A COMPUTERIZED SYSTEM FOR IMPARTING AN EXPRESSIVE MICROSTRUCTURE TO A MUSICAL SCORE

Abstract: A computerized system into which is fed the nominal values of a musical score, the system acting to process these values with respect to the amplitude contour of individual tones, the relative loudness of different tones in a succession thereof, changes in the duration of the tones and other deviations from the nominal values which together consti­ tute the microstructure of the music notated by the score. The system yields the specified tones of the score as modified by the microstructure, thereby imparting expressiv­ ity to the music that is lacking in the absence of the microstructure.

Description: BACKGROUND OF INVENTION Field of Invention : This invention relates generally to a technique for manipulating the nominal notational values of a musical score with respect to the amplitude contour of individual tones, the relative loudness of different tones, slight changes in tone duration and other deviations from the nominal values which together constitute the expressive microstructure or music. More particularly, the invention deals with a computerized system capable of manual or automatic operation for impressing an expressive microstructure on a musical score inputted therein in terms of nominal notational values, the system being usable for composing music that includes microstructure. The macrostructure of a musical composition is defined in the score by standard notation. If, therefore, one executes this score by being assiduously faithful to its macrostructure, the resultant performance, however expertly executed, will be bereft of vitality and expression. The term "microstructure" as used herein encompasses all subtle deviations from the nominal values of the macrostructure in terms of amplitude shaping, timing, timbre, vibrato and all other factors which impart expressiveness to music. The relationships which constitute the microstructure in music, though not explicit in the score, are vital to its appreciation. Essential also to an understanding of controllable microstructure in a system in accordance with the invention are A essentic forms; that is, the dynamic expressive forms of specific emotions; and B , the inner pulse of composers. These will now be separately considered. As explained in an article by Clynes and Nettheim (pp47-82) included in Music, Mind and Brain: The Neuropsychology of Music , M. Clynes (ed.), Plenum Press, New York (1982), touch expressions of specific emotions such as love, grief and hate, can be transformed into sound expressions of like emotions; i.e., the nature of the transforms was found so that the sound expresses the same emotional quality as the touch expression from which it is transformed. The inner pulse of specific composers such as Beethoven, Mozart and Schubert, are expressed by sentographic forms obtained by having a sensitive musician think the music of a selected composer in his mind and by concurrently expressing the pulse by "conducting the music on a sentograph with finger pressure". The resultant sentograms indicate that major composers, such as those previously identified, impart individual pulse forms to their music which characterize their creativity identity or personal idiom. This inner pulse characteristic of each composer is, to a degree, analogous to individualistic brush strokes which distinguish one painter from another, regardless of the subject matter of their paintings. (See M. Clynes, "Sentics, The Touch of Emotions" - published by Doubleday - 1977.) US-A-4 178 822, on which the preamble of the present claim 1 is based, discloses electronic apparatus for producing music in which the characteristics of the notes are produced by digital circuitry. The apparatus comprises a keyboard, a key switch and volume number generator assembly, a waveshape number generator, an attack-delay envelope number generator, conversion circuits, and an output system. The apparatus basically divides the characteristics of each note into two parts, a volume component and a waveshape-frequency characteristic. The amplitude characteristic, in turn, is divided into a volume component and an attack or decay envelope component. The waveshape number generator generates numbers representing the waveshape-frequency characteristic, the key switch and volume number generator assembly generates numbers representing the volume component of the note amplitude, and the envelope number generator generates numbers representing the envelope component of the note amplitude. As a key on the keyboard is moved, a circuit produces time-spaced volume numbers representing the average volume of the note. The performer can change the volume number by depressing the key to a greater or lesser extent and can generate a time-spaced series of digital volume numbers representing the volume component of the note amplitude. A frequency synthesizer receives a separate key signal from the key switches operated by each of the keys and produces a different series of output pulses for each different note on the keyboard. The volume numbers associated with each key are transmitted to a read control assigner. The read control assigner recognizes the presence of volume number signals on one of the volume number lines from the volume number generators and connects that line to a conversion circuit which is not in use. The attack-delay envelope generator is responsible for generating a time-spaced series of digital envelope numbers representing the attack or decay envelope component of the amplitude of a note at discrete instants in time. Each of the conversion circuits is used to produce a tone signal corresponding to a single note indicated by the depression of a single key on the keyboard. An exemplary conversion circuit includes digital latches and multiplying D-to-A converters. A first D-to-A converter multiplies the value of a DC reference signal by the digital volume numbers present on a data line in order to produce an analog volume signal. The volume signal is transmitted as the analog input to a second converter which multiplies the volume signal by the value of the envelope numbers transmitted over a data line to produce an analog amplitude signal having an amplitude which represents the combined volume and envelope characteristics of the desired tone signal. A third converter multiplies the value of the amplitude signal by the wave numbers transmitted over a data line in order to produce an analog tone signal which corresponds to the volume, envelope, waveshape and fundamental frequency characteristics represented by particular volume, envelope, and waveshape numbers. Tone signals are transmitted to a conventional audio mixer and the mixed tone signals are amplified by a conventional audio amplifier and converted into audible sound by a conventional loudspeaker transducer. In view of the foregoing, the main object of this invention is to provide a computerized system for processing the nominal values of a musical score to impart an expressive microstructure thereto. The present invention provides a computerized system for processing a musical score whose notation provides the nominal value for each tone in regard to its pitch and duration, the system comprising: (a) digital calculating means; (b) data entry means to enter into the digital calculating means data representing the pitch of each of the successive tones in the musical score to be processed; (c) means to enter into the digital calculating means data relating to the desired amplitude contour and duration changes for each tone in the succession thereof, the digital calculating means being programmed to process the data therein to yield in its output with respect to each tone in the succession thereof a series of digital values representing the desired amplitude contour; and (d) output-responsive means responsive to said output to generate and reproduce the tones of the said score; characterized in that: in order to impart an expressive microstructure to the respective tones in the score, the data entry means is arranged to enter into the digital calculating means the nominal pitch and duration of each of the successive tones, and the digital calculating means includes pulse matrix means operative to store relative amplitude sizes and duration changes for the component beats of an elemental musical measure, the elemental measure and the stored relative amplitude sizes and duration changes being herein referred to as the "pulse" and the "pulse matrix" respectively, and operative to modify the amplitude and the timing of the entered nominal durations of the successive tones throughout the score on the basis of the values for the elemental musical measure stored in the pulse matrix. The invention also provides a computerized system for processing a musical score whose notation provides the nominal value for each tone in regard to its pitch and duration, the system comprising: (a) digital calculating means; (b) data entry means to enter into the digital calculating means data representing the pitch of each of the successive tones in the musical score to be processed; (c) means to enter into the digital calculating means data relating to the desired amplitude contour and duration changes for each tone in the succession thereof, the digital calculating means being programmed to process the data therein to yield in its output with respect to each tone in the succession thereof a series of digital values representing the desired amplitude contour; and (d) output-responsive means responsive to said output to generate and reproduce the tones of the said score; characterized in that: in order to impart an expressive microstructure to the respective tones in the score, the data entry means is arranged to enter into the digital calculating means the nominal pitch and duration of each of the successive tones, and the first-mentioned digital calculating means determines the shaping function of the component tones of a melody as a deviation from a predetermined base shape and the system is arranged to provide an amplitude shape to each tone in accordance with melodic slope between the particular tone and the next following tone whereby the amplitude shape has a predictive function for the movement of the melodic line. Such systems are operable in an automatic mode wherein microstructure values are calculated from a shaping function responsive to the melodic contour and by means of pulse matrices having certain values relating to the amplitude and duration of pulse component tones stored in the system. Among the significant advantages of a system in accordance with the invention is that it makes it possible to enliven a musical score and render it highly expressive, the system thereby acting to deepen the user's understanding and appreciation of music and its structure. Briefly stated, these objects are attained in a computerized system into which is fed the nominal values of a musical score, the system acting to process these values with respect to the amplitude contour of individual tones, the relative loudness of different tones in a succession thereof, changes in the duration of the tones and other deviations from the nominal values which together constitute the microstructure of the music notated by the score. The system performs the specified tones in the score as modified by the microstructure, thereby imparting expressivity to the music that is lacking in the absence of the microstructure. The microstructure may include changes in pitch or vibrato, individually shaped for each tone. Ways of carrying out the invention will now be described, by way of example only, with reference to the accompanying drawings of which Figure 13 shows one specific embodiment, and in which: Fig. 1 illustrates a family of curves generated from one set of beta function values; Fig. 2 illustrates a family of curves generated from a second set of beta function values; Fig. 3 illustrates a family of curves generated from a third set of beta function values; Fig. 4 illustrates a family of curves generated from a fourth set of beta function values; Fig. 5 illustrates a family of curves generated from a fifth set of beta function values; Fig. 6 illustrates a family of curves generated from a sixth set of beta function values; Fig. 7 illustrates the notes of a Mozart theme below which are three graphs representing different microstructural aspects of the theme; Fig. 8 similarly illustrates the notes of a Chopin theme; Fig. 9 similarly illustrates the notes of a Beethoven theme; Fig. 10 is a block diagram of a computerized system which is operable in the manual mode; Fig. 11 is a graph illustrating how an amplitude shaped tone is obtained from a succession of digital values yielded by the calculator included in the system; Fig. 12 shows both a sinusoidal wave and a differentiated square wave which, when combined, produce a non-sinusoidal wave rich in harmonics; and Fig. 13 illustrates in block form a portion of a system in accordance with the invention operating in the automatic mode. DESCRIPTION OF INVENTION Microstructure and Expressiveness Amplitude modulation appears to be a basic mode of dynamic expression and the understanding of this should precede the analysis of the expressive effects of vibrato, timbre and of timbre variation. It has been found that a significant degree of expressiveness is indeed possible with these very simple means, and that many of the subtlest nuances can be realized. In electronic generation of musical sounds, it has heretorfore been conventional to specify tones using parameters of rise time, decay time, sustain time, release time and final decay, or some subset of these. These parameters, natural to the electronic engineer, do not really have a musical function of like aptness. Amplitude shapes of musical tones often need to be convex rather than concave (or vice versa) in particular portions of their course (e.g., convex in their termination), and hardly ever have sustained plateaux. Moreover, separation of the termination of a tone into a decay and a release is generally the result of the mechanical properties of keyboard instruments and not a musical requirement. We have found that the varied rounded forms available through the Beta Function allow a simple and time-economical realization of the multitude of nuances of musical tone amplitude forms. Beta Function is defined as: and is normalized for a maximum amplitude of 1 by dividing by a constant. for a particular set or values or p₁ and p₂. p₁, p₂ have values ≧ 0. The resulting shape is multiplied by a parameter G to give the amplitude size of the particular tone. The shape stretches over a number of points determined by the duration of the tone. By choosing suitable values of p₁ and p₂, a shape may be selected from families of shapes such as the ones shown in Figs. 1 to 6. Choosing the value 1 for both parameters gives rise to a symmetical, rounded form, and 0.89 for both parameters produces a form very close to a sine half wave. Smaller values of p₁ result in steeper rises; zero being a step function. Larger values than 1 for either p₁ or p₂ make the curve concave, at the corresponding regions. A combination of zero and 1 results in a sawtooth. Most commonly used p values for musical tones generally lie within the region of .5 to 5, and most frequently in the region of .7 to 2. Where required, a second or several more Beta Functions may be added to produce the desired shape--this is seldom necessary, however. Figs. 1 to 4 illustrate different families of Beta Function shapes, showing some of the kinds of shapes readily obtained by choosing appropriate p₁ and p₂ values. In each group of curves, pairs of p₁, p₂ values are given starting from the leftmost curve. Maximum amplitude is normalized as 1. Figs. 5 and 6 are Beta Function shapes illustrating degrees of skewness, starting from a symmetrical (1, 1) form, with pairs of p values forming a series as shown. These are types of shapes used for the amplitude of many musical tones (called A [left group] and P [right group] types). Computer Program for Shaping and Playing Melodies : The Beta Function is used in a computer program that calculates individual tone shapes. In this program, the amplitude character of a tone is specified by three numbers, respectively denoting the amplitude magnitude G, and parameters p₁ and p₂. We use a linear scale for the magnitude with a resolution of 1 part in 4096. This in accordance with our findings that such transient sound phenomena may often be better understood by changes in amplitude on a linear rather than logarithmic scale. It also presents a visually more tractable aspect. Silences of various durations in the millisecond and centisecond range can also be readily inserted between tones. The duration of each tone is specified by the number of points it occupies over which the Beta Function is calculated. The calculation for each tone is done without affecting the duration and number of points of other tones. The temporal resolution of tones is usually better than 1 millisecond. In practice, the amplitude contour may be constituted by a 12 bit DA Converter and modulates a voltage-controlled amplifier (VCA) of linearity better than 0.1% over a dynamic range of 1 to 4096. The frequency of the tones is set by another channel or a DA Converter which modulates a voltage-controlled oscillator (VCO). In practice, the invention may be realized with D to A Converters having 8 to 16 bits. One may also use a digitally-controlled VCA and VCO which can, in effect, be integrated within a digital synthesizer, in which event there is no need for a D to A Converter to operate the VCA and VCO. The FORTRAN IV program was run on a PDP 11-23 computer. The tempo can be varied over a very wide range. Parameters of any tone can be readily varied and the changed result listened to in a few seconds, typically 2 - 10 seconds. Any desired portion of the music can be listened to. The maximum length of the piece to be played is only limited by the length of the microscore that can be stored on the disc. In practice, many tens of thousands of tones can be stored. The method of sculpturing tones and melodies allows a musical artist, or music lover who cannot play a conventional instrument, to perfect the expression in much the same manner as a painter or a sculptor can, working with a painting for long periods of time, gradually perfecting the forms so that they correspond to his inner vision, a vision which itself becomes more perfect as the interaction grows. At what stage to say "it is enough" depends on a higher level of integration where another vision and its realization interact in a like manner. It is also in many ways similar to the process of practicing for a musical performance, in the course of which the artist, enamoured with the piece, refines his performance and understanding through repeated reciprocal interaction--feedforward and feedback. Mozart Quintet An example of a theme embodied by this method is the first eight bars of the Mozart Quintet in G minor, as shown in Fig. 7. In this figure, the stave on top shows the notes of the melody. Graph 1 below this represents the pitch of the sinusoidal tones. Small markers on this graph indicate repetition of the same note and micropauses. Graph 2 is the amplitude contour (in linear scale from 0 to 4096, the 200 point being thus equivalent to -26 dB referred to as the loudest level; 1000 being played at about 50 dB above threshold normally). Graph 3 represents the temporal deviations from the nominal values for each tone, in percent, upward deflection being slower. (Micropauses are often included in the representation.) The time marker at the bottom of all figures represents 1 second. The digital printout prints only every sixth point of the fucntions--actual resolution is thus six times greater than that shown in the illustration. The table shown below for the Mozart Quintet and similar ones give a list of all the tones and rests of the computer realization, specifying for each: 1. the duration of the tone, or rest, in points 2. amplitude size 3. amplitude shape (p₁, p₂). In some tables, where Beta Functions are used to span only part of the duraction of the tone, as may occur for staccato tones, the sound duration of staccato tones is given in parenthesis next to the total tone duration. Micropauses are indicated as "P", Rests as "R". When more than one Beta Function is used for a tone amplitude, they are listed in vertical sequence for that tone. Metronome mark for the nominal unit used (often a subdivision of a quarter note) is also given. The chosen unit of time in the melody (in this case, an eighth note) is assigned 100 points duration nominally, so that a quarter note becomes 200 points nominally, a half note 400 points, and so forth. The actual duration of each tone is modified from these so that a particular eighth tone may have a duration of 96, say, a halt tone 220; and so on, depending on its position and expressive requirements. In this example, all parameters (4 for each tone: duration, peak amplitude, p₁ and p₂) were chosen by trial and error; that is, by repeated listening and gradually improving the values as dictated by "the ear". The program allows us to play any portion or the entire theme, and will repeat as many times as desired (with a short pause between repetitions). The metronome mark entered (i.e. 230) refers to the nominal chosen unit of duration (in the present example, 100 points for an eighth note). If an actual tone has more or fewer number of points than 100, it will have a correspondingly different duration. Minute tempo variations within the theme arise from the differences from nominal values in the number of points for each of the tones. In this example, we may note the following: 1. Amplitude Relationship within a Four-tone Group (One Pulse) The amplitude relationship between the four eighth notes of the first bar shows that the second and fourth tones are much smaller, the fourth one being a little less than the second. The third tone is considerbly larger in amplitude than the second and fourth but less than the first. A similar pattern is repeated in the third bar, but the accentuation of the first tone is even greater. Throughout the theme, the first tone of each bar is considerably larger in amplitude. 2. Peak Amplitudes Outline Essentic Form The peak amplitudes form a descending curve from bar 3 to bar 4. The form of this descending curve combines with the frequency contour to produce an essentic form related to grief (this form may well be considered to be a mixed emotion: predominantly sad, with aspects of loneliness, anxiety, and perhaps regret). Bars 1 and 2 provide similar forms of diminishing amplitude, but in bar 1 combined with rising frequency. Pain and sadness are implicit in bar 2. Bar 1 suggests a resigned view, accepting fate, without the quality of hope; "this is how it is; there is nothing that can be done about it". The combined effect is a combination of grief with a stoical, strong acceptance of what is; without defiance or rebellion. 3. Individual Tone Shapes The shapes or each individual tone are governed by their place in the melodic context. The shorter tones may seem similar in shape on the graph, but in tact they are varied, as can be seen from the p values in Table 3. (Small changes in the p values noticeably affect the quality of the sound.) In the longer tones, such as the fifth tone of bars 1 and 2, first and fifth tones of bar 4, the shape of the termination of the tone is as important as its rise, for appropriate expression. For the shorter tones, the termination phase of the tone relates to the degree of legato that is achieved. Smaller p values result in greater legato. It is not generally necessary to include a DC component to maintain a legato between successive tones. The momentary drop in amplitude between tones shaped by the Beta Function is not perceived by the ear if it is quite short, as is the case for appropriately low p values. 4. Duration Deviations We may note systematic time deviations from the given note values. First notes in each bar are lengthened, the second shortened. Hardly any tones correspond in duration to the actual note value. Some tones are lengthened by as much as 39% (first tone bar 3). Specially lengthened are first notes of beats 5, 9, that correspond to accentuated dissonant tones, which like suspensions are resolved in the following, second tone of the bar. Such prolongations induce a lamenting quality in the expression. Chopin Ballade : As illustrated in Fig. 8, the opening theme of Chopin's Ballade Number 3 in A flat shows how a melody written for piano, an instrument of limited ability to vary amplitude shapes, can be expressed by varying amplitude shapes according to its character and not in violation of it. In this example, amplitude tone shapes are realized that are implicit in the melody, and are heard inwardly even when they are not actually produced. One thinks this melody with these shapes. Notable in this example is the strong rubato in the second part of the first bar. This quickening reaches its maximum extent on the fourth eighth note and is counterweighed by a slowing down in much of the second bar. The microscore for this Chopin piece is as follows: Beethoven Piano Concerto : Fig. 9 illustrates the first movement, second subject of the Beethoven Piano Concerto No. 1. The microscore for this piece which illustrates the automatic mode of operation, using both pulse matrix and automatic amplitude and shape calculations (p₁ & p₂ values) is as follows: A and P Classes of Amplitude Shapes : Let us consider these shapes to belong to a continuum between two classes with intermediate shapes between the two extremes. We may conveniently call these classes (A) assertive and (P) plaintive or pleading, respectively--without wishing at all thereby to tie the musical expression to such categories, of course. We can then consider an actual tone shape as placed somewhere along this continuum--and consider the nature of the influence that displaces it from a neutral position (the base shape) to the place on this continuum where it needs to be. We can describe forms along this continuum by pairs of p values, starting from a base shape (say 1,1) such that as the values or p₁ increase those of p₂ decrease in proportion, and vice versa. Thus, say, for example (.9, 1.11), (.8, 1.25), (.7, 1.42) etc. will give a series of shapes shifting gradually towards class (A) which has a relatively sharp rise time. The inverse series (1.11, .9), (1.25, .8), (1.42, .7) etc. will tend more and more towards class (P) (of gradual rise time). We then can consider the influence which causes the shift to be the slope of the pitch contour, which is also the slope of the essentic form. More particularly, the deviation from a base shape for a particular tone is seen to be a function of the slope of the pitch contour (essentic form) at that tone: both pitch and duration determine the deviation in such a way that: a) Downward (-ve) steps in pitch deviate the shape towards A, upward steps toward P, in proportion to the number of semitones between the tone and the next tone. b) Deviations are affected by the duration of the tone so that the longer the tone, the smaller the deviation (since the slope is correspondingly smaller). Further, in practice, the slope is measured from the beginning of the tone considered to the following tone . In measuring the slope between the tone and the next tone, rather than the previous tone, the amplitude shape acquires a predictive function. The first derivative of a function has a predictive property (lead in phase). The amplitude shape associated with a particular slope leads us to expect a melodic step in accordance with it. The movement of the melodic line is thus prepared. This gives a sense or continuity both musically and in terms of feeling. Experience shows that the proportionality constant needs to be an approximately 10% change in the p values per semitone, for tones of 250 msec duration. The shift is, of course, to be expected to be linear only over a limited range; a degree of nonlinearity for both the duration and pitch factors existing over a broader range. In order to see how the duration factor and the pitch factor may obey different power laws, the equation is put into the form: where s = number of semitones to next tone b = const. of p 1,2 by frequency a = const. of modulation p 1,2 by duration T = duration of tone in milliseconds p 1(i) , p 2(i) = base (initial values of p₁ and p₂) Experience has shown that preferred values are in the region of a = 0.00269 b = 0.20 for such music. It is to be understood that a simplified or linear equation may be substituted for equation (3) having approximately the same behavior within the range considered. Choice of Base Values : In music of different composers, and of different types, it would seem that certain preferred base values apply. Values in the vicinity of (1.2, .8) appear as an appropriate choice for much of Beethoven--giving a greater legato and more gradual attack. For Mozart, base values around (.9, 1.1) give a more rapid decaying sound, and a somewhat sharper attack. For Schubert, base values in the vicinity of (1.15, .9) are seen to be appropriate. These values are influenced by the type of instrumental sound that the style of the composer appears to require, and may also be linked to historical consideration of the instruments in use at the time. They may also be related to how the inner pulse affects the microstructure, which we will consider in the next section. Equation 3 relates to the use of Beta Functions to obtain the desired shift in amplitude shape. In practice, when one chooses not to employ Beta Functions, the amplitude shape may be modified as a function of the slope of melodic form using traditional expedients for individually shaping the component tones of a melody; that is, such expedients as attack, decay, sustain and release, which are appropriately varied. Expressiveness of Scales Also implied is that tones of scales have somewhat more (P) shape going up, and going down more (A) (the exact deviation depending on the tempo as given by equation (3)). In fact, scales become considerably more musical when this rule is appropriately observed. The Composer's Specific Pulse Expressed in Microstructure : The inner pulse of a given composer is not the same as the rhythm or meter of a piece; it is found in slow movements, in fast movements; in duple time, in triple time, or compound time. The tempo of the pulse has generally been considered to be in the range of 50 - 80 per minute. In slow movements, one pulse may correspond to an eighth note, even a sixteenth in a very slow movement; in a fast movement a half note; and in a moderate movement a quarter note. The inner pulse as a specific signature of a composer became established in Western music around the middle of the eighteenth century and continued until the advent of music in whose rhythmic motion there no longer was interfused an intimate revelation of the personality of the composer. In the music of Mozart, Haydn, Beethoven, Schubert, Schumann, Chopin, Brahms, for example, we find a clear and unique personal pulse which the composer has impregnated successfully into his music (the knowledge of which we ultimately acquire from the score). Indeed, because of the time course of the inner pulse (.7 - 1.2 sec. approx. per cycle), the matrix of its wave form is most prominently expressed in microstructure. Once initiated, the inner pulse can carry through the musical piece without need for further specific initiation of form, although the rate will be caused to vary to a degree. Small pauses can momentarily suspend the pulse, and act as punctuation, as it were, in the musical phrasing. "Neutral" passages acquire from the pulse the characteristic "flavor" of the composer. Pulse Matrix of Mozart, Beethoven and Schubert : A two-fold effect may be observed: The inner pulse affects 1. Relative amplitude sizes of its component tones. 2. Duration deviations of its component tones. Both 1 and 2 must occur. Either alone is insufficient. Accordingly, the influence of a composer's pulse is stated for a particular meter by a matrix that specifies (1) amplitude ratio, (2) duration deviations. The following matrices specify the influence of the inner pulse for Mozart, Beethoven and Schubert, respectively, for the 4/4/meter. For each tone, two numbers are given. One specifies the amplitude size ratio, referred to the first tone as 1. The other gives the duration referred to as 100 as a mean duration for the 4 components. Pulse matrix values for triple meters are as follows for the three composers illustrated: Values for duple meter are derived simply from the quadruple values by adding the duration of tones 1 and 2, and of tones 3 and 4, respectively, to obtain the duration proportions, and keeping the amplitude values for tones 1 and 3, which now become 1 and 2. Thus the matrix values for duple meter are: Pulse matrices for compound meters can be derived from the above as follows: The two matrices are combined so that amplitude ratio A c (i,j) = A₁(i)A₂(j) duration factors where A c (i,j) is the compound pulse amplitude D c (i,j) is the compound pulse duration A₁(i), A₂(j) are the simple pulse amplitudes and D₁(i), D₂(j) are the simple pulse durations respectively for the i th and j th tone of the simple pulses. To allow for different degrees of hierarchical dependence attenuation factors are introduced that allow the effectiveness of the subordinate pulse structure to be de-emphasised or emphasised, with the parameters n and m, so that when n = 1 and m = 1, a full hierarchical effect is obtained, and for smaller values the duration and/or amplitude effects of the subordinate pulse structure are relatively more attenuated. Thus amplitude ratio A c (i,j) = A₁(i)A₂(j) n duration factors values of n and m in the range of .7 to .8 are found to be often appropriate. For example, the 6/8 pulse for Beethoven is The effect is that each group of 3 tones constitutes a small 3-pulse and the two groups of 3 tones form a 2-pulse. A third level of hierarchy involving bar-sized units may be similarly incorporated. The third level numerical values are piece specific however, not composer specific. Applying the Pulse to a Melody Having Various Note Values: When a melody has a combination of notes of different values, as is generally the case (some larger and some smaller than the component values), the following appears to apply: 1. Duration deviations are proportioned according to the component tones of the pulses; e.g., a dotted quarter has the duration deviation of one tone plus half that of the next. 2. The amplitude is taken as that prevalent at the beginning of the tone; i.e., is not averaged; e.g., the dotted quarter has the same amplitude as the quarter would have had without the dot. While it appears that the range of 50 - 80 per minute is an approximately useful guideline in applying the pulse, some pieces may present alternate possibilities of a larger or smaller frame for the pulse. An example of automatic operation of the system using a pulse matrix and using automatic calculations of amplitude shape (p values) is given in Fig. 9. In general, it should be emphasized that the pulse and its effects in microstructure as described herein is in no way to be considered a binding Procrustes bed, but rather as a level from where fine artistic realization of the music can be more readily attempted, taking into account the individual concept of the piece, and personal interpretive preferences. Relation of Timbre to Microstructure : Timbre is essential for melodic expressiveness when there is more than one melodic line. Several sinusoids tend to coalesce and fuse--for distinctness of voice leading and contrast sounds with different dynamic proportions of harmonics are required. Within each tone it is possible to add timbre (and also vibrato) in various dynamic ways to the expressive forms already determined. Such individually-shaped time varying functions of timbre and vibrato augment expressiveness. The realisation of the pulse and its effects is seen to be necessary for the life, power and beauty of music. Among the advantages of imparting microstructure to a musical score in a computerized system in accordance with the invention are the following: 1. It improves artistic understanding and output. 2. It infuses life and livingness into music. 3. It tends to give us a degree of understanding of the very nature of that livingness. 4. It allows us to use imagination and creative insight from a higher point of view. The practical applications of a computerized system in accordance with the invention to music education are obvious and therefore need not be detailed. In an age of personal computers, the programs developed therefor can give access to creative interpretation to all so inclined without the need to acquire physical musical skills or manual dexterity. The invention is also useful to a serious or amateur composer, for it allows the composer to incorporate his own realization of microstructure into the macrostructure of his own composition, and it also allows him to experiment with inner pulse forms. The final product thereby reflects the imagination, feeling and discernment of the individual who shaped a musical composition. The computerized system serves as a tool which assists its user in thinking musically in a manner somewhat analogous to the relationship of an electronic calculator to a mathematical concept. The Computerized System. Referring now to Fig. 10, there is shown a manually-operated computerized system in accordance with the invention based on the technique disclosed hereinabove for processing the nominal tones of a raw score entered therein to impart an expressive microstructure thereto. The system includes a Beta Function calculator 10. In the calculator is entered by way of a computer keyboard or floppy disk represented by entry station 11, the successive tones of a music score in terms of their nominal pitch and duration values expressed in alpha-numeric terms. Thus the pitch of a given note, which depends on its position on the staff, is represented by an appropriate value, as is the duration of the same note. In practice, an electronic piano keyboard may be used. By depressing a selected key, there is produced an appropriate value for entry into the calculator. In that case, the tone duration will have to be normalized. Also entered manually into calculator 10 is the desired microscore of each nominal note. By "microscore" is meant digital values representing desired deviations from the nominal values of the note necessary to its processing to impart a microstructure thereto. Thus the p₁ and p₂ values required by the Beta Function to shape the amplitude contour of each note is entered as well as digital values representing changes in the duration of each note and values representing the relative amplitude of successive notes in the score. Also entered are micropauses and whatever other variables are to be processed by the system, such as timbre. From entry station 11, there are two channels C₁ and C₂ leading into calculator 10, channel C₁ conveying the amplitude and timing data, and channel C₂ the pitch and timbre data for each note. Calculaor 10 is programmed to process the data supplied thereto and to yield a series of equi-spaced digital values V during a specified interval, as shown in fig. 11, that represent the successive amplitude levels in the contoured tone T whose microstructure duration is interval P. In the absence of the microstructure impressed on the nominal tone, its form would be represented by a square wave of constant amplitude and predetermined duration, which depends on whether it is a whole note, a half note or whatever else is notated. The series of digital values V, which outline the amplitude shape, are applied to a D-to-A converter 12 to yield an analog voltage A₁ reflecting the amplitude contour or envelope of the processed note. The digital data derived from entry station 11, which represents the frequency of each note, is also fed to D/A converter 12 to yield an analog voltage A₂, reflecting the pitch of the tone to be played. Analog voltage A₁ representing the amplitude contour is applied to a voltage-controlled amplifier 13 (VCA) whose output is applied to a loudspeaker 14. Analog voltage A₂ representing the pitch is applied to a voltage-controlled oscillator 15 whose output frequency is in accordance with the pitch of the tone. The sinusoidal output of this oscillator may be applied directly to amplifer 13, in which event the reproduced tone is without a harmonic content but has the desired microstructure impressed thereon. Alternatively, the oscillator output may be applied to the amplifier through a timbre network 16 which changes the sinusoidal wave shape so that the resultant tone is rich in harmonics and therefore has a timbre depending on its harmonic content. Any known means may be used for introducing a varying harmonic content. One approach is to combine a sinusoidal wave SW, as shown in Fig. 12, with the differentiated form DW of a square wave having the same period, the resultant sharp pulses being adjustably clipped and rectified to provide sharp peaks which, when summed with the sinusoidal wave, produce a non-sinusoidal wave having a desired harmonic content that depends on the adjustment of clipping and rectification. The resultant sum may be further variably rectified to provide preponderantly even or odd harmonics. With each tone, the timbre is varied through a number of D to A control channels, typically up to 4 channels, each output of which is shaped by Beta Functions or equivalent means. All of these functions can also be carried out in an entirely digital manner in a digital synthesizer. It is to be understood that among the means usable for producing a varying harmonic content are additive or subtractive synthesizers, wave shaping and other means, realized either digitally or through analog means. It is to be understood that while calculator 10 is advantageously operated in accordance with the Beta Function disclosed herein requiring only two parameters (p₁ and p₂), in order to produce a desired amplitude contour, any known electronic means to effect amplitude shaping in response to applied digital parameters may be used for the same purpose. In operating a system in accordance with the invention in an automatic mode, all of the digital values with respect to amplitude and duration necessary to impart a microstructure to the nominal note values of the raw musical score entered therein may be stored, as shown in Fig. 13, in a pulse matrix 17 which in one output channel A₃ yields the amplitude and timing data required to process each note, and in another output channel A₄ yields the necessary pitch data for each note. The digital data from channel A₃ is applied to an amplitude-shape calculator 18, while digital data from channel A₄ is applied to a timbre calculator 19. The amplitude envelope from amplitude shape calculator 18 is applied to a tone generator 20, while tone shape data from timbre calculator 19 is also applied to the tone generator which generates tones having the desired microstructure. In the amplitude-shape calculator, the shaping function related to the melodic and essentic form is calculated as a deviation from a base shape in accordance with Equation 3, as explained previously. It is to be understood that when two or more tones are to be sounded simulataneously, separate calculations will be required for each tone and their outputs summed. While there has been shown and described a preferred embodiment of a computerized system for imparting an expressive microstructure to a musical score in accordance with the invention, it will be appreciated that many changes and modifications may be made therein within the scope of the appended claims. Thus, while the invention has been illustrated as it applies to classical music, the invention is by no means limited to this application, for it is fully applicable to all other forms of music, including popular and ethnic. It must also be noted that the microstructure elements set forth herein may be used to modulate visual presentations so that by employing video graphics, the shape, brightness and color of visually displayed forms may be variously modified to express visual counterparts to the expressiveness imparted to music by the microstructure. Simultaneous presentations of such sound and visual forms may further enhance their expressive quality. The visual presentations may assume free or abstract forms which, by reason of microstructural modulation, become more expressive and appear to move or dance and thereby take on a more animated character. For example, the visual presentation may be in the form of a conductor's baton whose movement is related to a musical score and its microstructure. Human body or facial expressions may be made responsive to microstructural modulations. Such microstructure can also be used to supplement or refine existing dance notation, such as Laban notation.

Claims: A computerized system for processing a musical score whose notation provides the nominal value for each tone in regard to its pitch and duration, the system comprising: (a) digital calculating means (10, 17); (b) data entry means to enter into the digital calculating means (10, 17) data representing the pitch of each of the successive tones in the musical score to be processed; (c) means to enter into the digital calculating means (10, 17) data relating to the desired amplitude contour and duration changes for each tone in the succession thereof, the digital calculating means (10, 17) being programmed to process the data therein to yield in its output with respect to each tone in the succession thereof a series of digital values representing the desired amplitude contour; and (d) output-responsive means (20) responsive to said output to generate and reproduce the tones of the said score; characterized in that: in order to impart an expressive microstructure to the respective tones in the score, the data entry means is arranged to enter into the digital calculating means (10, 17) the nominal pitch and duration of each of the successive tones, and the digital calculating means (10, 17) includes pulse matrix means (17) operative to store relative amplitude sizes and duration changes for the component beats of an elemental musical measure, the elemental measure and the stored relative amplitude sizes and duration changes being herein referred to as the "pulse" and the "pulse matrix" respectively, and operative to modify the amplitude and the timing of the entered nominal durations of the successive tones throughout the score on the basis of the values for the elemental musical measure stored in the pulse matrix. A system as claimed in claim 1, wherein the first-mentioned digital calculating means (10, 17) determines the shaping function of the component tones of a melody as a deviation from a predetermined base shape. A system as claimed in claim 2, wherein the system is arranged to provide an amplitude shape to each tone in accordance with the melodic slope between the particular tone and the next following tone whereby the amplitude shape has a predictive function for the movement of the melodic line. A computerized system for processing a musical score whose notation provides the nominal value for each tone in regard to its pitch and duration, the system comprising: (a) digital calculating means (10, 17); (b) data entry means to enter into the digital calculating means (10, 17) data representing the pitch of each of the successive tones in the musical score to be processed; (c) means to enter into the digital calculating means (10, 17) data relating to the desired amplitude contour and duration changes for each tone in the succession thereof, the digital calculating means (10, 17) being programmed to process the data therein to yield in its output with respect to each tone in the succession thereof a series of digital values representing the desired amplitude contour; and (d) output-responsive means (20) responsive to said output to generate and reproduce the tones of the said score; characterized in that: in order to impart an expressive microstructure to the respective tones in the score, the data entry means is arranged to enter into the digital calculating means (10, 17) the nominal pitch and duration of each of the successive tones, and the first-mentioned digital calculating means (10, 17) determines the shaping function of the component tones of a melody as a deviation from a predetermined base shape and the system is arranged to provide an amplitude shape to each tone in accordance with melodic slope between the particular tone and the next following tone whereby the amplitude shape has a predictive function for the movement of the melodic line. A system as set forth in any preceding claim, wherein the microstructure data entered into the first-mentioned digital calculating means (10, 17) for each tone in the score represents the desired amplitude contour thereof by two parameters of a Beta Function whereby the first-mentioned digital calculating means (10, 17), on the basis of these parameters, determines the desired contour. A system as claimed in claim 5 when dependent on claim 3 or claim 4, wherein the amplitude shape is described by pairs of p values in accordance with the following equation: p₁ = p 1(i) e bsexp(-aT) p₂ = p 2(i) e -bsexp(-aT) where s = number of semitones to next tone b = const. of p 1,2 by frequency a = const. of modulation p 1,2 by duration T = duration of tone in milliseconds p 1(i) , p 2(i) = base (initial values of p₁ and p₂) A system as claimed in claim 3 or claim 4, or claim 5 when dependent on claim 3 or claim 4, wherein downward steps in pitch deviate the amplitude shape towards a skewed-backward (assertive) shape, and upwards steps in pitch deviate the amplitude shape towards a skewed-forward (pleading) shape in proportion to the number of semitones between the particular tone and the next tone, and deviations are affected by the duration of the tone so that the longer the tone the smaller the deviation. A system as claimed in any preceding claim, further including second digital calculating means (19) into which microstructure data is entered, in use, relating to desired timbre variations of each nominal tone, and in which the output-responsive means (20) is responsive, in use, to the output of the second digital calculating means (19) to modify the timbre of the generated tones accordingly. A system as set forth in any preceding claim, wherein timbre is imparted to a tone of a given nominal pitch by means generating a sinusoidal wave of the same frequency and combining this wave with the clipped peaks of a differentiated square wave having the same period as the sinusoidal wave. A system as set forth in any preceding claim, wherein said output-responsive means (20) includes a digital-to-analog converter (12) to convert said series of digital values into a corresponding analog voltage. A system as set forth in claim 10, further including a voltage-controlled amplifier (13) to which said analog voltage is applied, said amplifier (13) functioning to amplify tones whose respective pitches correspond to those of the score being processed by the digital calculating means (10,17). A system as set forth in claim 9, wherein the combined wave is varyingly rectified. A system as set forth in claim 8, wherein the varying timbre is entered into said second calculator by a number of Beta Functions, each of which involves two parameters. A system as set forth in any preceding claim, wherein the microstructure data stored therein is used to modulate visual presentations with respect to their shapes, colors, brightness and movement concurrently with the production of sound. A system as set forth in any preceding claim, into which data is entered relating to desired vibrato variations of each nominal tone, and means to modify the vibrato of the generated tones. A system as set forth in claim 13, wherein individual timbre variations for each tone are calculated as in claim 2 with appropriate constants and parameters. A system as set forth in claim 1 or any claim dependent thereon, wherein the pulse matrix contains several lighter levels and attenuation factors between said levels.

Inventors: CLYNES, MANFRED
Applicants: CLYNES, MANFRED
Application year: 1984
Main classification: G10H1
IPC codes: G10H1, G10H5, G10H7