Cognition 55 (1995) 269-310.
Manfred Clynes
Western music is a combination of notated structure plus microstructure. Composer's pulses, as precise microstructural functions, were tested with 5 groups of subjects of graded musical proficiency, 1. 10 famous artists including Vladimir Ashkenazy, Yehudi Menuhin, Paul Badura-Skoda and others, 2. 14 Juilliard School of Music graduate students, 3. 19 Manhattan School of Music graduate students, 4. 51 Australian conservatory students, and 5. 41 non-music students (total, 135 subjects). Composer's pulses consist of combined amplitude and timing warps specific to each composer - the composer's pulse matrix. Each subject listened to and scored 40 versions of 10 short music examples (not selected by the author) of 8 bars each, composed by Beethoven, Mozart, Haydn and Schubert, performed by computer, in which composer's pulses, as developed by Clynes (1983,1985,1986,1987), were incorporated in a two-level hierarchic pulse configuration, and interchanged. Each example was heard with the pulses of those four composers in turn, in quasi-random sequence, one performance thus incorporating the 'right' pulse and three the 'wrong' ones. Results show dramatically that the greater the musical proficiency, the more marked the preference for the 'right' pulse (p<.0001). Non-musicians as a group showed a similar tendency of preference, but typically to a considerably less pronounced degree. Further studies suggest that longer excerpts (32 bars) and repeated hearing would help non-musicians also to better understand composers' pulses. A theory of music as a double stream is introduced. The results suggest that the composer's pulse matrices posited by Clynes as a first approximation are in fact appropriately meaningful. Brain function aspects of the meaningful discrimination of such tiny time differences are discussed.
For thousands of years, across all cultures people have liked music. Held by many to be a language of emotions, it enriches otherwise untouched aspects of our existences. As we come closer scientifically to understand that many aspects of our capabilities are genetically based, from language to consciousness, it is timely, given the basic relationship of music to our lives, to consider the appeal of music. More particularly, to look at the wide appeal of particular composers. The following is a search not focused at the acoustic properties of our hearing, but at the meaning of music, and some of the demands that this makes on central nervous system processing.
The paper is based on work of the author and others going back several decades. It is aided by the author's experience as a musician with classical music, as well as his research as neuroscientist. The author has found a 'pulse' for certain composers as an element of musical linguistics, readily and meaningfully recognizable by others. This article discusses the concept of composers' pulses, and testing music performed using the pulses, on various groups of people, over a wide range of musical proficiency. The results of the testing bear on subtle but powerful aspects of musical language.
The nature and concept of meaning in music needs to be
understood better. Relatively few workers in cognitive science
are yet engaged in this endeavor. The present work consists of a
modest step in that direction, through a precise microstructural
study. It introduces a double stream theory of music.
In Western music, preservation of music across centuries has been accomplished through notation. But this remarkable achievement has a price: as a result music has been divided in two, notated structure and unnotatable microstructure. The notated music itself is merely a skeleton of the musical thought. To bring it back to life, microstructure needs to be added.
In musical thought, in musical meaning and performance structure and microstructure combine, and they contribute conjointly to musical linguistics. The informational content of music is estimated to be 17 bits per note for microstructure and 12 bits per note for structure (Clynes, 1986). The addition of microstructure to structure is capable of producing performances that range from the trivial to the profound, playing the same notes. How does this happen?
Unnotated microstructure includes five types of variables: 1. time deviations of a note from the value given in the score, 2. amplitude of individual notes, 3. amplitude envelope shapes of individual notes, 4. vibrato, and 5. timbre changes within an individual note (amplitude in this paper is meant as correlative to loudness).
There are two kinds of precision in Western music, corresponding to structure and to microstructure respectively. The first kind is to play all the notes accurately as notated. For a computer this is not only possible, but can be taken for granted; for a human it is something one strives for, if not always completely successfully. Mathematically and musically speaking such accuracy is necessary but not sufficient. A computer performance with only this precision is boring and actually irritating; one cannot wait to shut it off. The meaning of the music is in limbo. The effect is somewhat similar to hearing words recited in a monotone, stilted delivery. Part of the reason for this unpleasant irritation (which itself is worth further study) is that listening to music involves both memory and anticipation. Notes played 'correctly' without microstructure constantly disappoint. We cannot think along with it.
The second kind of precision emends the printed score with microstructure, transforming it from irritating clangor to meaningful, living realizations. It attempts to recreate - one could say, second guess - the musical thought that could not be notated in detail by the composer.
Typically, a notated phrase permits several alternate realizations, each with different meaning. But within a chosen meaning class (which a composer might try to indicate by words on occasion, e.g. con amabilita, dolce, furioso, energico, con brio, mesto) , an optimization process is possible: The quality becomes most strongly defined and communicated when the microstructural parametric space is appropriately configured, i.e. the time-forms can be optimally shaped for that meaning. The more precisely the optimal forms are realized, the more powerful and specific the communication of that quality.
In Clynes and Nettheim (1982) and Clynes (1977, pp. 227-229) we have measured and shown, for example, how the same phrase by Bach can be expressed as sad or loving, depending on the microstructure. We have also shown in Clynes and Nettheim (1982), how to construct 28 different melodies including microstructure that predictably all sound sad. This second kind of precision, far more demanding than the first, is the daily work (both mental and executive) of the interpretive artist. As Roger Sessions (1970) said, "It is the quality and character of the musical gesture that constitutes the essence of music, the essential goal of the performer's endeavors.... it takes precise and characteristic shape .... there is nothing whatever fortuitious about it."
Notated structure, like fuzzy logic, provides a field of possibilities, and excludes others as highly unlikely or even impossible. Between two microstructure realizations of a phrase that express a different kind of meaning there may be many relatively meaningless ones in this field, or parametric space. A meaningful microstructure realization is like an island in a sea of meaninglessness (Clynes 1992).
The reason for this is presumably of biological origin: Different qualities of experience and emotions have innately different dynamic patterns by which they are expressed (Clynes 1977) (e.g. laughter and yawning). Hence also the impression that one is playing 'naturally' when one is playing well in this sense.
Such precise musical realizations activate not merely a feeling or emotion such as sadness or joy, and inner gesture (Sessions, 1970), but concurrently also the corresponding cognitive substrates of such feeling and gestures (eg. that the feeling of love inhibits lying, Clynes, Jurisevic and Rynn, 1990, and see also Clynes, 1986) some of which are innate. This is one reason why the musical 'story' is more than merely a sequence of feelings. It is an aspect of this second kind of precision1, brought to music by the microstructure which is the subject of our study.
There are two approaches to the study of the contribution of microstructure to musical language: measurement of actual performance microstructure and study of the effects of microstructure through computer synthesis. An advantage of the latter is that changes in musical meaning can be studied through changing the microstructure while keeping other variables constant. This approach has led to the study of the hierarchical pulse, in which aspects of structure and microstructure are linked. The pulse involves the first two of the five microstructural variables listed in the previous section of this paper, called for short hereafter, duration and amplitude.
The concept of the pulse matrix had its antecedents first in motor patterns observed of the movements of a finger "being conducted by the music - Begleitbewegungen " (Becking 1928), and later in measurements of motoric pulse form of musical artists while 'conducting' with finger pressure on a sentograph, as the artists mentally rehearsed (thought) the music of various composers (Clynes, 1968,1970). A sentograph is an instrument for measuring dynamic pressure transients (Clynes, 1969, 1973). 50 pulses at a tempo of one per second were averaged for each 'performance'. Each composer appeared to have a distinct motor pulse form, and the form was similar for different artist subjects, and for various pieces by the same composer. This movement pattern was considered to be an element of expression of musical thought (Fig. 1). ("Musical thought" is taken to mean throughout this paper: musical phrases or motivs shaped not alone by 'cold' structural requirements of the "notes" but by gestural, attitudinal and emotional significance).
It was later discovered (Clynes 1983) that this repetitive thought finds its expression in the music by a configuration of specific microstructure. The concept of the composer's pulse as a microstructure matrix of a combined time and amplitude warp specific to a composer (the pulse matrix, Clynes, 1983) has also made it possible to generate computer performances which incorporate the composer's pulse - for experimental purposes, and later, in its hierarchical application, as part of microstructure creating valued interpretations (Clynes, in preparation).
The author proceeded to test composer's pulses with individuals of varying musical abilities and training. This paper reports on the preferences of those individuals for four composers' pulses in a series of pieces in which the pulses are deliberately interchanged. The paper addresses he question of how the pulses would be perceived by subjects of different musical standing and experience. As in Repp (1990, 1989) and Thompson (1989), substitution of one composer's pulse matrix for another's was used in these experiments, rather than studying distinctions caused by changing only single pulse elements of the matrix. (The effect of changing single elements of the pulse matrix will be investigated in further studies.)
The composer's pulse is a systematic combined time and amplitude warp considered to be characteristic of the composer, which modifies the written note values 2. That is to say, a series of four eighth notes, or of sixteenth notes, printed in the score would not be played evenly, but typically would be modulated in duration and amplitude, as indicated in Table 1. The concept of pulse may also be applied to ethnic music (Clynes and Walker, 1982). Ethnic musical character (e.g. Hungarian, African, Spanish, Polish, South American etc.) can be conveyed by the corresponding microstructure of a pulse matrix.
An interesting question not covered in this paper, but presently being investigated sentographically, is how varied pulse microstructure, when applied to 'neutral' music (an arbitrary sequence of notes consisting largely of scale passages and the like) can itself cause or 'drive' varied motoric patterns. In other words, 'how music makes the dance' - is presently being investigated as an inverse transfer function of the central nervous system (i.e. inverse to the conductor's function in imparting musical microstructure through the motoric pulse of his movements)
Becking (1928) first proposed the notion of the composers' pulse, following the extensive work of Sievers (1885-1915) with pulses observed in literary works. Becking noted that as one mentally thinks a piece, one stumbles in this process of 'being conducted' if in the course of, say, a Beethoven piece, a particular phrase is thought of as composed by Mozart. With sensitive and insightful understanding he connected this notion of the "composer's pulse" extensively with musical meaning. He even, in 1928, made cogent observations on the pulse of Mahler, when Mahler was as yet hardly known. His work derived from music criticism and musicology and was directed toward understanding the music of specific composers. The pulse was viewed as a property of the composer's musical language - much as his teacher, Sievers, studied the prosody of writers and poets by the same means, investigating their identity and personality through the rhythms of their written language. Sievers and Becking described somewhat complex rhythmic finger movement patterns as curves expressive of the pulse of a particular composer. Within each movement pattern there were patterns of tension and relaxation, indicated in Becking's curves by variations in the thickness of the line, anticipating thus the work of Laban (1958) with dance notation and movement characterization (Laban's concepts of ' effort' and 'shape'). Trusalit (1938), in his monograph on shaping and motion in relation to music, (recently synopsized in English (1993) by Repp), notably intuited links between microstructure and implied movement, but showed little appreciation of the work of Becking.
In 1967 the author first scientifically measured the forms of the composer's motoric pulse, in experiments in which artists mentally rehearsed the music while intentionally expressing the pulse with finger pressure on a pressure-sensitive instrument, called the sentograph, a precise and reliable measurement technique (Fig.1). In this technique pressure replaced movement (Clynes 1969, 1972, 1973). The method was subsequently extended to measure two vector components of pressure (vertical and horizontal, in the horizontal direction of towards and away from the body). In these experiments, the finger remains in constant touch with the instrument, and the pulse contour obtained is the course of pressure, a reduced image of the fine structure of the internal musical beat; but it does not try to follow individual notes within the beat. While providing evidence for the motor pulse, these experiments yielding two-dimensional curves could not reveal how the pulse might be incorporated in the music. The pulse matrix which is the subject of this paper, provides the multidimensional, non-collapsed fine structure that accomplishes this .
In 1983 the author arrived at the insight conceptually that an integral time-amplitude warp matrix was required for the pulse, for the microstructure of a group of four pulse elements (say four eighths notes) whose nominal score duration values were even. He realized that neither time nor amplitude changes alone applied to the notes could adequately provide the meaning or Gestalt of the pulse expression, but only a specific integral, organic combination of both. (Amplitude and time deviation patterns of the pulse repeat in phasic synchrony.)
Commonly used musicological terms (e.g. accent and articulation) are not sufficiently accurate nor well defined to describe the precision and nature of the pulse, in which milliseconds and note subcomponents play a role. The pulse influences both effective accent and, often, articulation, although it is a distinct and more precise concept.
In speech, the sound of syllables has organically related amplitude and timing features to give it appropriate eloquence. These features are not at all interchangeable in speech: duration shortening and lengthening are not equivalent to decreasing or increasing amplitude. Yet in music, unnotated timing and amplitude deviations within the beat have been largely considered separately; even often as mutually compensating factors and not as organically combined entities. (For example, in organ and harpsichord performance increased duration is often made to serve the function of increased loudness in producing "accent".) This tendency is reinforced by the use of instruments (such as the organ and harpsichord) with physical limitations, on which that organic combination is mostly not possible and on which music is yet played.
The concept of an integral time-amplitude matrix resulted in understanding, through realization by computer synthesis, how each note of the music participated in the composer's pulse through its microstructure (Clynes 1983, 1985, 1986, 1987). It effectively revealed how the motoric pulse is imaged in musical microstructure.
The pulse matrix for a pulse with four elements, e.g. four sixteenth notes is six dimensional. There are three independent parameters for duration and three for amplitude (Table 1). The fourth element for both is always 100, or 1 respectively, providing normalization. If each variable may have just ten different values, as the limen permits, then such a matrix would allow for 106 or 1,000,000 composers, more than one is likely to encounter. In practice, the known composers are widely separated from one another in parametric space.
For a pulse with three elements, however, the corresponding matrix dimensionality is four, and only 10,000 composers could be so characterized. Differentiation is considerably less for a three element pulse.
The values for the component pulse elements of the time and amplitude deviations for a single-level pulse matrix had been determined for each composer not by actual measurement of recorded performances3 , but through synthesis by computer of specific melodies and sections of works of that composer, noting for what values of the matrix components the results sounded right, according to the musical understanding and feelings of the author. When four or five pieces sounded well with that matrix, it was found that further pieces by the same composer would then likewise sound right with that pulse matrix pattern (Clynes 1983). This appeared to justify the process. It was considered that this matrix pattern represented a linguistic element of music that was somehow inherent in the composer's music, and would be perceived also by others than the author not in an idiosyncratic way, but as representing certain personal qualities, e.g. strength, gracefulness, qualities that are mostly easier to recognize than to name.
Pulse matrix element values were determined for 4-element pulses, and for 3-element pulses in a preliminary way, for a number of composers (Table 1).
The choice of values was an artistic one, made possible by focusing on the meaning of the music. It could be made effectively only by someone who was, so to speak, on closely "intimate terms" with that composer, through his music. For instance, this author could not attempt to find the pulse of Richard Wagner, as his understanding of Wagner was insufficient, having quite inadequate experience with the interpretation of Wagner's music.
Initially it had been thought that the pulse was manifest mostly at frequencies of the order of 1-1.5 Hz or about MM 60-90 for a 4-element pulse. This makes the duration of each pulse component of the order of 165-250 ms (MM stands for the metronome marking in beats per minute). The time deviations on that level amount to about 10- 20 ms.
But once values of 4-element pulses and 3-element pulses were obtained, it then became evident that these relative relationships could be applied hierarchically. Three or four of such groups may in turn be grouped together by a higher level 3 or 4-element pulse (eg. four groups of sixteenth notes may constitute a group of four quarter notes ) 4 . Could one apply the same pulse matrix values to the higher group as to the lower, or, viewing the question more generally, would a different pulse matrix be more correct? It was found that the same pulse matrix could indeed be applied to the higher group with appropriate results. That is, the composer's pulse may be applied on several levels, albeit many times to an attenuated extent, typically with regard to the time deviations. It is not surprising that a dynamic phenomenon such as the pulse should appear not solely at one frequency region, but over a frequency band, with different degrees of manifestation at various frequencies; the pulse (i.e. the deviations) may be considered to have a frequency response.
But it is especially a musically and artistically important finding that the composer's pulse occurs integrally at several hierarchic levels in the composition. This supplants what otherwise would be a rigid pulse with one that is subtly varying throughout, varying moreover in a way that is also characteristic of the composer.
The durations of the notes given in a score are called nominal durations, in units of the metric, e.g. eighth notes, sixteenths, quarters, and so on. In the pulse matrix, component durations are given relative to a norm of 100. A pulse component duration of 109 for example would mean a duration 9% longer than required for evenness. As the general tempo fluctuates the actual pulse component time durations vary, but not their relative durations. Typically, a difference of 1 in the pulse component duration may correspond to a time difference of the order of 2 milliseconds - about one limen (Clynes, 1990a).
The pulse matrix, if chosen at a level of eighth notes for example, is applied as follows:
Rule 1. Duration: A note of any nominal duration, say a quarter note, is given the duration of the pulse components it occupies.
If we are considering a four component pulse, each component being an eighth note, then a quarter note would have an actual duration equal to the sum of the two pulse components it occupies.
Because each pulse component has a slightly different duration, this also means that its duration would be slightly different if the quarter note occupied pulse components 1, 2, from what it would be if it occupied pulse components 2, 3, or 3, 4.
Rule 2. Amplitude: The relative amplitude of the note is given by the amplitude of the first pulse component it occupies.
In a hierarchical pulse, a pulse of more than one level, the same quarter note is additionally modulated both in duration and amplitude in accordance with its position within the next higher level pulse group:
In a pulse configuration of more than one level, say 4 x 4, in which there are four groups of four, each of the four elements of a lower level group is multiplied by the first higher level pulse element, to provide the effective values of those four elements. A similar group of four lower level elements is then multiplied by the second of the higher level pulse elements, and so on, for the third and fourth higher level elements. There result sixteen pulse elements, all of which have individual amplitudes and durations, none of which are the same. Similarly, a three level pulse of 4 x 4 x 4 yields a pulse array of 64 pulse components, each of different duration and amplitude, yet all determined by the basic 4-pulse matrix, with possible attenuation factors. Such a pulse array resulting from a hierarchic tree defines the time and amplitude warp given to the music. The basic pulse is not rigid, but is modulated by its own self in a subtle and integral way, on a higher organizational plane.
Note that the warp applies regardless of whether there is a note or a rest in the music at that pulse element. (Thus a rest in a Beethoven piece will have a slightly different duration than if the same rest were part of a Mozart piece; both also depending on the position in the bar, as explained earlier.)
We may speculate that the composer probably composes with his pulse in mind in some manner, perhaps on several levels. He very likely may not be aware of this, yet his creations are in accordance with it, accents, and note densities, and other structural aspects follow this inclination. From the scores the pulse parameters cannot be quantitatively deduced; however, conversely we may in fact note the influence of the pulse on the specific choices of accent, of placements of notes the composer makes in his scores - they seem to fit (see Clynes 1986 for an analysis of this, also, cf. the processes of gait and handwriting.)
In the double stream theory of music developed by the author (1989,1990) to encompass these phenomena, music is regarded as embodying two simultaneous streams, one stream the repetitive and hierarchical pulse, the other the evolving, emotionally meaningful 'story' of the music.
The second stream consists of the phrases, as they unfold and develop, often embodying sentic forms (Clynes and Nettheim, 1982, Clynes 1983). Phrases, entities that are enchained in this stream, are typically 3 to 8 seconds long (by comparison, the repetitive low level pulse group of the other stream is typically about .5 - 1 seconds - one beat - long). Expectations and motoric processing are different for the two streams: the first stream, the pulse, arouses expectations of repetition; the second, unfolding stream brings thesis and antithesis, change and contrast (Clynes, 1986).
Figure 1 shows the measurement of averaged stream-one motoric forms (50 pulses, single level); the stream-two forms have consequently been averaged out. (In these experimental measurements the finger remains in constant touch with the pressure sensor, so that a shape is obtained that implies characteristic repetitive movement - a reflection of the 'inner' pulse, not the disjoint marking or beating of time.)
The two streams appear to be processed differently, but
conjointly by the central nervous system. The motoric processing
of the pulse stream readily tends to be directed to the feet as a
repetitive movement; the second stream is processed to varied
gesture, to the flow of gesture upon gesture. (Or, to picture
both in terms of conducting: the pulse with the right hand, and
the gesture stream with the left -- which is what right handed
conductors in fact often do). Several pulse element group
repetitions (at the lower level) tend to occur during a single
gesture. For these reasons the two streams may be well studied
and clearly experienced by separate but simultaneous expression
using two sentographs, the right hand expressing the pulse, and
the left the developing stream (Clynes and Nettheim, 1982), as
the music is being thought in real time, or as a
performance is listened to.5
Viewing the history of music, we may note a progression from
Gregorian chant which mainly employs the second stream, to rock
music which concentrates predominantly on the pulse. In Gregorian
chant pulse is downplayed; in rock, the second, melodic, stream
is subrogated. In the classical period (18th and 19th century) a
fine balance is achieved between the two streams. It was in that
period, we conjecture, that good composers discovered, largely
unawares, how to embody their own intimate pulse into music. The
study of pulses of earlier composers remains elusive and
difficult, and we are not able to say to what extent the concept
may apply to them.
In the kind of music tested in the present study, the repetitive pulse was considered to embody an element of the 'presence' of the composer, the identity of who is telling the story. It was assumed to involve pervasive personality traits (eg. strength, gracefulness, etc.) clearly felt but not as succinctly put into words. (Attempts at verbal descriptions may be found in Becking (1928) and in Clynes (1985, 1986, 1987)).
In making the brief test pieces of this study it was deliberately and largely refrained from adding independent microstructure to the second stream. There was no attempt at phrasing; only the infrequent explicit dynamic markings by the composer, and staccatos were realized.
The aim was to test whether the musical microstructure of the composer's pulse as defined above did in fact have a desirable effect on the composer's own pieces, compared with its effect on other composers' pieces, and further to test if groups of graded musical proficiency differed in their appreciation of the composer's pulse. The tests were also expected to shed some light on the ability of the central nervous system to consistently and meaningfully handle such small differences in timing (in the range of 3 - 15 ms), and associated differences in amplitude.
Subjects consisted of five groups of graded musical attainment. Musical attainment ranged from that of college students who were non-music majors, through that of first and second year undergraduate students at Australian music conservatories, to graduate students at Manhattan School of Music, and at the Juilliard School of Music, whose entrance requirements approximate the graduation level of the Australian conservatories, and finally to a group of highly successful mature artists who have been before the public through performance and recordings for many years.
1. 41 male and female college students, most of whom had some elementary home music training (average of 3.4 years of amateur home studies, 25 M, 16 F).
2. 51 first and second year students at the Conservatories in Melbourne, Australia (29 from the Victorian College of the Arts, and 22 from the University Conservatorium of Music, 20 M, 31 F). Their major instruments of specialization were piano (6), violin (5), voice (7), flute (7), clarinet (6), oboe (2), bassoon (1), horn (1), trumpet (4), trombone (3), percussion (2), guitar (5).
3. 19 graduate students at the Manhattan School of Music (5 M, 14 F). Major instruments: piano (9), violin (2), flute (1), bassoon (2), voice (1), harp (1), trumpet (1), bass (1).
4. 14 graduate students at the Juilliard School of Music (5 M,
7 F). Major instruments: piano (3), violin (1), viola (3), cello
(2), voice (1), bassoon (1), tuba(1).
5. 10 famous concert artists, including Vladimir Ashkenazy, Sir
Yehudi Menuhin, Paul Badura Skoda, and conductor Denis Vaughan (9
M, 1 F). (six pianists, two conductors, two violinists.)
A group of dance students at the Juilliard School of Music was also tested. Their results will be reported separately. Students were largely between the ages of 18-32. The group of famous artists was older, 35-75.
The musical microstructure was created through a program described in Clynes (1986,1987) originally developed on a DEC 11-73, but as implemented on an IBM clone. The score is entered in note names and nominal values for durations, C4 being middle C.. Amplitudes are all equal initially. The program regards the music as a number of 'horizontal' voices. Voices can be balanced for loudness, the balance adjustment applies to all notes of that voice equally. Microstructure is calculated for all voices according to the choice of pulse configuration. 'Pitch crescendo' can be globally incorporated in varying degree, and separately for each voice. This determines the scaling, eg. a fortepiano has a weaker bass and a weaker high treble than a modern grand; and melodic lines tend to favor increase in loudness with increasing pitch height. Microstructure can also be entered for single notes, in loudness, timing and staccato. Timing resolution is 1 ms.
MIDI was used to control a Roland MKS 20 module which specializes in piano sound. Piano sound 2 (a Boesendorfer likeness) was used, and sound quality was optimized by controlling the settings of high, mid range, and bass level, digital programmable features available on the module. The stereo outputs of the Roland MKS 20 were recorded using a Nakamichi Model 680 tape deck.
A. Pieces used. Three pieces each of Beethoven, Mozart and Haydn and one of Schubert, all piano sonatas and in duple or quadruple meter, were selected. Using the program referred to above, renditions for each excerpt were created and played in four versions, each with a different composer's pulse. Thus, one version for each piece incorporated its own composer's pulse ('right') while the other three versions of the same piece had the pulses of other composers ('wrong'). The examples were as follows:
Beethoven Op 7, 4th mvt.; Op 22, 4th mvt.; Op 101, 4th mvt.
Mozart K 576, 3rd mvt.; K281, 3rd mvt .; K 309, 3rd mvt.
Schubert Op 120, 1st mvt.
Haydn H 48, 4th mvt.; H 37, 1st mvt.; H 32 , 3rd mvt.
The first period of 8 bars was used in each case, except for Haydn H 48 and H 32 where 12 bars constituted the opening period. These 10 pieces were arbitrarily chosen among the 20 selected by Repp (1990) of similar length, keeping in mind the criteria for such research listed in Clynes (1990a), such as avoiding strongly ornamented excerpts, and pedal. Two additional pieces initially chosen, composed by Schubert (Op 94 and Op 142), proved to be contaminated. Their left hand accompaniment figures had persistently strong asymmetric note distributions (a circumstance infrequently encountered) which in a computer performance necessarily created a spurious rhythmic pattern that overlaid the pulse. (Other things being equal, as realized on a computer, three simultaneous notes sound considerably louder than just one note). While this can be compensated for, as is done by a human performer, the extent of such compensation in a computer version would have to have been necessarily ad hoc. It was therefore decided to omit or disregard these two examples in the tests. (This kind of problem occurs infrequently as most pieces tend to be well portrayed by a number of voices each of which has a 'horizontal' lineage, and do not regularly alternate note clusters with single notes.6 )
To make a musically usable example with a computer, the voices
were balanced as follows: the inner voices were attenuated, and
the bass voice was made stronger than the inner voices, but less
loud than the melodic line. Pitch crescendo, an increase in
amplitude depending only on pitch height, was applied in a
moderate way in the melodic (upper) voice. Composers' indications
in the score (Urtext) were observed. Staccatos indicated by the
composer were entered individually, and were left unchanged in
their silence duration when the composers' pulses were
interchanged.
No microstructure other than that due to the pulse was introduced
(except staccato as indicated by the composer). Thus there were
no deliberately introduced phrasings, dynamics (e.g. phrasing
crescendos and diminuendos), or superimposed timing changes for
expressive purposes.
Pulse configuration refers to the way the several hierarchic levels of the pulse are constituted. For the examples used, we may have a 4 x 4 configuration, or a 2 x 4 configuration, or a 4 x 2 configuration; each considers two levels of the pulse. The first listed is the level with the fastest notes. (The matrix values for the 2-element pulse are derived from the 4-element pulse using the two simple rules given in the section "Application of the pulse to the score", cf. also Fig. 2). Whether to use a 2 or a 4 on a particular hierarchic level cannot be simply deduced from the meter and time signature; the choice requires musical judgment on the part of the user. Mostly, it is not simply congruent with meter signature, i.e. the composer's choice of meter does not itself define the pulse configuration. The character of the piece is altered strongly with different pulse configurations. Since composers do not specify the levels (at least, they did not in the past), it is part of the interpretive task to chose an appropriate pulse configuration among several, most often two or three, alternatives.7 (Had the examples been longer, a three level pulse configuration would have been used, as is usual in the interpretation of entire pieces using the hierarchical pulse.)
This interpretive task is becoming increasingly focused by the concept of the hierarchical pulse structure. A contemporary composer now could specify this in his or her music, thus giving far more precise interpretive instructions than composers were able, consciously to do in the past. (A conductor often faces a somewhat similar but simplified question, as he or she decides whether to conduct a particular piece in "two" or "four". But in our considerations we are concerned also about the subdivisions of the beat).
A given piece in 2/4 time, with sixteenth notes, such as the Beethoven Op 7, fourth movt. example, could have a 4 x 2, a 4 x 4, a 2 x 4, or less plausibly a 2 x 2 two-level pulse configuration (we are not considering the third level here). 2 x 4 is the appropriate choice, with four eighth notes forming the second-level group - which here is the main pulse level - and two sixteenth notes forming the lowest level.
Occasionally, in some pieces, the relation between the second-level pulse and the notated meter is phase-shifted, from the beginning of the piece, i.e. there is a second-level-pulse upbeat. This was the case for the second Mozart piece (here we use the first eight bars; actually, later in the piece, after the first 16 bars, the pulse reverts to being in phase), and for the Schubert piece.
The values for the composers' pulses, as given in Table 1, were derived from a selected set of pieces for each composer (Clynes 1983). Experience has since shown that different hierarchic pulse levels within a piece, and pieces in different tempos, participate to a different degree in the pulse (ie.. have different 'loadings' of the pulse; that means the warp, usually the duration warp, is less pronounced, though of the same relative proportions). This is a second order effect and was anticipated. For this reason, almost from the outset we introduced attenuation factors (Clynes, 1983), which allowed one to vary the loading of the pulse, ie.. the degree of warp, at different hierarchic levels. Separate attenuation factors were made available for the time and the amplitude warp parameters of the pulse. The attenuation factor reduced or increased loading, (i.e. the deviations carried by all the pulse components) proportionally for all pulse components (either time, or amplitude), without changing their relative configuration and proportions.
We know now, that the points on the frequency (tempo)-dependent loading curve at which the original determinations were made in 1983, were not equivalent in tempo and character from one composer to another. For example, we used mostly songs and song-like melodies for Schubert, fast movements for Haydn, and so on. As a result, experience has shown that the attenuation factors with respect to the original values given in 1983 tend to need to be different for different composers at 'equivalent tempos', if there is such a thing, particularly for the duration parameters of the pulse.
The pieces selected required relatively little or no attenuation for the Haydn examples, nor for the Mozart duration parameters. For Beethoven and Schubert duration parameters however, an attenuation factor of the order of about 0.5 was often required for some higher pulse levels to avoid exaggeration. Such attenuation factors (given in Table 2) were of course also applied to the "wrong" pulses, without which they would have sounded more wrong.
With respect to amplitude there were serious constraints: by using the Roland MKS 20 piano module, which appears to have the best piano sound available for the purpose, and MIDI, we faced the limitations of a constricted total dynamic range (127 steps, 7 bits) with usable tone quality for less than half that range (the sound too rough and harsh at higher levels). One needs to balance the voices (inner voices softer), which uses up part of the range, so that only the top melodic line has even this restricted range available; the others are restricted to an even narrower range. When the pulse levels are multiplied together, as they are, the range of amplitudes required increases geometrically as a function of the number of levels (the ranges of each level are multiplied together). The available resolution through MIDI, especially for the softer accompanying voices is far from adequate.
A further considerable problem lies in the deliberate
nonlinearity even with respect to equal dB steps for equal
voltage steps of the design and construction by Roland. It
provides strongly changing harmonic content for single piano
tones of increasing loudness, so that they get louder as much
through increasing harmonic loading as they do through increasing
amplitude (higher overtones have a much lower voltage amplitude
for equivalent loudness). Accordingly it is not quite simple to
translate the linear amplitude parameters into an equivalent
scale using this module, and care needed to be taken in finding a
usable range, and scaling the amplitude parameters in that range.
A further complication is that 0 amplitude = - infinity db!
The amplitude values of Clynes (1983) were derived for sinusoidal
sound, for scientific reasons, to eliminate the effect of timbre
as a factor. The attenuation factors permit one to apply them
effectively to piano sound.
The examples chosen were realized with parameters shown in Table 2.
Fig 2. illustrates the first example by Haydn
and the pulse configuration used. The microscore for the first
four bars is shown in Table
3 with the Haydn pulse, and (in parentheses) with the Mozart
pulse .
Subjects were asked to listen to a recorded tape of all the pieces. Each piece was heard in four versions in succession, in quasi-randomized Latin square order, but so that the 'right' version was not the first version heard in any of the pieces. The tape was played once.
For most subjects, the music was presented in a group setting, with subjects sitting well apart so as to not influence or copy from one another. The music was reproduced only with high quality stereo speakers and audio equipment in carpeted rooms relatively free from excessive reverberation. (This is an important requirement for obtaining reliable results (Clynes,1990a)).
Subjects were instructed that ''You will hear a number of musical excerpts, performed in four versions. Consider the relative aspects of the performances for each. Indicate how musically appropriate to the piece and composer each version is, scoring each from 1 (poor) to 7 (very good). For each new piece, circle the most preferred version. Please be sure that all performances are marked and rated." Subjects were also asked to rate their familiarity with each piece on a scale of 0 to 2, 2 being very familiar.
The pieces were played in the same order for all subjects. The Beethoven pieces were played first, followed by the Mozart pieces, then Schubert, and then Haydn, in the order listed in the previous section. Subjects were given the composer of each piece. Performances were separated by about 10 seconds of silence. The duration of the tape was about sixteen minutes.
A few (5) subjects heard the tape individually on Hi-Fi equipment at the author's laboratory at Queens College, University of Melbourne. Seven of the famous artists did the test in their own homes. In those cases, the tape and the scoring forms were sent to them. It is not possible to be quite certain that some of these artists did not listen to some of the pieces more than once before scoring them, though they were requested not to do this. As professional perfectionists who are inclined to do any such task as perfectly as possible, the temptation may have been considerable in some cases.
Results were analyzed with ANOVA using repeated measures, with Groups, Composers, Pieces and Pulses as independent variables, with Ratings as the dependent variable. Results are depicted in Figures 3 - 7and Table 3 and Table 4. Results may be summarized in two main points:
1.) There was greater preference for the 'right' pulse, as evidenced by higher rating scores, as musical training and proficiency increased. This is shown by the patterns of scores given in figures 3 - 7
2.) There was a general stability across groups of relative preferences for performances of individual pieces, for pieces, and for composers. But preferences grew more differentiated, and patterns of choice grew more pronounced across the groups (figures 6,7).
The complete statistical summary of the results is presented in Table 4; highlights are here described verbally. For the absolute ratings, three out of four composers yielded Group effects, and typically this reflected the fact that the musically less experienced subjects gave higher ratings on average to the pieces than musically sophisticated subjects. The various pieces yielded different ratings: for Beethoven the third piece was rated reliably higher than the other two; for Mozart, the third piece was rated reliably higher than the other two; and for Haydn the first two pieces were rated reliably higher than the third. The Group x Piece interactions were typically not reliably different, and the marginally significant one for Beethoven reflected the lower ratings by experienced musicians for pieces one and two, but substantially higher ratings for the third piece. Inexperienced musicians liked all pieces more evenly.
Figure 5. "Right" and
"Wrong" scores for each group and each composer.
The effect of pulse was very substantial for all composers, and invariably this indicated that the 'right' pulse for each composer was always rated higher than the 'wrong' pulses. The reliable Group x Pulse interactions in all four analyses indicated that the experienced musicians exhibited selectively higher ratings for the pieces played with the appropriate pulse, while inexperienced musicians typically exhibited that relationship less clearly. The reliable Piece x Pulse interactions typically indicated that the correct pulse exhibited selectively higher ratings more for some pieces than for others. Indeed, for all three composers, the largest differential was apparent for the first piece of the series, which may suggest some type of primacy effect.
For the right minus wrong comparison, there were again reliable group effects, which generally indicated that better musicians exhibited larger differential scores than musically less proficient individuals. The fact that certain pieces exhibited reliably larger differentials was not deemed to be of theoretical importance, and the small Group by Piece interaction for Beethoven merely indicated that the best liked piece (#3) tended to be highly rated by everyone, while the other two pieces were rated somewhat lower by the experienced musicians.
The most important finding was the robust "Accuracy" effect, which reflected that for all composers the ratings for the correct pulse of a composer was always rated higher than the incorrect pulses. The reliable Groups by Accuracy interactions always indicated that this differential preference was always clearer for the more proficient musicians than for the less proficient ones. The Piece x Accuracy interaction indicated that this last effect was larger for certain pieces than for others: For Beethoven the largest differential was for the second piece; for both Mozart and Haydn, the largest differentials were for the first piece. The reliable three way interactions of Group x Piece x Accuracy for Mozart and Haydn indicated that these large differentials were quite prominent for the experienced musicians and not very large for the inexperienced ones.
Figure 3 shows the differences between the 'right' and 'wrong' scores for each group of subjects. The 'right' score is the score for the performance with the pulse matching the composer. This difference clearly increases with subjects' musical standing. The 'right' score minus the mean of the three 'wrong' scores for each performance was averaged across subjects.
Figure 4 shows mean 'right' and 'wrong' scores for each composer for all 112 musicians.
Figure 5 a, b, c, d, e shows 'right and 'wrong' choices for each group and for each composer, as well as for all composers together. The figure shows that scores for the 'wrong' pulses tended to decrease with increased musical standing, whereas scores for the 'right' pulse were relatively stable. Thus the differences between the 'right' and 'wrong' choice (Figure 3) increased with subjects' musical standing mostly as a result of a decrease in the scores for the 'wrong' pulses, not an increase in the scores for the right pulse.
Figure 6 a, b, c, d, e, f shows the mean scores for each of the 16 pulse-composer combinations, for the five groups separately, and also for all subjects together. Notable is the growth of the pattern across the groups, with the relative preferences becoming generally more accentuated with increased musical standing.
Table 5 shows the mean values for each of the 16 pulse-composer combinations for each of the five groups, and for all musicians together. The 'right' values are the highlighted diagonals of the square arrays, and these would be expected to have the highest values. This is true in every single instance for all the four musician groups. That means, that for all those groups the Beethoven pulse received the highest ratings in Beethoven's music, and similarly for each of the other composers.
But for the non-music students this was so only for Beethoven;
for Haydn and Schubert the 'right' values are second highest, and
for Mozart lowest.
The entire order of preference by the five groups is given in Table 6. The first data line, for example, indicates that for the Artists, the Beethoven pulse received highest ratings in the music of Beethoven, second highest in the music of Haydn, third highest in the music of Mozart, and lowest in the music of Schubert.
It is interesting also, in regard to the meaningfulness of the pulse, to note for which composer of the four each pulse was rated second best. The Beethoven pulse received the second highest ratings in Haydn's music, in all groups, including the Non-music Students. The Mozart pulse also received second highest ratings in Haydn's music by all four musician groups. The Schubert pulse received second highest ratings in the music of Haydn by the Artists, but not by the three other student musician groups, who rated it second highest in Beethoven. The Haydn pulse received second highest ratings in Schubert's music by the Artists, but not by the other three music student groups, who rated it second best in Beethoven.
The consistency of this order across musician groups is remarkable. This consistency comprises a non-commutative, nonlinear order. Thus, for example, the Beethoven pulse was consistently third and fourth in the music of Mozart and second in the music of Haydn and of Schubert; the Mozart pulse was third in Beethoven and fourth in Haydn; but the Haydn pulse was second in the music of Beethoven and in that of Mozart, and third in the music of Schubert.
Furthermore, a similar degree of consistency, with occasional pairs of subordinate choices inverted, is obtained when one looks at the order of preferences across composers, rather than across pulses as in the above, as the reader may readily note from the ratings results given in Table, comparing them in a vertical, rather than a horizontal direction.
Figure 7 shows right-wrong differences for each of the ten pieces, for different groups. The groups scored similarly relative to the pieces, but with increasing discrimination as musical standing increased. The figure shows increasing positive values; the right pulse was preferred in nine out of ten pieces. The third Mozart piece was the only piece for which the 'right-wrong' difference was negative, and it was so, remarkably, for all groups. It tended to be equally preferred with a Haydn pulse. The second Haydn piece tended to have rather low, but positive values.
The relative saliences of the rating scores of the various pieces tended also to be consistent across the various groups, notably including the non-musicians.
A statistically significant but small main effect was found for both Composer and Pulse.
Overall mean scores for Composer across all subjects was 4.01, 3.80, 3.67, 4.00 for Beethoven, Mozart, Schubert, and Haydn, respectively, with a standard error of .042.
For Pulses, the ratings were 3.99, 3.66, 3.95, and 4.04 respectively, with a standard error of .040. Thus on the average the pulses of Beethoven, Schubert and Haydn scored almost equally across pieces ('right' or 'wrong'), but the Mozart pulse scored somewhat less [ p < .0001 ]. No musical significance can be given to this observation, other than the suggestion that the Mozart pulse in the wrong music may be more invidious. The reason might lie in the sharper subdivision of the beat that occurs in the Mozart pulse (note the prominent 3rd amplitude component, Table 1).
Familiarity ratings obtained from subjects in regard to the different pieces (on a scale of 0, 1 or 2 with 2 being very familiar) showed no significant relation to rating scores.
Although it was attempted to minimize order effects, a small order effect was observed (p < .001) that tended to produce somewhat higher ratings for later versions as each piece was heard in four different versions (cf. Repp 1989). It was thought preferable however not to try to correct the data for this, as the effect was by no means uniform or linear.
On the whole, the task was experienced by subjects as an interesting one, but not an easy one.
The robustness with which incorrect pulses were rejected by the groups increased dramatically with musical expertise, thus supporting the appropriateness of the pulse parameter configurations given for those composers.
An interesting aspect of the results was that although the non-musically trained subjects had a generally poor recognition of the pulses, on the average even that group showed a trend to identify the appropriate pulses correctly for Beethoven and for Mozart. The pattern of scoring for individual pieces by non-musicians was largely similar to the other groups though less robustly distinguished.
The duration examples were only about 8-10 seconds. With such short musical examples, and a single hearing, the pulse substitution resulted in effects which seemed relatively subtle to the less musically astute subjects. Some interchanged pulses resulted in subtle distinctions even for the most highly musical subjects.
That the scores for the "wrong" performances decreased progressively as musical proficiency increased may be interpreted as a sign that on the whole the wrong pulse tends to be less appropriate (more unpleasant) for those who presumably understand the music best.
In this experiment not all substitutions of pulse could be considered equally grotesque or catastrophic to meaning. The more gross effects of substituting a Schubert pulse in Beethoven, or a Beethoven pulse in Mozart were contrasted with the more subtle differences produced by the substitution of a Haydn pulse in Mozart or in Beethoven. Such distinctions may reflect meaning inherent in the microstructure of the composers' pulse - they are not likely to be interpretable as style similarity or dissimilarity, but rather may be thought in some way to reflect a personal 'point of view' or 'Weltanschauung' of the composers (cf. Becking, 1928)8 . Thus also for example it may be a greater or at any rate a different kind of violation to put a Mozart pulse into Haydn than to put a Haydn pulse into Mozart. The results in Table 5 support such non-commutative asymmetry.
We may try to interpret these findings in accordance with the following considerations. The personality of Beethoven is probably somewhat better known generally than the others. The Haydn pulse seems playful, pleasant (for additional qualities, see Clynes 1987), so that it can to a degree give some positive and appealing aspects to some music where it does not really belong. The Mozart pulse appears to provide a degree of abstraction, and gracefulness, a 'spectator' point of view, rather than that of an 'actor' as does Beethoven (Clynes 1977, 1987). Accordingly, it may not be surprising that the Beethoven and Mozart pulses seem to be more opposed to one another than the others. The Schubert pulse has a special character in its elongation of the second pulse component; it tends to create a sense of longing for a [spiritual] home that makes it quite different from the others (Clynes, 1987). With increasing musical astuteness, it turns out that subjects attribute the pulses correctly to the right music in spite of alienating factors: joyful music of Beethoven is preferred with a Beethoven pulse rather than with a Haydn pulse, for example, even though the Haydn pulse itself has joyous aspects which the Beethoven pulse has not.
Exceptions: can we conjecture reasons why the third Mozart piece was rather consistently preferred with a Haydn pulse? It seems hardly correct to say that these first eight bars were more akin to Haydn's writing than to Mozart's. But we could perhaps venture that the theme is not particularly good Mozart; largely a downward scale, it is perhaps barely this side of banality (assuredly it is then followed by a most Mozartian episode, but this was not given to the hearers to enjoy). A less likely explanation might be that the pulse configuration chosen was incorrect for this piece. But other experience does suggest that nondescript music is made more pleasant by a Haydn type of pulse (Clynes, in preparation). The argument might perhaps be buttressed by considering that a scale-like passage is basically neutral; that it can take on any pulse, and does, whichever composer uses it. Given that, it may here show up the intrinsic pleasantness of the Haydn pulse. All this is only conjecture of course, and it would be good to do a separate experiment with a longer excerpt from this piece, to establish that then it too would be preferred with a Mozart pulse.
In the case of the second Haydn piece, we have a marginal instance: The piece has ornaments that give it extra accents, and it has a massive chord at the beginning, which cause methodological problems (Clynes 1991). Do those factors, given the short course of the excerpt, account for the comparatively low score in its favor? They may be expected to influence the result, but we cannot estimate well to what extent. Again, a longer section of the piece where these effects are diluted may provide the answer. Certainly one would then expect this piece to do well, being thoroughly Haydnesque.
In comparing the groups, overall, it was surprising that
musical perception, taste and judgment displayed such a
consistent picture in terms of relative ratings. Such stability
across groups lends support to the stability of musical
meaning, experience, and musical language across such
populations, and in particular to the pulse microstructure forms
as meaningful and understandable elements of musical language.
The author stresses that the pulse parameter values used in these tests are a first approximation to the composer's pulses (Clynes 1983). They are not definitive, but are expected to lead to refinements in the values with accumulated knowledge and experience, by artists with understanding of the composers concerned. Further refinements can then be tested with panels of artistic judges, as to agreement on values or changes in values.
It has been our experience since the original suggestions of pulse parameters in 1983, that the value of 107 for the first pulse component duration of a Mozart 4-element pulse produces an overall more graceful character of performance than the 105 value which was originally recommended.
Obviously, gracefulness is not always desired; and increasing the value beyond 107 does not continuingly increase gracefulness. However, gracefulness clearly has a place in the music of Mozart and an applicable parametric range, to be determined.
Studies in which otherwise identical Mozart performances are
compared by a panel of judges may now be conducted to confirm
this as a more general test of "gracefulness" both as a
concept and as its applicability to Mozart; as one investigation
of the effects of small changes in the parameters (Clynes 1990).
Similar studies may be expected to shed more detailed light on
the interrelation of pulse parameters and meaning.9 The gross substitution of one
composer's pulse for another, as in this study, is only a first
step.
The choice of attenuation factors at the various levels is
subject to artistic judgement, as is the tempo when not
prescribed in detail by the composer. These factors influence the
pulse values in a second order sense (a diminution or
enlargement, while they maintain the relative deviation
proportions). The choice of pulse configuration cannot be
automatized. Nor of course can the choice of tempo. It cannot be
emphasized too often that the pulse, and also predictive
amplitude shaping, are not mechanical: their application depends
on one's concept of the piece. They can give rise to a plurality
of interpretations with differing meaning.
Repp and also Thompson have reported results of experiments with the composer's pulse, some of which use the same music as in the present study. Viewing the results of Repp (1989, 1990) in light of the present study, the following points may be made:
The largely favorable results of the 1989 study were obtained with entire pieces, or major sections of pieces. The choice of pieces was Repp's, thus random with respect to all the pieces of that composer which might have been chosen and with which the author might have had experience. All the 'correct' pieces in quadruple time achieved highest scores, with the exception of the Beethoven piece (Op 10 No. 2, third Mvt.), which his subjects preferred with a Haydn pulse. That same piece was correctly recognized in Thompson's experiments (1990) in which he made sure that the music was appropriately reproduced. (Repp had played it in a classroom on a small portable tape recorder with an built-in speaker, and also without Dolby, in a class room, thereby accentuating the high frequencies and diminishing the bass the strong presence of which is important to realize the Beethovian character in that piece. His repeated runs using Dolby were done with only a small number of subjects.)
The studies of minuets in 3/4 time are not considered suitable for composer's pulse identification, as (a) the values for 3/4 pulse have not been as well established, (b) pieces in 3/4 time offer less opportunity for identification, having only four degrees of freedom instead of six for the 4/4 pulse, and (c) minuets have their own distinctive pulse character which may combine with the composer's pulse in a varied and unknown manner (Clynes 1990a).
Concerning Repp's (1990) study however that includes the same
examples as the present study, it needs to be noted that it was
made:
1. With very short excerpts, as in the present study
2. With different pulse configurations than in this study for
many of the examples
3. In single level pulse configurations
4. With a computer tick of 5 msec., not adequate to resolve the
pulse structure.
Repp's (1990) results were from a subject population largely
similar to the 'non musicians' of the present study. The results
of that study were generally statistically similar to those of
the group of 'non musicians' of our study, notwithstanding the
shortcomings of his microstructure realizations (an added 'noise'
element - in both the statistical and musical sense - that could
be expected to affect the scores of subjects). Ongoing work with
four times longer excerpts (32 bars), as well as Repp's own
(1989) study, suggest that non-musicians can discriminate better
when given a longer performance sample.
Regrettably, Repp did not systematically investigate groups of
graded musicality in regard to the pulse with appropriate musical
materials.
Thompson's and Repp's studies positively substantiate the ability of listeners to clearly and reliably discriminate pulse microstructure, when one composer's pulse is substituted for another. In addition, in the case of Repp, his findings document the reliable ability of listeners to distinguish between versions of music with or without microstructure.
It would have been possible to use a "finished" computer performance that included as much appropriate expressiveness as possible, and still exchange 'right' and 'wrong' pulses for test purposes, but this approach though useful was not taken in the present study. It would be interesting, to study whether different results are obtained by using performances perfected as far as possible with regard to an interpretation, before switching pulses are switched. The question is whether the favorable, maintained aspects of the performance would weigh towards excusing a 'wrong' pulse, and, if so, with what kind of listener. The experience of the author suggests that with more perfected performances, the wrong pulse becomes increasingly obnoxious to musically acute listeners, standing out as a single factor that is grossly inadequate. But for nonmusically-acute listeners, it is possible that the results may not be as clear.
This question is of relevance to studies of art in general. To what extent does each feature derive its appropriate meaning only in context of the whole? The question is, as with all non-linear phenomena, at what contextual stage can one intrude into these interactions experimentally and not be thrown into a different experimental domain.
Yet in the present examples, the pulse was by itself sufficiently expressive in some examples, so that Yehudi Menuhin wrote, after doing the test, that "only in the case of Haydn H 48, last movement, was it a 'finished performance' ". He wondered why all the examples were not as perfect as this! It could not be explained at the time to subjects that what they heard included only the pulse as microstructure.
The present study attempted to study the pulse as a linguistic element of music. Time-forms, as elements of musical linguistics, are the subjects of such research: time and amplitude work together to create meaningful time-forms, as in spoken speech - one without the other is rather like slicing a face in two to discover its expression. Musical linguistics aims to study time-forms as integral combinations of time and amplitude, and the other expressive variables listed at the beginning of this paper.
How may such time-forms be studied? They arise through the integral combination of structure and microstructure. In the musical interaction of pulse and structure, structure is represented by the musical design and by bar structure, from which the hierarchical pulse configuration is elucidated (stream one). Melodic structure combines directly with the microstructure of predictive amplitude shaping (Clynes 1983, 1985, 1986, 1987), to form meaningful time-forms, such as phrases, involved in telling the "emotional story" of the music (stream two). Phrases may frequently be formed by action of predictive amplitude shaping, and may turn out to be in accord with the composer's phrase indications; a natural phrasing process that often appears to work, unwittingly recreating the effect of the composers' markings. In Clynes (in preparation, MIT Press) these processes are described in detail, along with a CD disc that contains the corresponding music.
Nature's programmed communicative and contagious time-forms, such as those well-known ones of laughter and yawning, also are seen to act for specific emotions, such as joy, grief, anger, love, and reverence (Clynes 1973, 1980, 1988, Hama and Tsuda 1990, Aggleton and Mishkin 1986, Minsky 1987). Their respective trajectories are considered to be incorporated implicitly by composers (Clynes and Nettheim, 1982) by musical structure, often melodic structure, through pitch and amplitude time-forms. According to this view, such biologically based emotionally expressive forms (sentic forms) potentially built into melodic structure by the composer need to be specifically brought to life to the listener by amplitude shaping and microstructure (Clynes and Nettheim 1982, Clynes (1977, 1973, 1988).
The particular microstructure that provides meaning does so only in proper measure - when exaggerated the effect becomes grotesque. This is significant linguistic a property which needs further experimental study.
A dictionary of musical linguistics which one hopes will not be too long in forthcoming as an achievement of musical linguistics through computer synthesis, would represent what is being discovered in the field of musical linguistics through computer synthesis: Its entries would be entities of musical meaning - phrases and motifs together with their microstructure - joyful, sad etc, though verbal descriptions are too imprecise, generally. Computer synthesis can thus potentially resolve the seeming linguistic paradox that, as Felix Mendelssohn said : "Music cannot be expressed in words, not because it is vague but because it is more precise than words".
Serial processing remains one of the main largely-uncharted areas of central nervous system function. How does the brain organize and produce the serial nature of speech processes? Perceive them as serial? No one knows. Yet music can tell us a good deal about the nature of time consciousness, time perception, and memory processes. A few remarks concerning this may be permitted here. For a more detailed account, dscribing four distinct time brain processes involved in music (t1,t2,t3, t4) see Clynes (1994).
The precision of clocks in the brain enabling music to be thought and played with a time stability of one part in 500 under very widely varying conditions has been documented (Clynes and Walker, 1986). An entire well-studied piece of music appears to reside in the memory of a good performer extended as a fixed chunk of time (Clynes and Walker, 1986), so that changes in duration of one part often are compensated for by changes in another part that maintain the overall duration.
The perception and execution of the small time differences that create the personal quality of the composer's pulse however have a different mode of processing in the brain, it would seem, involving "local" temporal grouping. Typically in the range of + 20 milliseconds (corresponding to four sixteenth notes played at 80 MM. per quarter note), they thus typically involve the perception of a difference say between a duration of 200 msec, and 220 msec (100 and 110 in the pulse matrix). These durations fall in the realm of the "present moment" (about 180 msec, Clynes (1977) - the time during which a decision cannot be reversed, the time it takes for a syllable, and the time in which the minimum perceptible visual angle of motion can be traversed and yet be seen as stationary (cf. the minute hand on a watch). Such durations are perceived as single entities, a "tone", or a corresponding "rest". Four of these (or three, in triple time) are heard as a group, and together with other such groups provide the perception of "tempo". The pulse character, at its basic level, however, lies in the structure within the beat, and thus is perceptually separated from the experience of tempo (the same tempo may be played and heard with different pulses and vice versa).
Specificity and precision of thought is key to the right pattern within the beat. Precision here derives from the quality of feeling that goes with the pulse. Moreover, the pulse is repetitive: Once its quality has been thought, it can then be retriggered automatically without much further attention (timeform printing by the nervous system, see Clynes and Walker, 1982). Within a performance, differences to change the pulse character would have to be specifically commanded by the brain, otherwise it will tend to repeat the earlier pattern.
The higher level pulse concerns itself more with structural organization, the repetition and development of phrases, each time with a somewhat different character, giving a flow to the music. Here memory in the time range typically of 5 to 20 secs. plays a central role: the next phrase or motiv is always heard in context of the previous one - getting more emphasis or less emphasis, an "answer", or a subtly different character.
The brain automatically perceives these differences. It remembers them clearly, not by numbers, but by the feel. As in playing golf or in target practice, human 'expert systems ' can master these differences, programmed by the cerebellum and also the amygdala (Aggleton and Mishkin 1986), as the tools of the performing artist.
For further discussions of how small differences in time forms
can also make big differences in feeling and perception, through
predictive amplitude shaping and especially with sentic forms,
see Clynes (1977,1986 a,b), and Clynes and Nettheim (1982) and
Clynes, in preparation, MIT Press.
* * * * *
We may look forward therefore to the development of musical
linguistics in which meaningful time-forms can be investigated as
language elements, which would necessarily include
microstructure. Musical meaning cannot be studied from
macro-structural properties alone.10
Computer control of the minutiae of these forms11
- the achievement of microscores - can teach us about the
language of music and how that language may be founded in human
nature.
One may conclude from the present study that the composer's pulse is a valuable element of musical linguistics, one which appropriately enhances meaning. There are clear indications that a composer's pulse is favored as a constituent of microstructure for that composer's music; and favored the more, the higher the musical proficiency. Confidence in the findings is enhanced by the unexpected, and in itself remarkable stability of preferences across groups. Evidence of systematic interpretation by listeners of small changes in duration in the millisecond region in context of a meaningful pattern has been found. Further studies are indicated that could help to explore links between brain function, emotional expression and musical microstructure.
Knowledge of the microstructural principle of the composer's pulse can aid today's composers to define their own music in a way past composers have not been able to do. Ability to produce musical meaning in music that predated quantitative conscious knowledge of microstructure may be aided by cognitive science, in a way that could help to make our finest music heritage potentially be betİer understood, and of more interest İo a greater number of people. Perhaps it could gradually become clearer how a better understanding of the language of music is also a better understanding of ourselves.
The author wishes to thank the many musicians who contributed their time to this study, and especially those famous artists who might well have refrained from participating in view of the heavy demands on their time, if not for their interest in the subject, and for some, personal friendship. Robert Abramson who teaches at the Juilliard School of Music was responsible for testing the groups at Juilliard and Manhattan Schools of Music, and I wish to thank him for this, and for his continuing interest, understanding and support for the concepts behind this study. The Anova analysis, and description of its results were carried out most generously by Jaak Panksepp, of the Department of Psychology, Bowling Green State University, Bowling Green, Ohio. Helpful statistical assistance and advice was received from P. Patinson, of the Department of Psychology of the University of Melbourne. Martha Mills, of council, Smith, Williams and Lodge, Chicago and Lisa Turetzky, at the request of the editor, generously helped to edit the paper and increase its fluency and clarity. Assistance from a grant of the Australian Research Council, the help of Queen's College, University of Melbourne, its Department of Psychology, and of the Center for New Music and Audio Technologies at the University of California, Berkeley, is gratefully acknowledged.
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(under construction) Note: Copies of the test tape used are available from the author.
Figure 1. Reprinted by permission, from M.Clynes, Toward a View of Man, in Information Systems of the Nervous System, ed. N. Leibovic and J.J.Eccles 1969, Springer Verlag. The motoric composer's pulse measured through conducting on the sentograph with finger pressure, in a seated position, while thinking the music in real time (without sound). Each trace is an average of 50 pulses; tempo was constrained to be MM. 60 per minute with a synchronizing light. Shapes are distinctive for each composer, regardless of piece, and of subject, in this group of artists.
Figure 2. Haydn Sonata No. 48 (Hoboken), last movement, showing two-level pulse configuration. Level 1 is two sixteenth notes, level 2 is four eighth notes. See Table 2 for the microscore for the first four bars.
Figure 3. Differences between 'Right' and 'Wrong' scores for the five groups. The standard error of the mean is indicated above each bar.
Figure 4 'Right' and 'Wrong' scores for composers separately, all subjects except non-musicians.
Figure 5 a, b, c, d, e 'Right ' and 'Wrong' scores for each group and each composer.
Figure 6 a, b, c, d, e, f Mean scores for each of the 16 Pulse - Composer combinations, for all five groups, and for all subjects together. Standard errors of the mean indicated as in figure 1.
Figure 7 'Right'-'Wrong' differences for each of the ten pieces, shown here for three groups (instead of five groups, for ease of visual presentation).
Footnotes:
1. One of the noted poets of our century (E. Pound) said of this precision: "...[it is] the deepest secret of music, i.e. that precision with time which distinguishes the best from the competent, that precision which escapes many conductors... I remember two pleasures of the ear of this kind: one given by Wanda Landowska, the other by a blind beggar singing 'Pepina' in the streets of Ravenna." He might have included amplitude relationships, partaking of a similar precision as time in the eloquent realization of microstructure, were he aware of modern studies, or perhaps had he thought more about that singer.
2. By a "warp" we mean systematic deviations from the mathematical nominal values within a group of pulse elements (pulse components, e.g., four eighth notes or four sixteenth notes , so that four such notes would not be played perfectly evenly, but with small precise time deviations from evenness; and likewise for their amplitudes (with comparatively large deviations from evenness), so that these four notes receive particular amplitude relationships to one another. The time warp exists whether or not there are actual notes occupying that time slot. A note of several pulse components duration has a duration that is the sum of the pulse components it occupies; it has an aplitude given by the amplitude of its first pulse component. Other microstructure in general superimposes on this time-amplitude warp.
3. Under this theory, it is not to be expected that actual performances provide a completely consistent and sustained panorama of the pulse; rather that the pulse appears in various parts of the piece with greater or less consistency, perhaps somewhat like a signature that appears often. Measurement of these nuances from actual recorded performances are difficult, and generally have not been successfully carried out for amplitudes, only for timings, and only of piano performances of relatively simple pieces (for a view of pioneering work, see Gabrielsson, 1986). But it is easy to recognize, once the pattern is known, in actual performances at salient points of pieces, for example in the Beethoven performances by Klemperer, the Schubert performances of Bruno Walter (C major Symphony, New York Philharmonic), and so on. Note that the pulse may not be present in many performances by well-known artists who are relatively less au fait with the world of that composer.
4. Starting from sixteenths notes, eighth, quarter, half and whole notes each in turn have double nomnal duration.
5. In this process the motor pulse expressed by the right hand tends to be also modulated in intensity by the second expressive stream; that is, it is a conflated expression of both stream one and two; but the left hand expression does not contain the pulse, and is solely an expression of stream two.
6. This does not affect the generalizability of the pulse itself; it means only that at times one needs to accommodate extra notes outside the usual voice, which may or may not lead to locally increased loudness, depending upon the accommodation. The result could be a local coloristic harmonic effect, an accent, or both. In some cases the effect may be to produce syncopation, sometimes repeated syncopation, in which the composer's pulse is effectively temporarily denied, shifted or counterbalanced.
7. Note that changing the pulse configuration does not change the basic pulse matrix of the composer, only how the pulse acts at each level, for example whether it is a two- or a four-pulse at that leve. The timing and amplitude values of a two component pulse can always be derived from those of a four-component pulse by the two simple rules given in Section 1.6.
8. How are the emotional qualities of the pulse stream distinguished from those of the "story" stream? Is there not a confusion here, a lack of parsimony in the explanation, or theory? The emotional charge of the pulse has a different function of that of the second stream; it represents more an attitude, a perspective, even a bias, perhaps; a maintained stance from which the "story" is told by the narrator, whose personality is reflected, and to a degree communicated in the pulse. As a more widely familiar analogy, compare for example the "pulse" of a Clinton speech with that of Kennedy, or Reagan - a comparison entirely possible regardless of the content or "story" of the speeches.
9. The concept o the composers' pulse has been of considerable help in teaching performers to play with more meaning and expression, according to Robert Abramson of the Juilliard School of Music.
10. For example, Schenkerian analysis, harmony and counterpoint, and other kinds of analysis in which neither time nor amplitudes are given sufficiently detailed and quantitative consideration.
11. A recent performance of a Mozart piano sonata (K.330) by the computer with this method along with six of the best CD performances available (including Arrau, Horowitz, Alicia de Larrocha, Mitsuo Uchida, etc.) as a kind of musical Turing test showed that the audience, including several music panelists, at the Annual Meeting of the AAAS could not tell which performance was the computer, and moreover rated the computer version as second or third best among the seven performances (Clynes, 1993).
Manfred Clynes
