Abstract:
A speaker system features a plurality of transducers arranged to produce a sound field similar to that of an acoustic point source. The arrangement of transducers optimizes the sound field by reducing the sound energy directed towards the primary reflective surfaces within the room in which they are placed. In a preferred embodiment, four medium-size transducers (woofers) operate together to reproduce the low-range to mid-range frequencies with the woofers positioned so that no two woofers share a common vertical axis or a common horizontal axis, and so that the horizontal and vertical axes of the woofers are evenly spaced. Preferably a center of a fifth transducer, a high frequency tweeter, is placed at the center of a pattern formed by the center of the woofers. The fifth transducer is set at a depth within the enclosure that is at the same acoustic center as the acoustic center of the woofers.

Description:
RELATED APPLICATION 
     This application claims the benefit priority under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 60/161,154, filed Oct. 22, 1999, the entirety of which is hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to speaker systems. More specifically, this invention relates to speaker systems used by audio enthusiasts interested in recreating a sound field with a high degree of quality. 
     2. Description of the Related Art 
     Throughout the years, consumers have purchased acoustic playback systems for their entertainment, and these systems vary greatly in size, cost, appearance, and fidelity. A select group of consumers (audio enthusiasts) takes particular pride and enjoyment in their high fidelity acoustic playback systems, including their speaker systems. A true test characteristic and goal of a high fidelity acoustic playback system is the ability to reproduce a sound field with a high degree of accuracy. 
     The theoretical goal of an acoustic playback system is to reproduce the sound field as when it was originally made. To properly design a playback system, it must first be understood how sound fields are recorded and the environment in which the playback will typically occur. 
     When sounds are created, the sound waves (energy) are radiated in all directions. This total energy can be considered a sound field. A person listening to the original acoustical event is of small size in relation to the size of the total sound field, and could be considered as a point in the sound field. Likewise, when sounds are recorded, they are captured with a microphone, which is also of small size in relation to the sound field and would also be considered as a point in the sound field. 
     When reproducing such sounds, the optimum playback mechanism is through an acoustical point source. A point source is a theoretical, infinitely small sound source capable of reproducing all frequencies from the same physical location. One example of a point source is a single transducer. Unfortunately, no single transducer can reproduce sounds uniformly at typical listening levels over the entire audio frequency spectrum with minimal distortion. For example, it is well known in the art that a large low frequency transducer, such as a woofer, has difficulty generating high frequency sounds. Similarly, it is well known that a small high frequency transducer, such as a tweeter, has difficulty generating low frequency sounds. 
     To overcome some of the limitations of single transducer systems, one might use multiple transducers of different sizes to reproduce the full range of the audible frequency spectrum. In one approach, a speaker system includes a small high frequency transducer near the top of the mounting board and one or more larger transducers near the bottom. Such systems are commonly called “two-way” or “three-way” speaker systems. With this approach, however, the speaker system no longer emulates a point source, and a human ear can be sensitive to the direction of sound. A listener with a discerning ear can notice the different physical locations of these transducers. This arrangement also yields different path lengths from each transducer to the listener. Thus, the respective sounds do not arrive all at the same time. The result does not sound like the original source. 
     In addition, enthusiasts&#39; acoustic playback systems are typically used indoors, and when these systems reproduce sound, the generated sound waves travel in all directions. Ideally, the listener should hear only the sound waves traveling towards him. In actuality, the listener hears these sound waves and those reflected waves which bounce off the room&#39;s surfaces, primarily the walls, floor, and ceiling. Since these reflected sound waves have traveled a longer distance to the listener than the direct waves, they are delayed in relation to the direct sound. The waveform heard by the listener is therefore distorted by the combination of the direct and reflected sound. Thus, the listener is not hearing the sound field as it was originally generated or recorded. The ideal playback system would direct its sound only to the listener and not to the entire room. An example would be the use of earphones. 
     The efficient reproduction of low frequency sound generally requires physically large transducers to displace the necessary air volume. Large transducers can accurately reproduce low frequencies with minimal distortion, but with midrange or high frequencies, they usually exhibit large resonant peaks and associated distortions. Smaller transducers exhibit fewer resonant peaks in the midrange, but at the expense of limited low frequency reproduction capability. One approach that is used to accurately reproduce both low and midrange frequencies is to substitute a plurality or array of medium size transducers for the larger transducer. However, using conventional arrays that feature a plurality of transducers over a common frequency range will produce acoustical interference patterns and an increased prevalence of side lobes. These conventional arrays direct a portion of their sound towards the listener (main lobe) and a portion of their sound towards the sides (side lobes). When placed in a room, the sound waves in the side lobes reflect from surfaces such as walls, the ceiling, and the floor (room reflections). The reflected sound waves interact either constructively or destructively, depending on the delay time and frequency, with the direct sound waves. The listener is presented with a sound field that is a combination of the direct sound from the main lobe and the reflected and delayed sound from the side lobes. Although the speaker system may have exhibited a flat frequency response in an anechoic chamber, the frequency response in the room at the listener is anything but flat, with pronounced variations in the response. The result is the listener hears a severely distorted sound field that bears little resemblance to the original event. 
     In the quest for realism, audio enthusiasts have taken inconvenient measures to reduce the distortion due to reflections. To maintain the integrity of the reproduced sound field with a traditional speaker system, an audio enthusiast carefully positions a speaker system within a room. The strategic positioning of the speaker system enables the audio enthusiast to hear more of the direct sound and less of the reflected sounds. Some audio enthusiasts also take the expensive step of placing acoustical absorptive materials on the walls to further reduce the energy of the reflected sound waves. 
     SUMMARY OF THE INVENTION 
     Few conventional speaker systems approach an ideal of a high efficiency point source directional loudspeaker system. In fact, most conventional speaker systems are low in efficiency, lack phase coherency, and do not act as an apparent point source system. A speaker system in accordance with the present invention closely emulates a single point source. Embodiments of the present invention achieve this result by an advantageous arrangement of transducers. The arrangement of transducers minimizes the amplitude of the sound waves that can cause room reflections and the resultant distortion therein. 
     A plurality of transducers are attached to the front side of an enclosure such that the centers of the transducers are equally spaced along both horizontal and vertical axes and yet staggered so that the centers of the transducers form at least two parallel lines. Preferably, the transducers in the plurality of transducers are all identical medium size low frequency transducers (woofers). Preferably, the speaker system also includes a high frequency transducer (tweeter) mounted in the center of the plurality of transducers and further includes a grille to cover the front of the speaker system. 
     A speaker system includes four transducers mounted in a square pattern on the front of an enclosure. The square pattern formed by the transducers is rotated at an angle within the range of 18.4 to 31.0 degrees and is preferably rotated at an angle of 26.57 degrees. Preferably, the four transducers are identical medium size woofers that are also wired in series-parallel configuration. Preferably, the speaker system also includes a tweeter and a crossover network. The tweeter may be set back in the enclosure relative to the other transducers to synchronize sound waves emitted by the tweeter with sound waves emitted by the four transducers in an overlapping range of frequencies. A horn may also be used with the tweeter to set back the tweeter in the enclosure and to match the sound level of the tweeter to that of the four transducers. In one embodiment, the enclosure is a sealed box. 
     Another speaker system includes four transducers mounted in a square pattern on the front of the enclosure. The enclosure is rotatable to allow the square pattern formed by the four transducers to achieve an angle including 26.57 degrees. The enclosure includes a mounting device to hold the speaker system at a particular angle. In some embodiments, the speaker system can freely rotate to any angle. The speaker system may include a speaker stand serving as the mounting device. Preferably, the speaker system indicates when the square pattern has formed an angle of approximately 26.57 degrees. 
     Another speaker system includes an arrangement of enclosures. The enclosures can have one or more transducers per enclosure, and the enclosures attach so that the centers of the transducers form a square pattern rotated at an angle within the range of 18.4 to 31.0 degrees with respect to a horizontal axis. Such a speaker system includes four separate enclosures with one speaker each. The enclosures can be attached to each other by glue or other means and can be attached to a frame as well. Preferably, a decorative grille covers the transducers. 
     A method of using an angled speaker stand to rotate a speaker enclosure as viewed from the perspective of the listener. Using this method, a typical speaker array may attain benefits disclosed herewith. Such a stand may also include a leg for elevating the speaker array and an additional member for retaining the speaker array on the top of the speaker stand. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features of the invention will now be described with reference to the drawings summarized below. These drawings and the associated description are provided to illustrate a preferred embodiment of the invention, and not to limit the scope of the invention. 
     FIG. 1 illustrates a front view of a typical speaker array. 
     FIG. 2 illustrates a front view of another typical speaker array. 
     FIG. 3 illustrates a front view of an embodiment of the invention. 
     FIG. 4 illustrates a front view of an embodiment conforming to a mirror of the embodiment shown in FIG.  3 . 
     FIG. 5 illustrates a front view of another embodiment of the invention. 
     FIG. 6 illustrates a front view of another embodiment of the invention. 
     FIG. 7 illustrates a front view of an embodiment conforming to a mirror of the embodiment shown in FIG.  6 . 
     FIG. 8 illustrates a front view of another embodiment of the invention. 
     FIG. 9 illustrates a front view of another embodiment of the invention. 
     FIG. 10 illustrates a front view of another embodiment of the invention. 
     FIG. 11 illustrates a front view of another embodiment of the invention. 
     FIG. 12 illustrates a front view of another embodiment of the invention. 
     FIG. 13 illustrates a front view of another embodiment of the invention. 
     FIG. 14 illustrates a front view of another embodiment of the invention. 
     FIG. 15 illustrates a front view of another embodiment of the invention. 
     FIG. 16 illustrates a side view of an aspect of an embodiment of the invention. 
     FIG. 17 illustrates an example of series-parallel wiring. 
     FIG. 18 illustrates another example of series-parallel wiring. 
     FIG. 19 illustrates an example of a crossover network. 
     FIG. 20 illustrates an on-axis and off-axis frequency response “waterfall” plot for the typical speaker array  100  with a conventional square pattern shown in FIG.  1 . 
     FIG. 21 illustrates an on-axis and off-axis frequency response “waterfall” plot for the typical speaker array  200  with a conventional plus (+) pattern shown in FIG.  2 . 
     FIG. 22 illustrates an on-axis and off-axis frequency response “waterfall” plot for the embodiment  300  shown in FIG.  3 . 
     FIG. 23 illustrates an on-axis and off-axis frequency response “waterfall” plot for the embodiment  600  shown in FIG.  6 . 
     FIG. 24 illustrates a magnitude plot of the typical speaker array  100  shown in FIG.  1 . 
     FIG. 25 illustrates a magnitude plot of the typical speaker array  200  shown in FIG.  2 . 
     FIG. 26 illustrates a magnitude plot of the embodiment  300  shown in FIG.  3 . 
     FIG. 27 illustrates a magnitude plot of the embodiment  600  shown in FIG.  6 . 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Although this invention will be described in terms of certain preferred embodiments, other embodiments that are apparent to those of ordinary skill in the art, including embodiments which do not provide all of the benefits and features set forth herein, are also within the scope of this invention. Accordingly, the scope of the present invention is defined only by reference to the appended claims. 
     FIG. 1 illustrates a front view of a typical speaker array  100  in a conventional square pattern. The typical speaker array  100  has four transducers mounted in an enclosure  110 . Rectangular (x,y) coordinates are used herein to describe the relative placement of the centers of the components. Using a point centrally located in between the four transducers as an origin (0,0), a first transducer  120  is located at relative position (1,1). A second transducer  130  is located at relative position (−1,1). A third transducer  140  is located at relative position (−1,−1). A fourth transducer  150  is located at relative position (1,−1). 
     FIG. 2 illustrates a front view of a typical speaker array  200  in a plus (+) pattern. The typical speaker array  200  also has four transducers mounted in an enclosure  210 . Again using a point centrally located in between the four transducers as an origin, a first transducer  220  is located at relative position (1,0). A second transducer  230  is located at relative position (0,1). A third transducer  240  is located at relative position (−1,0). A fourth transducer  250  is located at relative position (0,−1). The arrangement of the transducers in the typical speaker array  200  is the same as the arrangement of the transducers in the typical speaker array  100 , except that a square pattern defined by the centers of the four transducers has been rotated 45 degrees. 
     FIG. 3 illustrates a front view of an embodiment  300  of the invention. The illustrated embodiment  300  includes four mid-size low frequency to mid frequency transducers, known in the art as woofers, in an enclosure  310 . The pattern of the centers of the four woofers forms a square, but the square in FIG. 3 is tilted relative to the horizontal axis at approximately 26.57 degrees. When viewed directly from the front, no two centers of the four woofers align either horizontally or vertically. The four woofers are also equally spaced along the horizontal and vertical axes. Again using a point centrally located in between the four woofers as an origin, a first woofer  320  is located at relative position (1,3). A second woofer  330  is located at relative position (−3,1). A third woofer  340  is located at relative position (−1,−3). A fourth woofer  350  is located at relative position (3,−1). The center of the four woofers  320 ,  330 ,  340 , and  350  are at angles of approximately 18.43 degrees clockwise, as indicated by “α,” from the nearest horizontal axis or vertical axis. Preferably, the embodiment  300  further includes a fifth transducer  360  located at the origin (0,0). The fifth transducer  360  is a high frequency transducer, which is also known in the art as a tweeter. The specification will provide additional details regarding the embodiment  300  following a discussion of the operation of the embodiment. 
     The geometric relationship between the woofers as shown in the embodiment  300  of FIG. 3 results in a sound field which maximizes the energy lobes directed toward the listener and minimizes the severity of the energy lobes directed towards reflecting surfaces and room boundaries. The embodiment reduces the severity of the magnitude of the side lobes through an advantageous arrangement of transducers, which minimizes the alignment of transducers along horizontal or vertical axes. Alignment of transducers along an axis results in severe standing wave interference of the sound waves from the transducers in alignment. As previously mentioned, a feature of the embodiment of  300  is that no two centers of the woofers align either horizontally or vertically. The four woofers have four distinct intercepts on both the horizontal and vertical axes. This contrasts to the typical speaker array  100  as shown in FIG. 1 where the four transducers align on two intercepts on both the horizontal and vertical axes. The typical speaker array  200 , with the plus (+) configuration shown in FIG. 2, improves upon the typical speaker array  100 . However, the first transducer  220  and the third transducer  240  are aligned horizontally, and the second transducer  230  and the fourth transducer  250  are aligned vertically. 
     Test Results 
     The “waterfall” plots of FIGS. 20 through 23 and the magnitude plots of FIGS. 24 through 27 graphically demonstrate the effect of the geometric relationship. The angles indicated on the waterfall plots and the magnitude plots correspond to the angle between a listener and a vector normal to the planar surface of the speaker system which houses the four woofers. 
     The test data presented reflect the results of standardized test conditions. Each speaker system under test used the same set of four transducers, being Peerless Fabrikkerne A/S model 850397 6.5 inch woofers, arranged in the same size square pattern, i.e., each speaker system used the same fixed distance of 9 inches between the centers of the woofers. Similarly, the output power to the speaker systems and the distance between each speaker system and the test equipment were also standardized during testing. The only variable among the speaker systems under test was the angular skew of each group of woofers (i.e., the square formed by the centers of the woofers remained the same dimension, but the angular orientation of the woofers varied among the configurations as shown in FIGS. 1 through 3, and  6 ). 
     A waterfall plot illustrates the sound dispersion characteristics of a speaker system by cascading the multiple frequency response curves of a speaker system taken at multiple angles. The waterfall plots of FIGS. 20 through 23 represent 10 frequency response measurements taken in 10-degree increments from 0 degrees (on-axis) to 90 degrees off-axis. The measurement curves cascade diagonally on top of one another, starting with the 0-degree on-axis curve (the rearmost curve) and ending with the 90-degree off-axis curve (the curve at the front). 
     FIG. 20 is an on-axis and off-axis frequency response waterfall plot  2000  for the typical speaker array  100  with a conventional square pattern shown in FIG.  1 . The measurement curve  2002  represents the 0-degree (on-axis) response of the typical speaker array  100 . The measurement curve  2004  represents the 10-degree off-axis response of the typical speaker array  100 . Similarly, the measurement curves  2006 ,  2008 ,  2010 ,  2012 ,  2014 ,  2016 ,  2018 , and  2020  respectively represent the off-axis response of the typical speaker array  100  taken at angles of 20, 30, 40, 50, 60, 70, 80, and 90 degrees. 
     FIG. 21 is a similar on-axis and off-axis frequency response waterfall plot  2100  for the typical speaker array  200  with a conventional plus pattern shown in FIG.  2 . FIG. 22 is a similar off-axis frequency response waterfall plot  2200  for the embodiment  300  shown in FIG.  3 . The waterfall plots illustrated in FIGS. 20,  21 , and  22  indicate that in the lower frequency range of 200 to 700 Hz, the performance of the systems is similar. At lower frequencies such as these, the wavelength of sound is quite large in relation to the relative spacing of the transducers such that interference does not occur to an appreciable degree. The wavelength of sound depends upon the frequency of sound and the speed of sound. The speed of sound in turn varies with factors such as barometric pressure (which varies with altitude), temperature, and humidity. Under typical room conditions, the speed of sound is approximately 1,130 feet/sec (344.4 meters/sec). Given this typical speed of sound, the wavelength of sound in a typical room at 200 Hz is 5.65 feet. At frequencies where the wavelengths are long relative to the dimensions of the speaker system, the advantages of the arrangement shown by the embodiment are not very apparent. However, if a larger speaker system were to be constructed, such as one for an auditorium or stadium, then the advantages would be apparent at lower frequencies such as 200 Hz as well. 
     However, above 700 Hz, the similarities among the systems ends and the differences now become quite apparent. FIG. 20 shows that the typical speaker array  100  produces significant sound energy off-axis from 800 to 4000 Hz. A side lobe occurs at 1350 Hz and reaches its maximum of 91 dB at 60 degrees off-axis. The side lobe at 1350 Hz is only 2 dB down from the on-axis level of 93 dB. At 30 degrees off-axis, the sound level is only 78 dB, while at 90 degrees off-axis, the sound level is 85 dB at 1350 Hz. 
     FIG. 21 shows that the typical speaker array  200  also produces substantial sound energy off-axis in the range of 800 to 4000 Hz. In comparison to measured results of the typical speaker array  100  as shown by FIG. 20, the sound level is reduced over this range. However, the typical array speaker array  200  also produces a prominent side lobe, this time at 1900 Hz. The side lobe reaches a maximum of 85 dB, again at 60 degrees off-axis, and is only 6 dB down from the 91 dB on-axis level. At 30 degrees off-axis, the sound level is a low 61 dB. At 90 degrees off-axis, the level is 78 dB. 
     FIG. 22 illustrates the significant reduction in off-axis sound energy produced by the embodiment  300  over the range of 800 to 4000 Hz. The largest side lobe is located at 1460 Hz and reaches a maximum of only 80 dB at 50 degrees off-axis, being over 13 dB down from the 93.5 dB on-axis level. At 30 degrees off-axis, the sound level is 75 dB, and is 66 dB at 90 degrees off-axis. With less energy directed towards the room walls, floor, and ceiling, the intensity of the room reflections decreases. This decreases the level of sounds that echoes within the room. A decreased level of room reflections can also result in a flatter frequency response in a room as the attenuated reflected waves interfere less with the sound waves in the main lobe. 
     Other Features of an Embodiment 
     Preferably, the four woofers in the embodiment  300  shown in FIG. 3 are electrically connected in a series-parallel configuration. FIGS. 17 and 18 illustrate two series-parallel configurations well known to those of ordinary skill in the art. An advantage of connecting four woofers in series-parallel configuration is that the impedance of the series-parallel connected woofers remains similar to the impedance of a single woofer (e.g., four eight-ohm speakers connected in series-parallel configuration have an overall impedance of eight ohms). Using four woofers in series-parallel configuration instead of a single woofer has the further advantage that each woofer in the series-parallel configuration operates at one quarter of the power than it would have as a single woofer. This reduces distortion when compared against a single woofer at an equal total output level. It also permits the use of smaller (i.e., lower power) woofers. 
     Preferably, the embodiment  300  includes a tweeter  360  located at the same acoustic center as the center of the four woofers. Central placement can allow a phase coherent system with minimal excess phase shift or group delay. Central placement of the tweeter also allows the speaker system to more closely approximate the sound field of a point source. To adjust and minimize path length differences between the tweeter  360  and the four woofers  320 ,  330 ,  340 , and  350 , the tweeter  360  may be set back in the enclosure as shown in FIG. 16, which is a side view of the embodiment  300 . A tweeter with a horn may advantageously optimize phase imbalance by providing another degree of freedom to adjust and minimize the path length differences between the tweeter  360  and the four woofers. A further benefit of a horn tweeter is that the horn can raise the sensitivity of an otherwise low sensitivity tweeter to match the sensitivity of the four woofers. 
     Preferably, the embodiment  300  further includes a crossover network. FIG. 19 illustrates an exemplary crossover network  1900 . The exemplary crossover network  1900  shown comprises a capacitor  1910  and an inductor  1920 . The capacitor  1910  provides a high pass filter to the tweeter  1930 . The inductor provides a low pass filter the series-parallel configuration  1940  of the woofers. It will be understood by one of ordinary skill in the art that the crossover network can comprise higher order filters such as 2 nd  order and 3 rd  order Butterworth, Chebyshev, and Bessel filters. Active crossover networks are also well known to those of ordinary skill in the art and may be advantageously used with an embodiment of the present invention. Note that as described herein, the four woofers operate over a first range of frequencies, from low frequencies to mid-range frequencies. The tweeter operates over a second range of frequencies, from mid-range frequencies to high frequencies. Thus, the range of frequencies generated by the tweeter is higher than the range of frequencies generated by the woofers. However, it should be understood that in the mid-range of frequencies, the frequencies generated by the tweeter and the frequencies generated by the woofers overlap such that both the tweeter and the woofers may generate the same signals at certain frequencies. As used herein and in the claims, a statement that the range of frequencies generated by the tweeter is higher than the range of frequencies generated by the woofers is intended to mean that the tweeter frequency range extends to higher frequencies than the woofer frequency range and that the woofer frequency range extends to lower frequencies than the tweeter frequency range. Such a statement is not intended to preclude overlapping of the frequency ranges, as provided by the crossover network. 
     As shown in FIG. 3, the transducers of the embodiment  300  mount into an enclosure  310 . The enclosure  310  or cabinet preferably comprises a substantially rigid and acoustically inert material, such as medium density fiberboard. Many styles of enclosure may be advantageously used by the embodiment  300  including a sealed box, a vented box, and an open baffle. The enclosure  310  has a front, which is also known as a front baffle. The front baffle is typically large because it houses four woofers around a centrally located tweeter. A large baffle area exhibits a favorable characteristic of a low cutoff frequency where the system transitions from 2π (half space) to 4π (full space) radiation. This favorable characteristic yields greater overall efficiency since less compensation is required to maintain a flat frequency response at low frequency. Preferably, the enclosure  300  further includes damping material. 
     Preferably, in a two-speaker stereo system, the user has one speaker system to the user&#39;s left and one speaker system to the user&#39;s right, and each speaker system is a mirror image of the other. A mirror image embodiment  400 , shown in FIG. 4 performs equally well as of the embodiment  300 . The mirror image embodiment  400  also includes four woofers in an enclosure  410 . The pattern generated by the centers of the four woofers of the mirror image embodiment  400  still forms a tilted square, but the square tilts in the opposite direction to the square pattern of the embodiment  300 . As with the embodiment  300 , when viewed directly from the front, no two centers of the four woofers are aligned either horizontally or vertically. The four woofers are also equally spaced along the horizontal and vertical axes. Using a point centrally located in between the four woofers as an origin, a first woofer  420  is located at relative position (−1,3). A second woofer  430  is located at relative position (−3,−1). A third woofer  440  is located at relative position (1,−3). A fourth woofer  450  is located at relative position (3,1). The center of the fourth woofer  450  is at an angle approximately 18.43 degrees counter-clockwise from a horizontal axis, as indicated by “α.” Preferably, the mirror image embodiment  400  further includes a fifth transducer  460  located at the origin (0,0). The fifth transducer  460  is again preferably a tweeter. 
     Other Embodiments 
     FIG. 5 illustrates a front view of another embodiment  500  of the invention. The embodiment  500  shown includes four woofers in an enclosure  510 . The pattern generated by the centers of the four woofers forms a rectangle tilted relative to the horizontal axis at approximately 45 degrees. When viewed directly from the front, no two centers of the four woofers align either horizontally or vertically. The four woofers are also equally spaced along the horizontal and vertical axes. Again using a point centrally located in between the four woofers as an origin, a first woofer  520  is located at relative position (−1,3). A second woofer  530  is located at relative position (−3,1). A third woofer  540  is located at relative position (1,−3). A fourth woofer  550  is located at relative position (3,−1). Preferably, the embodiment  500  further includes a tweeter  560  located at the origin (0,0). 
     Preferably, the embodiments of the present invention use an arrangement of transducers in a square pattern where the transducers are at angles of 18.43 degrees with respect to the nearest axis, as shown by the embodiments in FIGS. 3 and 4. Minor deviations from the 18.43-degree arrangement, as demonstrated by 22.5-degree arrangements in FIGS. 6 and 7, retain most of the benefits of the 18.43-degree arrangement. Minor deviations are considered within the scope of the present invention. 
     FIG. 6 illustrates an embodiment  600  with a 22.5-degree arrangement. The embodiment  600  includes an enclosure  610  and four woofers. The four woofers include a first woofer  620 , a second woofer  630 , a third woofer  640 , and a fourth woofer  650 . The pattern generated by the centers of the four woofers is a square. Using a point centrally located in between the four woofers as an origin, the center of each woofer is located at an angle of 22.5 degrees clockwise, as indicated by “β,” from the nearest horizontal axis or vertical axis. 
     FIG. 23 is the on-axis and off-axis “waterfall” plot for the four-woofer arrangement of the embodiment  600  shown in FIG.  6 . FIG. 6 demonstrates that in the 800 to 4000 Hz range, embodiment  600  also produces less off-axis sound energy than either the typical arrays  100  or  200 , but more off-axis sound energy than the embodiment  300 . FIG. 23 indicates the presence of a side lobe located at 1410 Hz with a maximum of 84 dB at 60 degrees off-axis. The side lobe is 9 dB down from the 93 dB on-axis level. The sound level is 76 dB at 30 degrees off axis and is 77 dB at 90 degrees off-axis. 
     FIG. 7 illustrates an embodiment  700  with a 22.5-degree arrangement which is a mirror image of the embodiment  600 . The operation of the embodiment  700  is the same as the operation of the embodiment  600 . The embodiment  700  includes an enclosure  710  and four woofers. The four woofers include a first woofer  720 , a second woofer  730 , a third woofer  740 , and a fourth woofer  750 . The pattern generated by the centers of the four woofers is a square. Using a point centrally located in between the four woofers as an origin, the center of the woofers are located at angles of 22.5 degrees counter-clockwise , as indicated by “β,” from the nearest horizontal axis or vertical axis. 
     FIG. 8 illustrates another embodiment  800  of the invention. The embodiment  800  includes an enclosure  810  and five transducers. The five transducers comprise a first transducer  820 , a second transducer  830 , a third transducer  840 , a fourth transducer  850 , and a fifth transducer  860 . The centers the first transducer  820 , the second transducer  830 , the fourth transducer  850 , and the fifth transducer  860  form a square. The third transducer  840  is located in the center of the pattern formed by the other transducers. Using the center of the third transducer  840  as an origin (0,0), the first transducer is located at (−2,1), the second transducer is located at (−1,−2), the third transducer  840  is located at (0,0), the fourth transducer  850  is located at (1,2) and the fifth transducer  860  is located at (2,−1). When viewed directly from the front, no two centers of the five transducers align either horizontally or vertically. The five transducers are also equally spaced along the horizontal and vertical axes. Preferably, the third transducer  840  is a tweeter and the other transducers are woofers. 
     FIG. 9 illustrates another embodiment  900  of the invention. The embodiment  900  includes a first enclosure  910  and a second enclosure  920 . The first enclosure  910  supports a first transducer  930  and a second transducer  940 . The second enclosure  920  supports a third transducer  950  and a fourth transducer  960 . In the illustrated embodiment  900 , the first and second enclosures  910  and  920  attach to each other with glue, screws, nails, or other interlocking members and without a frame. However, it will be understood by one of ordinary skill in the art that a frame could also be used. The embodiment  900  of FIG. 9 is adjustable to position the transducers in the tilted square pattern of the present invention as shown in FIG.  9 . 
     FIG. 10 illustrates another embodiment  1000  of the invention. The embodiment  1000  includes a first enclosure  1010 , a second enclosure  1020 , a third enclosure  1030 , and a fourth enclosure  1050 . The first enclosure  1010  supports a first transducer  1050 . The second enclosure  1020  supports a second transducer  1060 . The third enclosure  10 30 supports a third transducer  1070 . The fourth enclosure  1040  supports a fourth transducer  1080 . In the embodiment  1000  shown, the four enclosures attach to each other without a frame. As illustrated, the four enclosures are attached to each other so that the four transducers form the pattern of FIG.  3 . 
     FIG. 11 illustrates another embodiment  1100  of the invention. The embodiment  1100  also uses four enclosures as in the embodiment  1000 , but also incorporates a frame  1190 . The embodiment  1100  includes a first enclosure  1110 , a second enclosure  1120 , a third enclosure  1130 , and a fourth enclosure  1150 . The first enclosure  1110  holds a first transducer  1150 . The second enclosure  1120  holds a second transducer  1160 . The third enclosure  1130  holds a third transducer  1170 . The fourth enclosure  1140  holds a fourth transducer  1180 . The enclosures attach to the frame  1190  to align the transducers in accordance with an arrangement of the invention. It will be understood by one of ordinary skill in the art that particularly when the transducers in an embodiment are small, the speaker system may be advantageously combined with a subwoofer system to provide more low frequency sound. 
     FIG. 12 illustrates another embodiment  1200  of the invention. The embodiment  1200  includes an enclosure  1210  with four transducers  1220  and a bracket  1230 . The bracket  1230  may be attached with screws  1240  or the like to a wall, ceiling, bookshelf, or the like. The bracket  1230  attaches to the enclosure  1210  to hold the enclosure  1210  such that the four transducers  1220  are aligned in accordance with the invention. Preferably, the attaching members further include an adjustable component, shown here as a knob  1250  attached to a threaded rod  1260  which passes through an orifice in the bracket  1230  and to a reinforced area  1270  within the enclosure  1210 . The adjustable component allows rotation of the enclosure  1210  to one of the patterns shown in FIGS. 3 and 4. In other embodiments, the embodiment further includes a tweeter (not shown) centrally located between the other transducers. 
     FIG. 13 illustrates another embodiment  1300  of the invention. The embodiment  1300  includes a speaker stand  1310  and an enclosure  1320 . The enclosure  1320  contains a first transducer  1340 , a second transducer  1350 , a third transducer  1360 , and a fourth transducer  1370 . The enclosure  1320  has a bottom shape which advantageously allows the enclosure to rotate the square pattern formed by the four transducers to a selected angle, including the preferred angle of 18.43 degrees. A convenient shape for the enclosure  1320  includes a cylinder, as shown in FIG.  13 . Preferably, the enclosure  1320  further includes an indicator, such as angle marks or a bubble sight, to indicate alignment of the four transducers in the preferred 18.43-degree pattern. Such an indicator advantageously includes a flat spot  1380  on the enclosure that can be used to rest a bubble level indicator commonly found in many hardware stores. 
     FIG. 14 illustrates a method  1400  of practicing the invention. The method  1400  shown comprises using a ramp  1410  and a typical speaker array  100  to align the transducers in the typical speaker array  100  in accordance with the invention. The ramp  1410  comprises a first surface  1420  and a second surface  1430 . The angle between the first surface  1420  and the second surface  1430  is preferably 26.57 degrees. It will be understood by one of ordinary skill in the art that the ramp  1410  can also be used with the typical speaker array  200  in which case a preferred angle is 18.43 degrees. It will similarly be understood that any number of possible rotation angles of the square pattern of the four transducers is possible, and a corresponding ramp used to align the transducers in accordance with the invention. 
     FIG. 15 illustrates another method  1500  of practicing the invention. The method  1500  comprises using a speaker stand  1510  and a typical speaker array  100  to align the transducers in the speaker array in accordance with the invention. The speaker stand  1510  comprises a first plate  1512 , a second plate  1514 , a third plate  1516 , and at least one leg  1518 . The first plate  1512  includes a first surface  1520 . The second plate  1514  includes a second surface  1522 . The third plate  1516  includes a third surface  1524 . The leg  1518  attaches the first plate  1512  to the second plate  1514  and elevates the typical speaker array  100  from the ground surface. With the first plate  1512  attached to the second plate  1514  through the leg  1518 , the first surface  1520  of the first plate  1512  and the second surface  1522  of the second plate  1514  are preferably angled at 26.57 degrees from each other when used with a speaker system such as the typical speaker array  100 . Similarly, the first surface  1520  of the first plate  1512  and the second surface  1522  of the second plate  1514  are preferably angled at 18.43 degrees when used with a speaker system such as the typical speaker array  200 . The third plate  1516  attaches to the first plate  1512  such that the third surface  1524  is normal to the first surface  1520 . As illustrated, the speaker stand  1510  supports the typical speaker array  100  so that the typical speaker array  100  is oriented according to the preferred pattern of the present invention with respect to the horizontal and vertical axes of the speaker stand  1510 . 
     FIG. 24 illustrates a magnitude plot  2400  of the typical speaker array  100  shown in FIG.  1 . FIG. 24 includes the magnitude response of the typical speaker array  100  versus frequency at 4 angles of rotation (0, 30, 60, and 90 degrees) away from a vector normal to the front surface of the typical speaker array  100 . Measurement curve  2402  represents the on-axis (0-degree) magnitude response. Measurement curves  2404 ,  2406 , and  2408  respectively represent magnitude plots taken at 30, 60, and 90 degrees of rotation. 
     FIG. 25 illustrates a magnitude plot  2500  of the typical speaker array  200  shown in FIG.  2 . FIG. 25 includes the magnitude response of the typical speaker array  200  versus frequency at 4 angles of rotation (0, 30, 60, and 90 degrees) away from a vector normal to the front surface of the typical speaker array  200 . Measurement curve  2502  represents the on-axis (0-degree) magnitude response. Measurement curves  2504 ,  2506 , and  2508  respectively represent magnitude plots taken at 30, 60, and 90 degrees of rotation. 
     FIG. 26 illustrates a magnitude plot  2600  of the embodiment  300  shown in FIG.  3 . FIG. 26 includes the magnitude response of the embodiment  300  versus frequency at 4 angles of rotation (0, 30, 60, and 90 degrees) away from a vector normal to the front surface of the embodiment  300 . Measurement curve  2602  represents the on-axis (0-degree) magnitude response. Measurement curves  2604 ,  2606 , and  2608  respectively represent magnitude plots taken at 30, 60, and 90 degrees of rotation. 
     FIG. 27 illustrates a magnitude plot  2700  of the embodiment  600  shown in FIG.  6 . FIG. 27 includes the magnitude response of the embodiment  600  versus frequency at 4 angles of rotation (0, 30, 60, and 90 degrees) away from a vector normal to the front surface of the embodiment  600 . Measurement curve  2702  represents the on-axis (0-degree) magnitude response. Measurement curves  2704 ,  2706 , and  2708  respectively represent magnitude plots taken at 30, 60, and 90 degrees of rotation. 
     Although described above in connection with particular embodiments of the present invention, it should be understood the descriptions of the embodiments are illustrative of the invention and are not intended to be limiting. Various modifications and applications may occur to those skilled in the art without departing from the true spirit and scope of the invention as defined in the appended claims.