  is not depressed, the upper end of the second spring  57  is apart from the second movable supporting member  58 . 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained. In a state where the lever  40  is not depressed, the first movable supporting member  53  is urged downward by the first spring  56  to be in contact with the first movable supporting member lower limit stopper  54 . Resultantly, the rear part of the lever  40  is urged downward through the drive rod  52 . As a result, the undersurface of the rear part of the lever  40  is in contact with the upper limit stopper  44 , so that the lever  40  stands still to be in a state shown in  FIG. 18 . In this state, the second movable supporting member  58  is in contact with the second movable supporting member lower limit stopper  59  by the urging force of the third spring  61  and the weight of the second movable supporting member  58 . 
     If the player depresses the lever  40  in spite of the urging force exerted by the first spring  56 , the lever  40  starts pivoting counterclockwise about the rotary shaft  42  in  FIG. 18 , so that the rear part of the lever  40  is displaced upward. By this displacement, the drive rod  52  causes the first movable supporting member  53  to be displaced upward. As a result, the first spring  56  is extended to increase the urging force exerted on the lever  40  by the first spring  56  (A 0  of  FIG. 14A ). At this time, the upper end of the second spring  57  is apart from the undersurface of the second movable supporting member  58 . In this operational range, therefore, the reaction force of the lever  40  and the change in the reaction force are brought about by the first spring  56  (A 0  of  FIG. 14D ). 
     If the player depresses the lever  40  further to increase the amount of the displacement of the lever  40 , the urging force exerted by the first spring  56  on the lever  40  increases further (A 1  of  FIG. 14A ). The upper end of the second spring  57  comes into contact with the undersurface of the second movable supporting member  58 . The amount of depression of the lever  40  at the time of the contact of the upper end of the second spring  57  with the undersurface of the second movable supporting member  58  is referred to as the second amount of depression. If the urging force exerted by the second spring  57  is smaller than the combined force formed of the urging force exerted by the third spring  61  to urge the second movable supporting member  58  downward and the weight of the second movable supporting member  58 , the second movable supporting member  58  remains to be in contact with the second movable supporting member lower limit stopper  59 . By the upward displacement of the first movable supporting member  53 , as a result, the second spring  57  also starts compressing to increase the urging force exerted by the second spring  57  (A 1  of  FIG. 14B ). In this operational range, therefore, the reaction force of the lever  40  and the change in the reaction force are brought about by the first spring  56  and the second spring  57  (A 1  of  FIG. 14D ). 
     If the amount of the displacement of the lever  40  increases further, the urging forces of the first spring  56  and the second spring  57  also increase further (A 1  of  FIG. 14A  and  FIG. 14B ). Then, if the urging force exerted by the second spring  57  exceeds the combined force formed of the urging force exerted by the third spring  61  to urge the second movable supporting member  58  downward and the weight of the second movable supporting member  58 , the second movable supporting member  58  moves upward. The amount of depression of the lever  40  at the time of the start of upward move of the second movable supporting member  58  is referred to as the first amount of depression. Similarly to the second embodiment, the spring constant of the third spring  61  is sufficiently small, compared with the second spring  57 . If the amount of displacement of the lever  40  increases, therefore, the third spring  61  is extended to increase the urging force of the third spring  61 . However, the second spring  57  will be hardly compressed any further with little increase in the urging force of the second spring  57  (A 2  of  FIG. 14B  and  FIG. 14C ). In this operational range, therefore, the reaction force of the lever  40  is brought about by the first spring  56 , the second spring  57  and the third spring  61 . Strictly speaking, the change in the reaction force is brought about by the first spring  56 , the second spring  57  and the third spring  61 . However, the spring constant of the third spring  61  is sufficiently smaller than that of the second spring  57 , resulting in little compression of the second spring  57  and little increase in the urging force exerted by the second spring  57 . Therefore, it can be considered that the change in the reaction force is brought about by the first spring  56  and the third spring  61  (A 2  of  FIG. 14D ). In this case as well, therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 14D ) can be reduced, compared with the reaction force of the operational range of A 1  of  FIG. 14D . Even if the spring constant of the third spring  61  is not sufficiently smaller than that of the second spring  57 , or is larger than that of the second spring  57 , in the operational range (A 2  of  FIG. 14D ) equivalent to the range of A 2  of  FIG. 34 , the serial connection of the second spring  57  and the third spring  61  results in the spring constant of the combined springs of the second spring  57  and the third spring  61  being smaller than the spring constant of the second spring  57 . In this case as well, therefore, the rate of change in the reaction force in the operational range (A 2  of FIG.  14 D) can be reduced, compared with the reaction force of the operational range of A 1  of  FIG. 14D . Therefore, the pedal apparatus  12  of the embodiment can realize the characteristics of the acoustic piano as shown by the solid line in  FIG. 34 . 
     Then, the undersurface of the middle part of the lever  40  comes into contact with the lower limit stopper  43  to restrict downward displacement of the forward part of the lever  40 . If the depression of the lever  40  is released, the urging forces exerted by the first spring  56 , the second spring  57  and the third spring  61  cause the lever  40  to operate in the order opposite to that in which the lever  40  has operated on the depression of the lever  40 . More specifically, the lever  40  pivots clockwise about the rotary shaft  42  in  FIG. 18 , so that the undersurface of the rear part of the lever  40  comes into contact with the upper limit stopper  44  to recover to the original state ( FIG. 18 ). The load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment to control the damper effect and musical tone elements of musical tones to be generated as in the case of the first embodiment. In the above-described explanation, the weight of the second movable supporting member  58  is taken into account. In a case where the second movable supporting member  58  is made of a light material such as resin, however, the weight of the second movable supporting member  58  can be ignored. 
     Similarly to the fourth embodiment, as for the pedal apparatus according to the embodiment configured as described above, the urging forces exerted by the first spring  56 , the second spring  57  and the third spring  61  change according to the ranges equivalent to the respective operational ranges shown in  FIG. 34 . As a result, the pedal apparatus according to the present embodiment can achieve the characteristics ( FIG. 14D ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the solid line in  FIG. 34 . 
     In the present embodiment, similarly to the second embodiment, in the case where the player deeply depresses the lever  40  and then sharply decreases the amount of depression, and in the case where the player periodically changes the amount of depression of the lever  40 , the second movable supporting member  58  can temporarily oscillate due to collaboration of inertial force and spring force. Furthermore, the second movable supporting member  58  can collide with the second movable supporting member lower limit stopper  59  to cause oscillation of the second movable supporting member  58 . As for the present embodiment as well, however, the respective spring forces of the second spring  57  and the third spring  61  act on the second movable supporting member  58  in the directions opposite to each other. Therefore, the pedal apparatus  12  is able to suppress or quickly cease the oscillation. Furthermore, because the force of the springs acting on the lever  40  is divided into the spring force exerted by the first spring  56 , and the spring force exerted by the second spring  57  and the third spring  61 , the spring force exerted by the second spring  57  and the third spring  61  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  can stabilize the reaction force of the lever  40 . 
     In the above description, the weight of the second movable supporting member  58  is taken into account. However, if the second movable supporting member  58  is made of a light material such as resin, the weight of the second movable supporting member  58  can be ignored. In this case, because the inertial force acting on the second movable supporting member  58  can be also ignored, such a light second movable supporting member  58  prevents the unnatural reaction force, also achieving reduction in weight of the pedal apparatus  12 . 
     In addition, because the load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  40  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated and timbre, resonance (acoustic effect) and the like of musical tones to be generated. 
     Between the first movable supporting member  53  and the second movable supporting member  58 , the capstan CS similar to that of the modification of the first embodiment may be provided. Such a modification also achieves the effect similar to the modification of the first embodiment. 
     Similarly to the modification of the second embodiment, in addition, the respective positions where the first to third springs  56 ,  57 ,  61  are provided may be changed. As shown in  FIG. 19 , furthermore, the first movable supporting member  53  and the second movable supporting member  58  may be replaced with a first movable supporting member  53 A and a second movable supporting member  58 A which pivot in response to the lever  40 . The modification shown in  FIG. 19  is obtained by modifying the modification of the second embodiment shown in  FIG. 9  such that the lower end of the second spring  57 A in a state where the lever  40  is not depressed is apart from the top surface of the first movable supporting member  53 A. Such modifications can also achieve the effect similar to that of the fifth embodiment. 
     g. Sixth Embodiment 
     Next, a sixth embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 20  is a side view of the pedal apparatus  12  of the present embodiment. This embodiment is configured almost similarly to the third embodiment shown in  FIG. 10 . Unlike the third embodiment, however, in a state where the lever  40  is not depressed, the pressing member  84  is apart from the movable supporting member  85 . 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained.  FIG. 21A ,  FIG. 21B , and  FIG. 21C  show the urging force exerted by the first spring  82 , the second spring  83  and the third spring  90  with respect to the amount of displacement of the lever  40 .  FIG. 21D  shows the reaction force generated by the lever  40  according to displacement of the lever  40 . In  FIG. 21A  and  FIG. 21C , the urging force exerted in a direction resisting depression of the lever  40  is regarded as positive. In  FIG. 21B , the urging force exerted in a direction facilitating depression of the lever  40  is regarded as positive. In a state where the lever  40  is not depressed, the urging force exerted by the first spring  82  to urge the lever  40  upward causes the lever  40  to pivot clockwise about the rotary shaft  81  in  FIG. 20  to push up the pressing member  84  so that the top surface of the pressing member  84  comes into contact with the pressing member upper limit stopper  86  to make the lever  40  stand still to be in the state of  FIG. 20 . In this state, both the first spring  82  and the second spring  83  are compressed. 
     If the player depresses the lever  40  in spite of the urging force exerted by the first spring  82 , the lever  40  starts pivoting counterclockwise about the rotary shaft  81  in  FIG. 20 , so that the forward part of the lever  40  is displaced downward. On this displacement, the first spring  82  is compressed to increase the urging force exerted by the first spring  82  (A 0  of  FIG. 21A ). Because the second spring  83  is released from compression, the urging force exerted by the second spring  83  decreases (A 0  of  FIG. 21B ). In this operational range, the third spring  90  will not urge the lever  40 . The direction in which the first spring  82  urges the lever  40  is the direction resisting the depression of the lever  40 , while the direction in which the second spring  83  urges the lever  40  is the direction facilitating the depression. As a result, the reaction force of the lever  40  is obtained by subtracting the urging force of the second spring  83  from the urging force of the first spring  82 . Therefore, the change in the reaction force of the lever  40  is brought about by the first spring  82  and the second spring  83  (A 0  of  FIG. 21D ). 
     If the lever  40  is depressed further to increase the amount of displacement of the lever  40 , the urging force exerted by the first spring  82  also increases further (A 1  of  FIG. 21A ). In addition, the circular plate portion of the pressing member  84  comes into contact with the top surface of the movable supporting member  85 . The amount of depression of the lever  40  at the time of the contact of the circular plate portion of the pressing member  84  with the top surface of the movable supporting member  85  is referred to as the second amount of depression. The second spring  83  urges the lever  40  downward, also urging the movable supporting member  85  downward. As a result, the third spring  90  is extended to increase its urging force (A 1  of  FIG. 21C ). The urging force of the second spring  83  and the third spring  90  at the start of depression of the lever  40  is adjusted such that, in this operational range (A 1  of  FIG. 21 ), the urging force of the third spring  90  is smaller than the urging force of the second spring  83 . The reaction force of the lever  40  is obtained by subtracting the urging force of the second spring  83  from the force in which the urging force of the third spring  90  is added to the urging force of the first spring  82 . Therefore, the change in the reaction force is brought about by the first spring  82 , the second spring  83  and the third spring  90  (A 1  of  FIG. 21D ). 
     If the amount of displacement of the lever  40  increases further, the urging force exerted by the first spring  82  also increases further (A 2  of  FIG. 21A ). The undersurface of the movable supporting member  85  comes into contact with the movable supporting member lower limit stopper  88  to restrict downward displacement of the movable supporting member  85 , so that the tip of the pressing member  84  leaves the top surface of the lever  40 . The amount of depression of the lever which triggers the restriction of downward displacement of the movable supporting member  85  is referred to as the first amount of depression. In this operational range, therefore, the reaction force which resists depression of the lever  40  is brought about only by the first spring  82 , while the change in the reaction force is also brought about only by the first spring (A 2  of  FIG. 21D ). 
     Then, the undersurface of the middle part of the lever  40  comes into contact with the lower limit stopper  43  to restrict downward displacement of the forward part of the lever  40 . If the depression of the lever  40  is released, the urging forces exerted by the first spring  82 , the second spring  83  and the third spring  90  cause the lever  40  to operate in the order opposite to that in which the lever  40  has operated on the depression of the lever  40 . More specifically, the lever  40  pivots clockwise about the rotary shaft  81  in  FIG. 20  to push up the pressing member  84 , so that the top surface of the pressing member  84  comes into contact with the pressing member upper limit stopper  86  to stand still. As a result, the pedal apparatus  12  recovers to the original state ( FIG. 20 ). The load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment. 
     The pedal apparatus according to the present embodiment configured as described above can also achieve the characteristics similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the solid line in  FIG. 34 . In the operational range (A 0  of  FIG. 21D ) equivalent to A 0  of  FIG. 34 , more specifically, the urging force exerted on the lever  40  by the first spring  82  is canceled by a large amount by the urging force exerted by the second spring  83 . The parallel connection of the first and second springs  82 ,  83  results in the spring constant of the combined springs being larger than the spring constant of the first spring  82 . 
     In the operational range (A 1  of  FIG. 21D ) equivalent to A 1  of  FIG. 34 , although part of the urging force exerted by the first spring  82  is canceled by the urging force exerted by the second spring  83 , part of the urging force of the second spring  83  is canceled by the third spring  90 . The parallel connection of the first to third springs  82 ,  83 ,  90  results in the spring constant of the combined springs being larger than the spring constant of the combined springs formed of the first spring  82  and the second spring  83 . Compared with the operational range (A 0  of  FIG. 21D ) equivalent to A 0  of  FIG. 34 , therefore, the rate of change in the reaction force in the operational range (A 1  of  FIG. 21D ) equivalent to A 1  of  FIG. 34  can be increased. 
     In the operational range (A 2  of  FIG. 21D ) equivalent to A 2  of  FIG. 34 , the urging force of the first spring  82  is designed not to be canceled by the second spring  83  and the third spring  90 . Compared with the operational range (A 1  of  FIG. 21D ) equivalent to A 1  of  FIG. 34 , therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 21D ) equivalent to A 2  of  FIG. 34  can be reduced. As a result, the pedal apparatus  12  according to the present embodiment achieves the characteristics of the acoustic piano shown by the solid line in  FIG. 34 . 
     In the present embodiment, similarly to the third embodiment, in the case where the player sharply decreases the amount of depression of the lever  40  or in the case where the player periodically changes the amount of depression of the lever  40 , the lever  40  occasionally collides with the pressing member  84 . The impact caused by the collisions of the lever  40  with the pressing member  84  is absorbed by the first spring  82  and the second spring  83 . Therefore, the present embodiment can stabilize the reaction force of the lever  40 . 
     In addition, because the load sensor  50  and the displacement sensor  51  operate similarly to the first embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  40  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated and timbre, resonance (acoustic effect) and the like of musical tones to be generated. 
     Similarly to the modification of the third embodiment, in addition, the respective positions where the first to third springs  82 ,  83 ,  90  are provided may be changed. Furthermore, the compression springs may be replaced with extension springs. Such modifications can also achieve the effect similar to that of the sixth embodiment. 
     h. Seventh Embodiment 
     Next, a seventh embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 22A  shows a side view of the pedal apparatus of the electronic musical instrument according to the present embodiment. A lever  140  is a long plate-shaped member. The forward part (left side in  FIG. 22A ) of the lever  140  is a wide depression part on which a player steps. The lever  140  is supported at a middle part thereof by a lever supporting portion  141  provided on the frame FR so that the front end of the lever  140  can pivot upward and downward about a rotary shaft  142 . Below the middle part of the lever  140 , a long lower limit stopper  143  made of a shock-absorbing member such as felt extends in a lateral direction to be fixed to the frame FR. The lower limit stopper  143  restricts downward displacement of the forward part of the lever  140 . The frame FR is a structural body for supporting various parts of the pedal apparatus  12  and a housing itself of the pedal apparatus  12 . Below the rear part of the lever  140 , an upper limit stopper  144  which is similar to the lower limit stopper  143  is fixed to the frame FR to restrict upward displacement of the forward part of the lever  140 . 
     Behind the rotary shaft  142  of the lever  140 , the top end of a first spring  145  is fixed to the frame FR so that the top end of the first spring  145  is situated above the rear part of the lever  140 . The lower end of the first spring  145  is inserted into a concave portion  140   a  provided on the top surface of the lever  140  behind the rotary shaft  142  of the lever  140  so that the lower end of the first spring  145  is in contact with the bottom surface of the concave portion  140   a  to urge the rear part of the lever  140  downward. The first spring  145  is a compression spring. Behind the rotary shaft  142  of the lever  140 , a metal weight  146  serving as a movable supporting member is provided above the rear part of the lever  140 . The weight  146  is allowed to move only upward and downward by a guide member which is not shown. The downward displacement of the weight  146  is restricted by a weight lower limit stopper  147  fixed to the frame FR. The weight  146  may be molded by resin to be fixed to a resin member formed by molding a metal massive body. The weight lower limit stopper  147  is made of a shock-absorbing member such as felt to prevent shock noise that would be generated when the weight  146  collides with the frame FR. On the undersurface of the weight  146 , a concave portion  146   a  is provided. The top end of a second spring  148  is inserted into the concave portion  146   a  to be fixed to the upper bottom surface of the concave portion  146   a  to be supported. The lower end of the second spring  148  is in contact with a part of the top surface of the lever  140 , the part being situated behind the rotary shaft  142 . The second spring  148  is also a compression spring. 
     Into the concave portion  146   a  of the weight  146 , a load sensor  150  for sensing the urging force of the second spring  148  (load applied to the lever  140  which is the pedal apparatus  12 ) is incorporated. By electrically sensing elastic deformation caused by the urging force of the second spring  148  (e.g., with a strain gauge), the load sensor  150  obtains the urging force of the second spring  148 . Above the middle part of the lever  140 , furthermore, a displacement sensor  151  for sensing the amount of displacement of the lever  140  is provided. By electrically or optically sensing the distance to the top surface of the lever  140  (e.g., by reflection of laser light), the displacement sensor  151  obtains the amount of displacement of the lever  140 . The displacement sensor  151  may be replaced with a sensor for mechanically and electrically sensing the amount of upward and downward displacement of the lever  140  (e.g., variable resistance). 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained.  FIG. 23A  through  FIG. 23C  show various states in which the lever  140  and the weight  146  are displaced, with the first spring  145  and the second spring  148  being compressed.  FIG. 24A  and  FIG. 24B  show the urging force of the first spring  145  and the second spring  148  with respect to the amount of displacement of the lever  140 .  FIG. 24C  shows the reaction force generated by the lever  140  according to the displacement of the lever  140 . In a state where the lever  140  is not depressed, the rear part of the lever  140  is urged downward by the first spring  145 . As a result, the undersurface of the rear part of the lever  140  is in contact with the upper limit stopper  144 , so that the lever  140  stands still to be in a state shown in  FIG. 23A . In this state, the second spring  148  is in its natural length, resulting in the urging force exerted on the lever  140  of “0”. Because of the weight of the weight  146 , in this state, the weight  146  is in contact with the weight lower limit stopper  147  to stand still. In this state, furthermore, although the second spring  148  may be slightly compressed to urge the lever  140 , the urging force of the second spring  148  is designed to be smaller than the weight of the weight  146  so that the weight  146  is in contact with the weight lower limit stopper  147 . 
     If the player depresses the lever  140  in spite of the urging force exerted by the first spring  145 , the lever  140  starts pivoting counterclockwise about the rotary shaft  142  in  FIG. 23A , so that the rear part of the lever  140  is displaced upward. This displacement causes compression of the first spring  145  to increase the urging force exerted by the first spring  145  (A 1  of  FIG. 24A ). If the urging force exerted by the second spring  148  is smaller than the weight of the weight  146 , furthermore, the weight  146  remains to be in contact with the weight lower limit stopper  147 . As a result, the second spring  148  also starts compressing to increase the urging force exerted by the second spring  148  as well (A 1  of  FIG. 24B ). In this operational range (from  FIG. 23A  to  FIG. 23B ), therefore, the reaction force of the lever  140  and the change in the reaction force are brought about by not only the first spring  145  but also the second spring  148  (A 1  of  FIG. 24C ). 
     If the amount of displacement of the lever  140  increases further, the urging force of the first spring  145  increases further (A 2  of  FIG. 24A ). If the urging force of the second spring  148  exceeds the weight of the weight  146 , the weight  146  moves upward. As a result, the second spring  148  will not be compressed any further, with little increase in the urging force of the second spring  148  (A 2  of  FIG. 24B ). In this operational range (from  FIG. 23B  to  FIG. 23C ), therefore, although the reaction force of the lever  140  is brought about by the first spring  145  and the second spring  148 , the changes in the reaction force is brought about only by the first spring  145  (A 2  of  FIG. 24C ). The amount of depression of the lever  140  at the time of the start of upward move of the weight  146  is referred to as the first amount of depression. 
     Then, the undersurface of the middle part of the lever  140  comes into contact with the lower limit stopper  143  to restrict downward displacement of the forward part of the lever  140 . If the depression of the lever  140  is released, the urging force of the first spring  145 , the urging force of the second spring  148  and the weight of the weight  146  which serves as a movable supporting member cause the lever  140  to operate in the order opposite to that in which the lever  140  has operated on the depression of the lever  140 . More specifically, the lever  140  pivots clockwise about the rotary shaft  142  in  FIG. 23C , so that the undersurface of the rear part of the lever  140  comes into contact with the upper limit stopper  144  to recover to the original state ( FIG. 23A ). 
     The detection circuit  23  detects a point where the rate of change in the reaction force of the lever  140  changes on the basis of the change in the urging force exerted by the second spring  148  detected by the load sensor  150 . Furthermore, the displacement sensor  151  detects the amount of displacement of the lever  140 . In accordance with the changing point of the rate of change in the reaction force and the information on the amount of displacement of the lever  140 , the electronic musical instrument  10  adds a damper effect to a musical tone to be generated, also controlling musical tone elements such as timbre and resonance (acoustic effect) of the musical tone to be generated. In a range AH of  FIG. 24C  corresponding to the above-described half pedal range AH of  FIG. 34 , particularly, on the basis of the load detected by the load sensor  150  and the amount of displacement detected by the displacement sensor  151 , the tone generator  15  and the effect circuit  26  subtly change the musical tone elements such as timbre and resonance (acoustic effect) of musical tones to be generated in accordance with pedal manipulation of the player. The above-described control of the musical tone elements may be done on the basis of either of the load detected by the load sensor  150  or the amount of displacement detected by the displacement sensor  151 . 
     The pedal apparatus according to the present embodiment configured as described above can achieve the characteristics ( FIG. 24C ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the dashed line in  FIG. 34 . In the operational range (A 1  of  FIG. 24C ) equivalent to A 0  and A 1  of  FIG. 34 , more specifically, the urging force exerted by the first spring  145  and the second spring  148  to urge the lever  140  changes, whereas in the operational range (A 2  of  FIG. 24C ) equivalent to A 2  of  FIG. 34 , the urging force exerted on the lever  140  by the first spring  145  changes. Therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 24C ) equivalent to the range of A 2  of  FIG. 34  can be reduced, compared with the operational range (A 1  of  FIG. 24C ) equivalent to the range of A 0  and A 1  of  FIG. 34 . 
     As for the acoustic piano, the range of A 3  of  FIG. 34  indicates a relationship between the amount of the displacement of the lever caused by the lever and a linkage mechanism coming into contact with various stopper members to slightly compress the stopper members and the reaction force. This range is equivalent to a state of the pedal apparatus  12  of the present embodiment where the undersurface of the forward part of the lever  140  is in contact with the lower limit stopper  143 . Therefore, the pedal apparatus  12  of the embodiment can realize the characteristics of the acoustic piano as shown by the dashed line in  FIG. 34 . 
     In a case where the player deeply depresses the lever  140  and then sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever  140 , the weight  146  can temporarily oscillate due to collaboration of inertial force and spring force applied to the weight  146 . Furthermore, the weight  146  can collide with the weight lower limit stopper  147  to cause oscillation of the weight  146 . In a case where the player periodically changes the amount of depression of the lever  140  in the neighborhood of the range AH of  FIG. 24C , particularly, if the frequency of the periodic changes is close to the natural frequency of the second spring  148 , the amplitude of the weight  146  can grow to cause periodic collision of the weight  146  with the weight lower limit stopper  147 . In this case, however, because the force of the springs acting on the lever  140  is divided into the spring force exerted by the first spring  145  and the spring force exerted by the second spring  148 , the spring force exerted by the second spring  148  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  configured as described above can stabilize the reaction force of the lever  140 . 
     Due to variations in the spring constant of the first spring  145  and the second spring  148 , and depending on assembling accuracy of various parts, variations occur in the relationship between the amount of displacement of the lever  140  and the reaction force. As for the pedal apparatus  12  of the present embodiment, however, the load sensor  150  detects the reaction force of the lever  140  to find out a point where the rate of change in the reaction force changes. Therefore, the pedal apparatus  12  of the embodiment can reliably distinguish a range equivalent to the current amount of displacement of the lever  140  from among the ranges of  FIG. 34 . As a result, the pedal apparatus  12  of the embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  140  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated and timbre, resonance (acoustic effect) and the like of musical tones to be generated. Furthermore, the present embodiment realizes the pedal apparatus having a simple structure. 
     As shown in  FIG. 22B , furthermore, a capstan CS may be added. The capstan CS has a cylindrical head portion CSa. Downward from the undersurface of the head portion CSa, a screw portion CSb whose diameter is slightly smaller than that of the head portion CSa extends. With a screw hole being provided on the top surface of the lever  140 , the screw portion CSb is screwed into the screw hole to fix the capstan CS to the lever  140 . The capstan CS is designed to have an outer diameter smaller than the interior diameter of the second spring  148  so that the central axis of the second spring  148  is overlaid with the central axis of the capstan CS. In other words, the capstan CS is situated inside the second spring  148 . In a state where the lever  140  is not depressed, the top end of the head portion CSa is apart from the weight  146  to oppose to the undersurface of the weight  146 . The length of the capstan CS is adjusted such that when the lever  140  is depressed to balance between the weight of the weight  146  and the urging force of the second spring  148 , the capstan CS comes into contact with the undersurface of the weight  146 . 
     In the case where the pedal apparatus  12  is configured as described above, while the weight  146  is apart from the weight lower limit stopper  147  to be displaced upward, the weight  146  is supported by the capstan CS to prevent further compression of the second spring  148 . Therefore, the weight  146  can stably move upward and downward, resulting in stable reaction force exerted by the lever  140 . 
     The length of the capstan CS may be adjusted such that before the urging force of the second spring  148  exceeds the weight of the weight  146  after the depression of the lever  140 , the capstan CS comes into contact with the undersurface of the weight  146 . The respective urging forces of the first spring  145  and the second spring  148  with respect to the amount of displacement of the lever  140  configured as described above are shown in  FIG. 25A  and  FIG. 25B . The reaction force exerted by the lever  140  according to the displacement of the lever  140  is shown in  FIG. 25C . For comparison, the respective urging forces of the respective springs and the reaction force of the lever  140  without the capstan CS are shown by dashed lines in  FIG. 25B  and  FIG. 25C . In this case, from the start of a depression of the lever  140  until the contact of the capstan CS with the weight  146 , the urging forces of the first spring  145  and the second spring  148  increase (A 1  of  FIG. 25A  and  FIG. 25B ). Once the capstan CS comes into contact with the weight  146 , the second spring  148  will not be compressed any further with no increase in the urging force any more (A 2  of  FIG. 25B ). As a result, as long as the force exerted by the lever  140  to lift the weight  146  through the capstan CS and the second spring  148  is smaller than the weight of the weight  146 , the weight  146  is in contact with the weight lower limit stopper  147  to stand still. If the force exerted by the lever  140  to lift the weight  146  through the capstan CS and the second spring  148  exceeds the weight of the weight  146 , the weight  146  starts being displaced upward. In addition, the urging force of the first spring  145  also increases with the increase in the amount of depression of the lever  140  (A 2  of  FIG. 25A ). Therefore, the reaction force of the lever  140  increases stepwise when the capstan CS comes into contact with the weight  146 . Compared with the rate of change in the reaction force before the contact of the capstan CS with the weight  146 , the rate of change in the reaction force after the contact is small ( FIG. 25C ). 
     As for this modification, on the boundary between the range where the rate of change in the reaction force is great and the range where the rate of change is small, the reaction force of the lever  140  changes stepwise. The stepwise change in the reaction force facilitates player&#39;s perception of the boundary. Compared with the pedal apparatus  12  without the capstan CS, furthermore, the pedal apparatus  12  having the capstan CS can narrow the range where the rate of change in the reaction force is great (A 1  of  FIG. 25C ) and widen the range where the rate of change in the reaction force is small (A 2  of  FIG. 25C ). 
     Although this modification is designed such that the capstan CS is situated inside the second spring  148 , the capstan CS may be placed anywhere as long as the top end of the capstan CS opposes to the undersurface of the weight  146 . Alternatively, the capstan CS may be placed on the weight  146  side so that the head portion CSa of the capstan CS opposes to the top surface of the lever  140 . 
     The above-described seventh embodiment is designed such that the top end of the first spring  145  is fixed to the frame FR situated above the rear part of the lever  140 , with the lower end of the first spring  145  being in contact with the top surface of the rear part of the lever  140 . However, the seventh embodiment may be modified such that the lower end of the first spring  145  is fixed to the frame FR situated below the forward part of the lever  140 , with the top end of the first spring  145  being contact with a part of the undersurface of the lever  140 , the part being situated in front of the rotary shaft  142 . Furthermore, the seventh embodiment is designed such that the top end of the second spring  148  is inserted into the concave portion  146   a  of the weight  146  to be fixed to the upper bottom surface of the concave portion  146   a  to be supported. However, the seventh embodiment may be modified such that the lever  140  has a concave portion on its top surface so that the lower end of the second spring  148  is fixed to the bottom surface of the concave portion to be supported, with the top end of the second spring  148  being inserted into the concave portion  146   a  of the weight  146  to be in contact with the weight  146 . 
     The seventh embodiment is designed such that the weight  146  can move upward and downward. However, the embodiment may be modified to have a weight lever  153  and a weight  157  which pivot in response to the lever  140  as shown in  FIG. 26 . In this modification, the lever  140 , the lever supporting portion  141 , the lower limit stopper  143  and the upper limit stopper  144  are configured similarly to those of the seventh embodiment. Below the forward part of the lever  140 , the lower end of a first spring  152  is fixed to the frame FR, with the top end of the first spring  152  being inserted into a concave portion  140   b  provided on a part of the undersurface of the lever  140 , the part being situated in front of the rotary shaft  142  of the lever  140 . The top end of the first spring  152  is in contact with the upper bottom surface of the concave portion  140   b  so that the first spring  152  urges the forward part of the lever  140  upward. The first spring  152  is a compression spring. 
     Above the rear part of the lever  140 , the weight lever  153  serving as a movable supporting member is provided. The weight lever  153 , which is a plate-shaped member, is supported at its front end by a weight lever supporting portion  154  provided on the frame FR so that the rear end of the weight lever  153  can pivot upward and downward about a rotary shaft  155 . Above the rear part of the lever  140 , a weight lever lower limit stopper  156  is provided to restrict downward displacement of the rear part of the weight lever  153 . The weight lever lower limit stopper  156  is also made of a shock-absorbing member such as felt in order to prevent shock noise. On the top surface of the rear part of the weight lever  153 , the weight  157  which is part of the movable supporting member is provided. On the undersurface of the rear part of the weight lever  153 , a concave portion  153   a  is provided. The top end of a second spring  158  is inserted into the concave portion  153   a  to be fixed to the upper bottom surface of the concave portion  153   a  to be supported. The lower end of the second spring  158  is in contact with a part of the top surface of the lever  140 , the part being situated behind the rotary shaft  142  of the lever  140 . The second spring  158  is a compression spring. Similarly to the seventh embodiment, in addition, the load sensor  150  is incorporated into the undersurface of the rear part of the weight lever  153 , with the displacement sensor  151  being provided on the frame FR. Such a modification can also achieve the effect similar to that of the seventh embodiment. 
     The example having the weight lever  153  is designed such that the lower end of the first spring  152  is fixed to the frame FR situated below the middle part of the lever  140 , with the top end being in contact with the undersurface of the middle part of the lever  140 . However, the example may be modified such that a spring supporting portion is provided on the top surface of the lever  140  to be situated in front of the rotary shaft of the lever  140  so that the lower end of an extension spring is supported by the spring supporting portion with the top end of the extension spring being fixed to the frame FR situated above the middle part of the lever  140 . Furthermore, the modification is designed such that the top end of the second spring  158  is inserted into the concave portion  153   a  of the weight lever  153  to be fixed to the upper bottom surface of the concave portion  153   a  to be supported. However, the modification may be modified such that a concave portion is provided on the top surface of the lever  140  to be situated behind the rotary shaft  142  of the lever  140  so that the lower end of the second spring  158  is fixed to the bottom surface of the concave portion to be supported, with the top end of the second spring  158  being inserted into the concave portion  153   a  of the weight lever  153  to be in contact with the weight lever  153 . 
     i. Eighth Embodiment 
     Next, an eighth embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 27  is a side view of the pedal apparatus  12  according to the present embodiment. The lever  140 , the lever supporting portion  141 , the lower limit stopper  143  and the upper limit stopper  144  are similar to those of the seventh embodiment. Into a concave portion  140   c  provided on the top surface of the rear part of the lever  140  to be situated behind the rotary shaft  142  of the lever  140 , the lower end of a drive rod  160  is inserted to be in contact with the bottom surface of the concave portion  140   c . The drive rod  160 , which is a long member, extends upward from the rear part of the lever  140 . Above the rear part of the lever  140 , a first movable supporting member  161  is provided so that the top end of the drive rod  160  is inserted into a concave portion  161   a  provided on the undersurface of the first movable supporting member  161  to be in contact with the upper bottom surface of the concave portion  161   a . By a guide member which is not shown, the drive rod  160  is allowed to move only upward and downward. 
     The first movable supporting member  161  is a plate-shaped member which extends from the front toward the rear of the pedal apparatus  12 . The first movable supporting member  161  is supported at the rear part thereof by a supporting portion  162  fixed to the frame FR so that the front end of the first movable supporting member  161  can pivot upward and downward about a rotary shaft  163 . Above the first movable supporting member  161 , a second movable supporting member  163  is provided. Similarly to the first movable supporting member  161 , the second movable supporting member  163  is a plate-shaped member which extends from the front toward the rear of the pedal apparatus  12 . The second movable supporting member  163  is supported at the rear part thereof by the supporting member  162  so that the front end of the second movable supporting member  163  can pivot upward and downward about the rotary shaft  163 . Above the forward part of the first movable supporting member  161 , a second movable supporting member lower limit stopper  164  fixed to the frame FR is provided to restrict downward displacement of the forward part of the second movable supporting member  163 . The second movable supporting member lower limit stopper  164  is also made of shock-absorbing member such as felt in order to lessen shock noise. On the forward part of the second movable supporting member  163 , a weight  165  is provided. Integrally with the second movable supporting member  163 , the weight  165  serves as a movable supporting member. Into a concave portion  161   b  provided on the top surface of the forward part of the first movable supporting member  161 , the lower end of a first spring  166  is inserted to be fixed to the bottom surface of the concave portion  161   b  to be supported. The top end of the first spring  166  is fixed to the frame FR situated above. The first spring  166  is a compression spring. The first spring  166  urges the front end of the lever  140  upward through the drive rod  160 . Into a concave portion  161   c  provided on the top surface of the middle part of the first movable supporting member  161 , the lower end of a second spring  167  is inserted to be fixed to the bottom surface of the concave portion  161   c  to be supported. The top end of the second spring  167  is in contact with the undersurface of the forward part of the second movable supporting member  163 . Similarly to the seventh embodiment, the load sensor  150  is incorporated into the undersurface of the forward part of the second movable supporting member  163 , while the displacement sensor  151  is provided on the frame FR. 
     Next, the operation of the pedal apparatus  12  configured as described above will be described. Although the configuration of the present embodiment is different from that of the seventh embodiment, the present embodiment operates almost similarly to the seventh embodiment. In a state where the lever  140  is not depressed, the first movable supporting member  161  is urged downward by the first spring  166 , so that the rear part of the lever  140  is urged downward through the drive rod  160 . Resultantly, the undersurface of the rear part of the lever  140  is in contact with the upper limit stopper  144 , so that the lever  140  stands still to be in the state shown in  FIG. 27 . In this state, the second spring  167  is in its natural length, resulting in the urging force exerted on the lever  140  of “0”. In this state, furthermore, the second movable supporting member  163  is in contact with the second movable supporting member lower limit stopper  164  by the weight of the second movable supporting member  163  and the weight  165 . In this state, although the second spring  167  may be slightly compressed to urge the second movable supporting member  163 , the urging force of the second spring  167  is designed to be smaller than a combined force formed of the weight of the second movable supporting member  163  and the weight of the weight  165  so that the second movable supporting member  163  is in contact with the second movable supporting member lower limit stopper  164 . 
     If the player depresses the lever  140  in spite of the urging force exerted by the first spring  166 , the lever  140  starts pivoting counterclockwise about the rotary shaft  142  in  FIG. 27 , so that the rear part of the lever  140  is displaced upward. By this displacement, the drive rod  160  causes the forward part of the first movable supporting member  161  to be displaced upward. As a result, the first spring  166  is compressed to increase the urging force exerted on the lever  140  by the first spring  166  (A 1  of  FIG. 24A ). If the urging force exerted by the second spring  167  is smaller than the combined force formed of the weight of the second movable supporting member  163  and the weight of the weight  165 , the second movable supporting member  163  remains to be in contact with the second movable supporting member lower limit stopper  164 . As a result, the second spring  167  also starts compressing to increase the urging force exerted by the second spring  167  (A 1  of  FIG. 24B ). In this operational range, therefore, the reaction force of the lever  140  and the change in the reaction force are brought about by the first spring  166  and the second spring  167  (A 1  of  FIG. 24C ). 
     Then, if the urging force exerted by the second spring  167  exceeds the weight of the second movable supporting member  163  and the weight  165 , the forward part of the second movable supporting member  163  moves upward. As a result, the second spring  167  will be hardly compressed any further with little increase in the urging force of the second spring  167 . In this operational range, therefore, although the reaction force of the lever  140  is brought about by the first spring  166  and the second spring  167 , the change in the reaction force is brought about only by the first spring  166  (A 2  of  FIG. 24C ). The amount of depression of the lever  140  at the time of the start of upward move of the forward part of the second movable supporting member  163  is referred to as the first amount of depression. 
     Then, the undersurface of the middle part of the lever  140  comes into contact with the lower limit stopper  143  to restrict downward displacement of the forward part of the lever  140 . If the depression of the lever  140  is released, the urging forces exerted by the first spring  166  and the second spring  167  and the weight of the first movable supporting member  161  and the second movable supporting member  163  cause the lever  140  to operate in the order opposite to that in which the lever  140  has operated on the depression of the lever  140 . More specifically, the lever  140  pivots clockwise about the rotary shaft  142  in  FIG. 27 , so that the undersurface of the rear part of the lever  140  comes into contact with the upper limit stopper  144  to recover to the original state ( FIG. 27 ). The load sensor  150  and the displacement sensor  151  operate similarly to the seventh embodiment to control the damper effect and musical tone elements of musical tones to be generated as in the case of the seventh embodiment. 
     As for the pedal apparatus according to the eighth embodiment configured as described above, similarly to the seventh embodiment, the urging forces exerted by the first spring  166  and the second spring  167  change according to the ranges equivalent to the respective operational ranges shown in  FIG. 34 . As a result, the pedal apparatus according to the present embodiment can achieve the characteristics ( FIG. 24C ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the dashed line in  FIG. 34 . 
     In the present embodiment, similarly to the seventh embodiment, in the case where the player sharply decreases the amount of depression of the lever  140 , and in the case where the player periodically changes the amount of depression of the lever  140 , the second movable supporting member  163  can temporarily oscillate due to collaboration of inertial force and spring force acting on the second movable supporting member  163  and the weight  165 . Furthermore, the second movable supporting member  163  can collide with the second movable supporting member lower limit stopper  164  to cause oscillation of the second movable supporting member  163 . In this case, because the force of the springs acting on the lever  140  is divided into the spring force exerted by the first spring  166  and the spring force exerted by the second spring  167 , the spring force exerted by the second spring  167  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  can stabilize the reaction force of the lever  140 . 
     In addition, because the load sensor  150  and the displacement sensor  151  operate similarly to the seventh embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  140  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated, and timbre, resonance (acoustic effect) and the like of musical tones to be generated. Furthermore, the present embodiment realizes the pedal apparatus having a simple structure. 
     Between the first movable supporting member  161  and the second movable supporting member  163 , the capstan CS similar to that of the modification of the seventh embodiment may be provided. Such a modification also achieves the effect similar to the modification of the seventh embodiment. 
     The eighth embodiment is designed such that the lower end of the first spring  166  is inserted into the concave portion  161   b  provided on the first movable supporting member  161  to be fixed to the bottom surface of the concave portion  161  to be supported. However, the eighth embodiment may be modified such that a spring supporting portion is provided on the forward part of the first movable supporting member  161  so that the top end of an extension spring is supported by the spring supporting portion with the lower end of the extension spring being fixed to the frame FR situated below the first movable supporting member  161 . Such a modification can achieve the effect similar to the eighth embodiment. 
     j. Ninth Embodiment 
     Next, a ninth embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 28  is a side view of the pedal apparatus of the electronic musical instrument according to the present embodiment. This embodiment is configured almost similarly to the seventh embodiment shown in  FIG. 22A . Unlike the seventh embodiment, however, in a state where the lever  140  is not depressed, the lower end of the second spring  148  is apart from the lever  140 . 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained.  FIG. 29A  through  FIG. 29D  show various states in which the lever  140  and the weight  146  are displaced, with the first spring  145  and the second spring  148  being compressed.  FIG. 30A  and  FIG. 30B  show the urging force of the first spring  145  and the second spring  148  with respect to the amount of displacement of the lever  140 . FIG.  30 C shows the reaction force generated by the lever  140  according to the displacement of the lever  140 . In a state where the lever  140  is not depressed, the rear part of the lever  140  is urged downward by the first spring  145 . As a result, the undersurface of the rear part of the lever  140  is in contact with the upper limit stopper  144 , so that the lever  140  stands still to be in a state shown in  FIG. 29A . In this state, the weight  146  is in contact with the weight lower limit stopper  147  by the weight of the weight  146 , so that the weight  146  stands still. 
     If the player depresses the lever  140  in spite of the urging force exerted by the first spring  145 , the lever  140  starts pivoting counterclockwise about the rotary shaft  142  in  FIG. 29A , so that the rear part of the lever  140  is displaced upward. This displacement causes compression of the first spring  145  to increase the urging force exerted by the first spring  145  (A 0  of  FIG. 30A ). In this operational range (from  FIG. 29A  to  FIG. 29B ), the lower end of the second spring  148  is not in contact with the lever  140 . In this operational range, therefore, the reaction force of the lever  140  and the change in the reaction force are brought about by the first spring  145  (A 0  of  FIG. 30C ). 
     If the player depresses the lever  140  further to increase the amount of the displacement of the lever  140 , the urging force exerted by the first spring  145  on the lever  140  increases further (A 1  of  FIG. 30A ). The lower end of the second spring  148  comes into contact with the top surface of the lever  140 . If the urging force exerted by the second spring  148  is smaller than the weight of the weight  146 , the weight  146  remains to be in contact with the weight lower limit stopper  147 . As a result, the second spring  148  also starts compressing to increase the urging force exerted by the second spring  148  (A 1  of  FIG. 30B ). In this operational range (from  FIG. 29B  to  FIG. 29C ), therefore, the reaction force of the lever  140  and the change in the reaction force are brought about by the first spring  145  and the second spring  148  (A 1  of  FIG. 30C ). The amount of depression of the lever  140  at the time of the contact of the lower end of the second spring  148  with the top surface of the lever  140  is referred to as the second amount of depression. 
     If the amount of the displacement of the lever  140  increases further, the urging force of the first spring  145  also increases further (A 2  of  FIG. 30A ). Then, if the urging force exerted by the second spring  148  exceeds the weight of the weight  146 , the weight  146  moves upward. As a result, the second spring  148  will be hardly compressed any further without any increase in the urging force of the second spring  148  (A 2  of  FIG. 30B ). 
     In this operational range (from  FIG. 29C  to  FIG. 29D ), therefore, although the reaction force of the lever  140  is brought about by the first spring  145  and the second spring  148 , the change in the reaction force is brought about only by the first spring  145  (A 2  of  FIG. 30C ). The amount of depression of the lever  140  at the time of the start of upward move of the weight  146  is referred to as the first amount of depression. 
     Then, the undersurface of the middle part of the lever  140  comes into contact with the lower limit stopper  143  to restrict downward displacement of the forward part of the lever  140 . If the depression of the lever  140  is released, the urging forces exerted by the first spring  145  and the second spring  148 , and the weight of the weight  146  which serves as a movable supporting member cause the lever  140  to operate in the order opposite to that in which the lever  140  has operated on the depression of the lever  140 . More specifically, the lever  140  pivots clockwise about the rotary shaft  142  in  FIG. 29D , so that the undersurface of the rear part of the lever  140  comes into contact with the upper limit stopper  144  to recover to the original state ( FIG. 29A ). The load sensor  150  and the displacement sensor  151  operate similarly to the seventh embodiment to control the damper effect and musical tone elements of musical tones to be generated as in the case of the seventh embodiment. 
     The pedal apparatus according to the embodiment configured as described above can achieve the characteristics ( FIG. 30C ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the solid line in  FIG. 34 . In the operational range (A 0  of  FIG. 30C ) equivalent to A 0  of  FIG. 34 , more specifically, the urging force exerted by the first spring  145  to urge the lever  140  changes, whereas in the operational range (A 1  of  FIG. 30C ) equivalent to A 1  of  FIG. 34 , the urging force exerted by the second spring  148  also changes in addition to the urging force of the first spring  145 . Compared with the operational range (A 0  of  FIG. 30C ) equivalent to A 0  of  FIG. 34 , therefore, the rate of change in the reaction force can be increased in the operational range (A 1  of  FIG. 30C ) equivalent to A 1  of  FIG. 34 . In the operational range (A 2  of  FIG. 30C ) equivalent to A 2  of  FIG. 34 , the urging force of only the first spring  145  changes. Compared with the operational range (A 1  of  FIG. 30C ) equivalent to the range of A 1  of  FIG. 34 , therefore, the rate of change in the reaction force in the operational range (A 2  of  FIG. 30C ) equivalent to the range of A 2  of  FIG. 34  can be reduced. Therefore, the pedal apparatus  12  of the embodiment can realize the characteristics of the acoustic piano as shown by the solid line in  FIG. 34 . 
     In the present embodiment, similarly to the seventh embodiment, in a case where the player sharply decreases the amount of depression, and in a case where the player periodically changes the amount of depression of the lever  140 , the weight  146  can temporarily oscillate due to collaboration of inertial force and spring force applied to the weight  146 . Furthermore, the weight  146  can collide with the weight lower limit stopper  147  to cause oscillation of the weight  146 . In this case, however, because the force of the springs acting on the lever  140  is divided into the spring force exerted by the first spring  145  and the spring force exerted by the second spring  148 , the spring force exerted by the second spring  148  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  configured as described above can stabilize the reaction force of the lever  140 . 
     In addition, because the load sensor  150  and the displacement sensor  151  operate similarly to the seventh embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  140  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated, and timbre, resonance (acoustic effect) and the like of musical tones to be generated. Furthermore, the present embodiment realizes the pedal apparatus having a simple structure. 
     Between the weight  146  and the lever  140 , the capstan CS similar to that of the modification of the seventh embodiment may be provided. Such a modification can stabilize reaction force of the lever  140  as in the case of the modification of the seventh embodiment. In addition, the modification of the ninth embodiment may be further modified such that the capstan CS comes into contact with the weight  146  before the urging force of the second spring  148  exceeds the weight of the weight  146 . The respective urging forces of the first spring  145  and the second spring  148  with respect to the amount of displacement of the lever  140  in this modification are shown in  FIG. 31A  and  FIG. 31B .  FIG. 31C  shows the reaction force generated by the lever  140  according to the displacement of the lever  140 . For comparison, the respective urging forces of the respective springs and the reaction force of the lever  140  without the capstan CS are shown by dashed lines in  FIG. 31 . From the start of a depression of the lever  140  until the contact of the second spring  148  with the lever  140 , the urging force of only the first spring  145  increases (A 0  of  FIG. 31A ). From the contact of the second spring  148  with the lever  140  until the capstan CS comes into contact with the weight  146 , the urging forces of the first spring  145  and the second spring  148  increase (A 1  of  FIG. 31A  and A 1  of  FIG. 31B ). If the contact of the capstan CS with the weight  146  is followed by the further increase in the amount of the depression of the lever  140 , the urging force of the first spring  145  increases according to the increase in the amount of the depression, without any further increase in the urging force of the second spring  148  (A 2  of  FIG. 31A  to  FIG. 31C ). As for this modification, on the boundary between the range where the rate of change in the reaction force is great and the range where the rate of change is small, the reaction force of the lever  140  changes stepwise. The stepwise change in the reaction force facilitates player&#39;s perception of the boundary. Compared with the pedal apparatus  12  without the capstan CS, furthermore, the pedal apparatus  12  having the capstan CS can narrow the range where the rate of change in the reaction force is great (A 1  of  FIG. 31C ) and widen the range where the rate of change in the reaction force is small (A 2  of  FIG. 31C ). 
     Similarly to the modification of the seventh embodiment, in addition, the position where the first spring  145  is provided may be changed. Furthermore, the ninth embodiment is designed such that in a state where the lever  140  is not depressed, the lower end of the second spring  148  is apart from the lever  140 . However, the ninth embodiment may be modified such that a concave portion is provided on the top surface of the lever  140  so that the lower end of the second spring  148  is inserted into the concave portion to be fixed to the concave portion with the top end of the second spring  148  being apart from the weight  146 . As shown in  FIG. 32 , furthermore, the weight  146  may be replaced with the weight lever  153  and the weight  157  which pivot in response to the lever  140 . The modification shown in  FIG. 32  is obtained by modifying the modification of the seventh embodiment shown in  FIG. 26  such that the lower end of the second spring  158  in a state where the lever  140  is not depressed is apart from the lever  140 . In addition, this modification may be also modified such that a concave portion is provided on the top surface of the lever  140  so that the lower end of the second spring  158  is inserted into the concave portion to be fixed to the concave portion with the top end of the second spring  158  being apart from the weight lever  153 . Such modifications can also achieve the effect similar to that of the ninth embodiment. 
     k. Tenth Embodiment 
     Next, a tenth embodiment of the pedal apparatus  12  according to the present invention will be described in detail.  FIG. 33  is a side view of the pedal apparatus  12  of the present embodiment. This embodiment is configured almost similarly to the eighth embodiment shown in  FIG. 27 . Unlike the eighth embodiment, however, in a state where the lever  140  is not depressed, the lower end of the second spring  167  is apart from the first movable supporting member  161 . 
     Next, the operation of the pedal apparatus  12  configured as described above will be explained. In a state where the lever  140  is not depressed, the first movable supporting member  161  is urged downward by the first spring  166  to urge the rear part of the lever  140  downward through the drive rod  160 . As a result, the undersurface of the rear part of the lever  140  is in contact with the upper limit stopper  144 , so that the lever  140  stands still to be in a state shown in  FIG. 33 . In this state, the second movable supporting member  163  pivots counterclockwise about the rotary shaft  163  in  FIG. 33  by the weight of the weight  165  and the second movable supporting member  163 , so that the undersurface of the forward part of the second movable supporting member  163  comes into contact with the second movable supporting member lower limit stopper  164  to stand still. 
     If the player depresses the lever  140  in spite of the urging force exerted by the first spring  166 , the lever  140  starts pivoting counterclockwise about the rotary shaft  142  in  FIG. 33 , so that the rear part of the lever  140  is displaced upward. By this displacement, the drive rod  160  causes the forward part of the first movable supporting member  161  to be displaced upward. As a result, the first spring  166  is compressed to increase the urging force exerted on the lever  140  by the first spring  166  (A 0  of  FIG. 30A ). In this operational range, the lower end of the second spring  167  is not in contact with the first movable supporting member  161 . In this operational range, therefore, the reaction force of the lever  140  and the change in the reaction force are brought about by the first spring  166  (A 0  of  FIG. 30C ). 
     If the player depresses the lever  140  further to increase the amount of the displacement of the lever  140 , the urging force exerted by the first spring  166  on the lever  140  increases further (A 1  of  FIG. 30A ). The lower end of the second spring  167  comes into contact with the top surface of the first movable supporting member  161 . If the urging force exerted by the second spring  167  is smaller than the weight of the second movable supporting member  163  and the weight  165 , the second movable supporting member  163  remains to be in contact with the second movable supporting member lower limit stopper  164 . As a result, the second spring  167  also starts compressing to increase the urging force exerted by the second spring  167  (A 1  of  FIG. 30B ). In this operational range, therefore, the reaction force of the lever  140  and the change in the reaction force are brought about by the first spring  166  and the second spring  167  (A 1  of  FIG. 30C ). The amount of depression of the lever  140  at the time of the contact of the lower end of the second spring  167  with the top surface of the first movable supporting member  161  is referred to as the second amount of depression. 
     Then, if the urging force of the second spring  167  exceeds the combined force formed of the respective weights of the second movable supporting member  163  and the weight  165 , the forward part of the second movable supporting member  163  is displaced upward. As a result, the second spring  167  will not be compressed any further, with no increase in the urging force of the second spring  167 . Therefore, although the reaction force of the lever  140  is brought about by the first spring  166  and the second spring  167 , the change in the reaction force is brought about only by the first spring  166  (A 2  of  FIG. 30C ). The amount of depression of the lever  140  at the time of the start of upward displacement of the forward part of the second movable supporting member  163  is referred to as the first amount of depression. 
     Then, the undersurface of the middle part of the lever  140  comes into contact with the lower limit stopper  143  to restrict downward displacement of the forward part of the lever  140 . If the depression of the lever  140  is released, the urging forces exerted by the first spring  166  and the second spring  167 , and the weight of the first movable supporting member  161  cause the lever  140  to operate in the order opposite to that in which the lever  140  has operated on the depression of the lever  140 . More specifically, the lever  140  pivots clockwise about the rotary shaft  142  in  FIG. 33 , so that the undersurface of the rear part of the lever  140  comes into contact with the upper limit stopper  144  to recover to the original state ( FIG. 33 ). The load sensor  150  and the displacement sensor  151  operate similarly to the seventh embodiment to control the damper effect and musical tone elements of musical tones to be generated as in the case of the seventh embodiment. 
     As for the pedal apparatus according to the tenth embodiment configured as described above, similarly to the ninth embodiment, the urging forces exerted by the first spring  166  and the second spring  167  change according to the ranges equivalent to the respective operational ranges shown in  FIG. 34 . As a result, the pedal apparatus according to the present embodiment can achieve the characteristics ( FIG. 30C ) similar to those of the relationship between the amount of displacement of the lever from the start to the end of a depression of a pedal of an acoustic piano and the reaction force perceived by the player through the pedal as shown by the solid line in  FIG. 34 . 
     In the present embodiment, similarly to the seventh embodiment, in the case where the player sharply decreases the amount of depression of the lever  140 , and in the case where the player periodically changes the amount of depression of the lever  140 , the second movable supporting member  163  can temporarily oscillate due to collaboration of inertial force and spring force acting on the second movable supporting member  163  and the weight  165 . Furthermore, the second movable supporting member  163  can collide with the second movable supporting member lower limit stopper  164  to cause oscillation of the second movable supporting member  163 . In this case, because the force of the springs acting on the lever  140  is divided into the spring force exerted by the first spring  166  and the spring force exerted by the second spring  167 , the spring force exerted by the second spring  167  is small. As a result, the unnatural reaction force of the lever caused by the oscillation can be reduced. Therefore, the pedal apparatus  12  can stabilize the reaction force of the lever  140 . 
     In addition, because the load sensor  150  and the displacement sensor  151  operate similarly to the seventh embodiment, the pedal apparatus  12  of the present embodiment can synchronize the feeling perceived by the player on the manipulation of the lever  140  with the start and the end of musical tone elements including damper effect to be added to musical tones to be generated, and timbre, resonance (acoustic effect) and the like of musical tones to be generated. Furthermore, the present embodiment realizes the pedal apparatus having a simple structure. 
     Furthermore, the present embodiment may be modified to have the capstan CS similar to that of the modification of the seventh embodiment between the first movable supporting member  161  and the second movable supporting member  163 . Similarly to the modification of the eighth embodiment, in addition, the present embodiment may be modified to replace the first spring  166  with an extension spring. Furthermore, the tenth embodiment is designed such that in a state where the lever  140  is not depressed, the lower end of the second spring  167  is apart from the first movable supporting member  161 . However, the embodiment may be modified such that the lower end of the second spring  167  is inserted into the concave portion  161   c  to be fixed to the concave portion with the upper end of the second spring  167  being apart from the second movable supporting member  163 . Such modifications can achieve the effect similar to the modifications of the seventh embodiment. 
     In the first to tenth embodiments, the pedal apparatus  12  is applied to the damper pedal of the electronic musical instrument. However, the pedal apparatus  12  can be applied to the other pedals such as a sostenuto pedal and soft pedal of an electronic musical instrument.