Harmony: A Psychoacoustical Approach by Richard Parncutt

Reviewed by David Huron

Psychology of Music, Vol. 19, No. 2 (1991) pp. 219-222.
Richard Parncutt, Harmony: A Psychoacoustical Approach. Berlin: Springer-Verlag, 1989. 206pp. ISBN 0-387-51279-9.

The first thing that captures one's attention about this book is the price. Barely 1 cm in thickness, if scholarly value was measured by the cost per volume of print, this book would be a poor purchase. Fortunately, Harmony: A Psychoacoustical Approach turns out to be something of a gem, which, if not worth its weight in gold, at least takes some of the sting out of the purchase price.

Based on Parncutt's doctoral dissertation at the University of New England (Australia), this book is an attempt to explain conventional Western harmony using psychoacoustic principles. From a historical point of view, one can view this book as a modern update of Rameau's theory of harmony deriving from the perception of a single tone. The premise is that both tones and chords are species of vertical sonorities or simultaneities, and that the perceptual difference between tones and chords is a matter of degree rather than kind. Rameau in essence employed this premise in relating the root of a chord (basse fondamentale) to the fundamental frequency of a harmonic series. In contemporary terms, we might say that Rameau understood the manner in which listeners extract the root of a chord to be akin to the way listeners perceive the pitch of a complex tone.

In the last few decades, psychoacousticians have developed quite powerful models of pitch perception. A successful model of pitch perception invites a more sophisticated exposition and update of Rameau's theory. Ernst Terhardt was the first to propose such an exposition in applying his own model of pitch perception to the analysis of all types of sonorities (tones, dyads, triads, etc.). Parncutt's work follows closely in Terhardt's footsteps, but extends the path in new and notable directions.

The book divides into two parts. The first half of the book provides a lucid (if breathless) review of current research pertaining to psychoacoustics and pitch-related elements of music perception. This is a clear and succinct account of a considerable sweep of historical and empirical views. Indeed, the first half of the book would make a fine text for a graduate or post-graduate course in music perception.

Parncutt's model takes as an input some spectrum representing a vertical sonority or simultaneity (such as a chord or complex tone). This spectrum is reconstituted by the model so that the effects of auditory masking are taken into account. Masking tends to eliminate or attenuate the audibility of certain partials. A template representing the harmonic series is then swept over the sonority to determine any complex tone or tones that may be deemed to be present.

In Parncutt's model several properties of the sonority can be determined -- such as tonalness, multiplicity, and salience. Parncutt defines tonalness as the degree to which a sonority evokes the sensation of a single pitched tone. In short, tonalness is a measure of how "tone-like" or cohesive the sonority is. Single tones, octave dyads, and major chords have relatively high tonalness values, whereas half-diminished chords, minor ninth dyads, and bell-like sonorities have relatively low tonalness values.

In addition, Parncutt characterises a sonority by its multiplicity -- that is, by the apparent number of tones noticed or evident in the sonority. For a single complex tone, the multiplicity may exceed the nominal value 1.0 due to the presence of audible harmonics, however for most chords the apparent number of tones is less than the "actual" number of constituent tones.

The model also generates information pertaining to pitch salience -- that is, the perceptual importance, prominence or noticeability of a given pitch within the sonority. The saliences for all of the pitches can then be summed together across each of the 12 chroma categories and the root of a simultaneity may be defined psychoacoustically as that chroma in the spectrum with the greatest aggregate salience.

A noteworthy feature of the model is that it can be modified to reflect the degree to which a listener behaves in an attentive or analytic manner. For example, an analytic listener is more apt to be able to discern various component tones within a given chord, as well as be able to resolve the individual partials of a complex tone.

In addition to these static properties, Parncutt proposes two dynamic properties related to successions of sonorities (e.g. chord progressions). Successive sonorities can be analysed in terms of pitch commonality -- that is, the degree to which two successive sonorities have (noticed) pitches in common, and pitch distance, that is the aggregate pitch proximity of the components of two successive sonorities.

Finally, Parncutt proposes an analytic scheme by which the overall "consonance" of a chord progression can be characterised. The scheme is dependent upon four factors: "[1] the consonances of individual chords in the progression; [2] the consonances of pairs of [successive] chords, i.e. how well they are perceived to go with each other; [3] the unifying effect of melodic streaming; and [4] the strength of the tonal structure (tonality) of the progression." [p.75]. Parncutt points out that these four factors provide a useful analytic framework within which different harmonic styles can be distinguished: "some impressionist styles have consonant chords but dissonant chord relationships and weak melodic [streaming] and tonal structure; and some jazz styles have dissonant chords, but consonant chord relationships and strong melodic and tonal structure." [p.75].

The model is presented in a formal (computable) way. Although there are several dozen equations, there are no nasty integrals to intimidate the mathematically timid. If you understand exponents, logarithms and summation, you will be able to decipher Parncutt's model. The model itself is based loosely on Terhardt, Stoll and Seewann's (1982) pitch extraction algorithm. The Terhardt et al. model is oriented toward the precise prediction of perceived pitch for an arbitrary sonority. Parncutt's model is simplified in several respects (it does not deal with subtle phenomena such as pitch shifting or stretched octaves), but Parncutt's model pays more attention to ambiguous or ambivalent pitch perceptions.

In Chapter 5, Parncutt describes several experiments that he carried out in order to test and fine-tune the model. One experiment, for example, uses a method similar to Krumhansl's probe tone technique in order to measure the saliences of different tones within a given sonority. The experiments are well designed and clearly presented. Especially laudible is Parncutt's inclusion of non-Western musicians in his subject pool in order to assure some cross-cultural validity.

One problem with Parncutt's model is evident with regard to the multiplicity of a sonority (the number of tones simultaneously noticed in a musical sound). Parncutt's experimental results are consistent with the values predicted by his model, but the fit is not particularly good. Only six of ten predicted values lie within the 95% data intervals established by the corresponding experiment. The correlation is especially weak in light of the fact that Parncutt was able to fine-tune two free variables in order to achieve an optimum fit. Having recently completed my own (unpublished) experiment along similar lines, I was eager to compare this new data with Parncutt's model. In my own experiment (70 subjects; 69 sonorities), I found that chords with open spellings are judged by listeners as having more perceivable tones than equivalent chords spelled in closed position. (Equivalent chords were defined as chords of the same type and inversion, having the same number of constituent tones, the same degree of pitch-class duplication, and the same chord centroid (or average pitch).) Using Parncutt's model, I calculated the "multiplicity" values for several dozen chords -- including different chord types, inversions, and spellings. Unfortunately, as chords are spelled from closed position, to successively more open spellings, Parncutt's multiplicity values decrease rather than increase. The model thus predicts that hearing-out tones in closed position chords (e.g. C4-E4-G4) is easier than hearing-out tones in open position chords (e.g. C3-G4-E5). This is contrary to both my experimental results, and musical intuition. It suggests that Parncutt's multiplicity measure could be improved by taking into account pitch-proximity effects.

One of the most curious parts of Parncutt's book is the lengthy digression concerning prenatal auditory conditioning. The impetus for Parncutt to deal with nature versus nurture issues appears to be that Terhardt's model of pitch perception evidently rests on the assumption that sensitivity to the harmonic series is acquired rather than innate. This is very much a point of dispute in psychoacoustic circles. Hearing scientists agree about the special status of the harmonic series in auditory perception, but they disagree whether people are (genetically) endowed with a harmonically-sensitive apparatus or whether this sensitivity develops through experience with the natural world. On this issue, Parncutt has hitched his wagon to Terhardt's "nurture" view. Parncutt wants to assure the reader that his model of harmony is not based on the "naturalness" of the harmonic series as an acoustical phenomenon, but on the familiarity of the auditory system with the harmonic series due to the plethora of harmonic tones experienced in the environment.

Since pitch perception is evident in early infancy, it would appear that the principle formative environment for harmonic conditioning must be the womb in the last months of pregnancy. I do not find the arguments here especially convincing. The sounds experienced by the foetus in the womb include vocalisations by the mother, eating, drinking, digestion, foot-falls, heartbeat and breathing. Although the foetus is exposed to a veritable symphony of sounds, the majority of these sounds have inharmonic rather than harmonic spectra. This raises doubts about harmonic template conditioning in the womb.

Other prenatal claims are unduly speculative or misleading. For example, Parncutt interprets Kronman and Sundberg (1987) as suggesting prenatal learning of a link between musical tempo fluctations and changes in the walking speed of the mother (p.52). Kronman and Sundberg's work implies that perceptions of tempo fluctuations arise from experience with real-world phenomena, but their work does not distinguish between prenatal and postnatal experiences. Parncutt also claims that since heartbeat and walking sounds consist predominantly of low frequencies, the foetus is conditioned to hearing rhythms with the lower sounds falling on the beat. This conditioning is offered as an explanation for the predominance of lower bass notes falling on the beat (as in a `stride bass' accompaniment). Many musical textures do indeed exhibit such characteristic patterns, but the purported rhythmic salience of low pitches is neither an experimentally determined fact nor an established principle in musical practice. Indeed, several music theorists claim that it is the relatively higher pitch that receives greater rhythmic salience (e.g. Benward and White, 1989; p.151).

The nature-nurture debate is not without interest. It is also a refreshing reversal of the stereotype to see a psychoacoustician arguing in favour of the importance of environmental and cultural factors in music perception. But I feel that the nature-nurture discussion deserves a place of its own outside of this volume. There is nothing in Parncutt's model of harmony that requires the harmonic series to be an acquired rather than an innate perceptual disposition. For many readers, the discussion on prenatal conditioning is apt to be seen as a distraction from the strength of Parncutt's model.

In summary, a great deal has been achieved in this impressive work. I believe that Parncutt and Terhardt have introduced a valuable conceptual language through which to explore and understand musical harmony. The dichotomy between "tone" and "chord" has been bridged and both have been placed in an integrated analytic continuum. A meaningful way has been provided to deal with ambiguous percepts -- such as competing claims over the root of a given chord. The concept of chord root has been related to the perception of virtual or residual pitch in a way that is insightful for the analysis of harmony. Parncutt's model is notably successful in providing a satisfactory account for the root of a minor triad -- a problem that has bedevilled traditional theories based on frequency ratios. He has shown a sensitivity to cross-cultural and nature/nurture issues which is exemplary in a field prone to discount the role of culture in human perception. All in all, Harmony: A Psychoacoustical Approach, is a stimulating and important contribution to music scholarship.


David Huron
Ohio State University


References

Benward, B. and White, G. (1977/1989). Music in Theory and Practice: Vol. 1. Dubuque, Iowa: W.C. Brown Publishers; 4th ed.

Kronman, U. and Sundberg, J. (1987). Is the musical ritard an allusion to physical motion? In A. Gabrielsson (Ed.), Action and Perception in Rhythm and Music. Stockholm: Royal Swedish Academy of Music.

Terhardt, E., Stoll, G. and Seewann, M. (1982). Algorithm for extraction of pitch and pitch salience from complex tonal signals. Journal of the Acoustical Society of America, 71, 679-688.
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