Music Theory, Theories of Music, and Systematic Musicology

  • PDF: https://www.jstor.org/stable/40374146


INTRODUCTION

It is a sobering experience to serve as the respondent to a series of articles which has "Developing Theories of Music" as its general concern. My response will not offer novel theories, but it will examine the literature in the areas of sociomusicology, psychoacoustics, and psychomusicology, and it will offer observations that must be made and questions that must be addressed somewhere during the process of theory formulation.

In presenting some of these observations and questions, I will take the role of music theorist; in presenting others I will take the role of music theory teacher. As later discussion will indicate, these two vantage points can be remarkably dissimilar. "Music theory" as a member of the undergraduate music curriculum is a breed apart from many "theories of music" discussed in graduate seminars and at professional conferences. There are those in our fold who make a snide distinction between the "real theorist" and the "mere theory teacher." However, most of us get to wear our music theorist hats just for the duration of meetings and then exchange them for our theory teacher hats when we return to our own campuses.

I will begin by taking a somewhat irreverent look at the domain of music theory. I will then examine some past and present relationships between music theory and the human behavioral areas of systematic musicology, with an emphasis on measures of pitch pattern perception. I hope that this examination will help to identify some problematic aspects of research methodology in both domains. My intention is simply to address some of the obstacles in our common path.

MUSIC THEORY AND THE EXPERIMENTAL DOMAIN

The mainstream of music theory today may be compared to the mainstream of psychology as it existed around the time of Gustav Fechner. Music theory is (and psychology in the mid-nineteenth-century was) primarily a philosophical domain dealing in qualitative assertions produced by deduction and supported by the testimony of experience. Since the time of Fechner and Pavlov, psychology has increasingly emulated the so-called "hard" sciences both in its definition of theory and in its manner of theory testing. For the scientist, a theory—no matter how plausible, no matter how provocative—must be tested before it gains full acceptance. To the extent that it can be tested in a systematic and specifiable manner, and those tests replicated, the theory is substantiated. Musicians who deal in theories of music have largely managed to escape this set of Germanic biases. "Music theory" commonly consists of a description of materials and conventions of construction found in artifacts crafted by the best musical artisans of some earlier time. Theories of music tend to be neither predictive nor testable—supportive excerpts from the performance literature and persuasive argument suffice where controlled experimentation does not seem to fit.

Theories of music have predominantly taken as their foundations either superparticular numbers or seductively similar relationships of the physical components of complex sound waves. Poland and Deutsch have examined the historical literature and have identified opposing schools of opinion on the foundations of music. One faction—which can be traced back to Aristoxenus—maintains that music is after all a human endeavor, and that a meaningful exposition of music would have to account for human sensory abilities and limitations. The opposing faction—which can be traced back through Heraclitus and ultimately to the Pythagoreans—argues the rationalistic position that we can only distrust our senses and that the truth of music lies in numeric relationships. Down through the centuries the latter position has been the more influential, and the mainstream of music-theoretic literature has tended to give people short shrift, so short in fact that when reading the music theory literature it is easy to stumble across such curious anthropomorphisms as the leading tone that "wants" to move to the tonic, or the tense dominant structure that "begs" resolution, and with it, blissful repose.

This situation would be problematic enough, but there is more to cloud the discussion. I fear that there is not full agreement as to what music theory is, and what it is not, even among musicians. Relatively few, even within the ranks of trained musicians, get a glimpse of any real theorizing by music theorists. Certainly, the baccalaureate music curriculum typically offers only a catechism of introductory terminology and symbology, followed by an historical introduction to conventions of surface level harmonic juxtapositions, formal schemata, and counterpoint. It is probably exceedingly rare that the more formal ideas of Zarlino, Rameau, Schenker, or Yasser get any sort of exposition outside the graduate music theory classroom.

There is more yet to cloud the discussion. A large portion of the experimental literature published in the areas of human musical behavior is contributed by sociologists, physicists, psychologists, linguists, and neuro-surgeons. Symposia that attempt to promote scholarly intercourse between musicians and this bewildering array of experimentalists are usually well attended by people affiliated with music education divisions. People affiliated with music theory divisions are conspicuous by their almost total lack of attendance. This has produced the unsettling predicament that experimentalists, interested in designing stimuli of increasing musical sophistication, have mostly been denied access to those who specialize in rules (and the formulation of rules) of musical composition. Instead these experimentalists have had to go to the music theory texts to find out what they need to know, and the texts have too often presented distorted conceptions of musical rules. Music theory texts tend to begin their descriptions of what music is either by deriving musical scales based on mathematico-acoustic foundations, or by deriving musical scales based on common practice. Regardless of the way scales are derived, the prominence that naturally accrues from their presentation and discussion in the opening pages of virtually all music theory texts appears to have misled some psychologists into believing that scales are tonality generators. There appears to be a pervasive belief among psychologists that scales and the triads derived from them are inherently grammatic, and that these scales and triads function as perceptual templates during the process of musical cognition (e.g., Shepard, Cuddy, Cohen and Miller; Krumhansl; Krumhansl and Shepard). The model and reality have become confused at this point. Scales are no more than collections of notes (if written) or tones (if heard) that are displayed in arrays of convenience (conventionally, with members one step apart). In other words, scales are a musician's alphabet. Like the linguist's alphabet, which prescribes nothing of the time ordering of its members that will ultimately produce grammar and syntax, the musical scale is nonprescriptive with respect to how a composer may choose to order its members across musical time. There are rules for tonal grammar. They might be found in the top cell of Taylor's first flow chart (see article by Jack A. Taylor in this volume of Symposium) and they may sometimes be found lurking in obscure places in music theory texts. They will not be found in a musical scale.

THE EXPERIMENTAL DOMAIN AND MUSICIANS

It is encouraging to find that we face problems such as identifying the role of the scale in musical cognition. Such problems indicate that the study of musical perception is experiencing growing pains; psychologists are starting to encounter problems for which music theorists have no pat solutions. However, it is still too easy to find inherently unmusical paradigms, investigated through inherently nonmusical testing strategies and reported in the literature of this aggregate domain. For example consider the portion of the psychophysical literature on pitch scaling that deals with minimum durations of stimulus tones. The acoustical and psychoacoustical literature (e.g., Olson 1967, Backus 1969) has commonly asserted that pitches must have a minimum duration of 13 milliseconds (msec) to be perceptually identifiable. In fact, Meyer-Eppler1 showed a frequency dependency for such absolute identifications:


 

Hz: 100 200 500 1000 2000 3000 4000 6000
Msec: 45 30 26 20 13 14 14 18

Frequency dependency (in Hertz) of minimum tone durations (in milliseconds) for pitch reported in Meyer-Epler (Note 1).


subjects could identify 13-msec tones in the frequency midrange of about 2 kHz, but tones above and below this optimal frequency range had to be significantly longer before veridical identification could be made. Two factors should be noted in these studies: (1) there was no indication that the subjects possessed any musical listening skills, and (2) the experimental strategy employed classical psychological testing methods in which stimulus tones were presented in isolation or in pairs. Divenyi and Hirsh (1974) studied this durational threshold, but with two significant changes in method. First, the subjects used by Divenyi and Hirsh were all identified as having "some musical training," and all subjects were given intensive training in the experimental procedure. Second, the subjects were presented with a series of three contiguous tones and asked to identify pitch relationships by identifying the pitch contour of the series. This study differed from its predecessors in that both the test subjects and the reporting task were somewhat musical. Two striking results of this study were that the subjects would identify the order of the series components even when the components had an average duration of between 2 and 7 msec; and with frequencies evenly distributed on a Logarithmic scale (physicist's jargon which roughly translates as "equal temperament"), frequency range for this percept appeared to be insignificant, as long as the pitch intervals within the series were sufficiently large.2 Some psychologists might respond that these results are just one more example of perceptual "chunking" and they might be right. But there is a lesson here that should be quite plain. Population differences among the subjects, and reporting mode and judgment task differences can have a significant influence on test results. By the way, a three-tone series with a single-tone duration of 4 msec can be represented in conventional musical notation by drawing a set of three sixteenth notes in 4/4 meter with a metronomic setting of the quarter note equal to 3,750 beats per minute! Just before the metronome would explode, its ticks would produce the rough pitch equivalent of B in the contra octave of the piano. Psychophysical phenomena exist in this microscopic time domain, but music does not. Imagine a set of tones, each 4.5 msec in duration, with a silent interval of about one half-second between each tone. These 500-msec gaps are more nearly representative of the time increments with which musicians work, although a half-second can be a very long time to a psychophysicist. How would you describe this tone series in musical terms? In an informal study employing about half-a-dozen music graduate students and faculty, I found that no one had any trouble describing this series. Descriptions included "notes one, three, four and five of a major scale," "do, mi, fa, sol," and "the first four notes of When the Saints Go Marching In. My example above does not refute the psychophysical thresholds; it does indicate that psychophysical limits are not necessarily the same things as musical limits.

White states that a musical acoustics which ignores psychoacoustics can mislead us (see article by Glenn D. White in this volume of Symposium). We can and should extend this assertion to state that a psychoacoustics of music that ignores higher-order musical cognitive processes can also mislead us. You draw musical implications from psychophysical test results at your own risk.

MUSICIANS AND MUSICIANS

Taylor's review indicates that there have recently been innovations in experimental method: rigid psychophysical measures are increasingly being replaced by testing methods that are more musical. But I think that it would be to our great benefit to attend more closely to our subject populations when we solicit cognitive responses to musical stimuli. Taylor's 1976 study of tonality perception used subjects who were carefully grouped according to various levels of listening skills, but this sort of attention to subject population homogeneity appears to be atypical. The experimental literature in pitch scaling and melodic perception in general contains an amazing looseness in the definition of the prototypical "musical" test subject. You qualify as a "musical" subject in one study if you have performed in any sort of musical group for two years or more, regardless of your formal training in music. You qualify in another study if you own a large enough record collection. You qualify in a third study if you are a music major. Having taught ear training courses to music majors for the past ten years, I know that even the third criterion can hardly be expected to produce a homogeneous grouping of skilled music listeners. Not only do students in music courses vary significantly in listening expertise, but they possess a broader range of listening skills than the experimental literature indicates. A list of those skills which I believe I have identified among my students is shown in Figure 2.

 

I. ABSOLUTE PITCH
A. Absolute pitch recall
B. Absolute pitch recognition
C. Conditional absolute pitch
(Probably dependent on timbral and transient attributes of tones. For example, the ability of an oboist who has apparent absolute pitch recognition when listening to the sound of an oboe, but not to other instrumental sounds.)

II. A. RELATIVE PITCH
B. TONALITY SENSE

III. PERFORMANCE DIAGNOSTIC ABILITIES
(Includes capacities to render astute critical judgments about rhythmic accuracy, dynamics levels, melodic rendition (e.g., phrasing, interpretation), intonation, vocal/instrumental tone quality, ensemble blend or balance.)

IV. PSYCHOPHYSICAL SENSE
(Includes capacities to render astute critical judgments about room ambience characteristics, "sound reinforced" and recorded music fidelities.)

V. EMOTIONAL AND EXTRA-MUSICAL SENSITIVITIES



Although these skills are entered discretely in this list, a musician may possess them all to some degree. Conversely, possession of one skill does not necessarily predicate possession of any other skill. I am only concerned with the first two entries on this list.

"Absolute pitch recall," sometimes called "active" absolute pitch, denotes the ability to produce accurately and instantly any pitch demanded, without cues. "Absolute pitch recognition," also known as "passive" absolute pitch, describes the ability to name any given stimulus pitch without any referential cues. The literature commonly distinguishes between these two well-known types of absolute pitch. On the other hand there is relatively little experimental literature to indicate the power or prevalence of "conditional" absolute pitch, although it is not that rare in my classroom.

"Relative" pitch, the ability to distinguish pitches of tones after having been given a referential pitch, is much more common than absolute pitch. I think that it is commonly assumed that people with absolute pitch also possess good relative pitch. I am not convinced of this. In fact I suspect that many who possess absolute pitch may not possess good relative pitch, but given the types of listening and reporting tasks that both our music students and our test subjects have to perform, absolute pitch can masquerade as relative pitch. Relative pitch deals in intervallic relationships. If these judgments were not instantaneous and nonverbal, they might sound like, "If this tone is that much higher than that tone, this must be an A-flat." Absolute pitch deals in pitch chromas; these judgments might sound like, "This pitch sounds like an A-flat, so it must be an A-flat." In other words, people with absolute pitch (I suspect) use pitch chroma information in their musical cognition, and people with relative pitch use pitch distance information in theirs. Pitch distance information can be useful when brought to bear on such musical problems as tonality judgments. Pitch chroma information does not serve this purpose well, since tonality information is embedded in pitch relations and not in the pitches themselves.

"Tonality sense" may be defined as the ability to make swift and sure identifications of tonal center when listening to a tonal musical composition. Tonality sense is related to, but exists on a musical cognitive level different from relative pitch. I doubt that tonality sense is related to absolute pitch in any way whatever. There may be no positive and universal correlation between absolute pitch and tonality sense. Please do not infer from this that there must then exist some inverse correlation: indeed, there do exist those who possess both absolute pitch and tonality sense.

SUMMARY

I hope that I have shown that we live in a complex corner of the research world. Systematic musicology encompasses several research domains. Each brings to music a different history, a different lexicon, and perhaps a different notion of what constitutes proper research. We have in systematic musicology all the makings of a modern-day tower of Babel. If only for this reason we should never underestimate the importance of open and constructive discourse with one another.



REFERENCES

Backus, J. The Acoustical Foundations of Music. New York: Norton, 1969.

Butler, D. "Some Remarks on Tonality Cues and Tonal Stimuli," paper presented at the Third Workshop on Physical and Neuropsychological Foundations of Music, August 8-12, 1980, Ossiach, Austria.

Cuddy, L., and J. Miller. "Melody Recognition: The Experimental Applications of Musical Rules," Canadian Journal of Psychology, 1979, Vol. 33, No. 3, pp.148-157.

Deutsch, D. "Musical Perception," The Musical Quarterly, 1980, Vol. 66, No. 2, pp. 165-179.

Divenyi, R., and I. Hirsh. "Identification of Temporal Order in Three-Tone Sequences," Journal of the Acoustical Society of America, 1974, Vol. 56, No.1, pp. 144-151.

Krumhansl, C., and R. Shepard. "Quantification of the Hierarchy of Tonal Context," Cognitive Psychology, 1979, Vol. 11, pp. 346-374.

__________. "Quantification of the Hierarchy of Tonal Functions Within a Diatonic Context," Journal of Experimental Psychology: Human Perception and Performance, 1979, Vol. 5, No. 4, pp. 579-594.

Miller, G. "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information," The Psychological Review, 1956, Vol. 63, No. 2, pp. 81-97.

Olson, H. Music, Physics, and Engineering, 2nd ed. New York: Dover, 1967.

Poland, W. "The Perception of Sound as Music," paper presented to the AAAS Symposium on Musical Perception, December 28, 1971, Philadelphia, Pa.

Shepard, R. "Circularity in Judgments of Relative Pitch," Journal of the Acoustical Society of America, 1964, Vol. 36, pp. 2346-2353.

Taylor, J. "Perception of Tonality in Short Melodies," Journal of Research in Music Education, 1976, Vol. 24, No. 4, pp. 197-208.


1Werner Meyer-Eppler, The Mathematical-Acoustical Fundamentals of Electrical Sound Composition, English translation by H.A.G. Nathan, Technical translation TT-608, National Research Council of Canada.

2P. Divenyi and I. Hirsh, "Identification of Temporal Order in Three-Tone Sequences," Journal of the Acoustical Society of America, 1974, Vol. 56, No. 1, p. 151.

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Last modified on Thursday, 25/10/2018

David Butler

David Butler is professor emeritus of music theory at The Ohio State University. He taught music theory at Ohio State for 28 years, and also served as associate director of the School of Music and associate dean of the College of the Arts. His book, Musician’s Guide to Perception and Cognition, was released by Schirmer Books in 1992.   Butler has published articles and reviews in Music Theory Spectrum, Music Perception, Psychology of Music, Journal of Music Theory, Perception & Psychophysics, and Journal of Experimental Psychology.   He was editor of College Music Symposium, and founding editor of Empirical Musicology Review.

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