To the Editors:
I enjoyed reading Normal Cook's article on "Seeing Harmony" (July–August). It's a nice theory, but is there any data to support it? A multidimensional scaling experiment conducted in several different cultures would be worthwhile. Subjects could make a simple "sounds similar" rating for pairs of stimuli and then could rate the pairs for emotional similarity. I know that there is a long-standing impressionistic literature, but that would not be sufficient for a detailed analysis. I have seen two recent papers in the journal Science that treat harmonic relationships as a geometric manifold. I wonder how Dr. Cook's work relates to those papers, which mainly concern chord sequences and voice-leading?
University of Oxford, England
To the Editors:
I found Norman Cook's article to be very interesting, and it motivated me to investigate further the findings of Helmholtz. I have a feeling that Helmholtz overestimated the importance of overtones—and underestimated the importance of the fundamental—in the perception of dissonance/consonance. Has anyone studied whether perceptions of dissonance/consonance change when overtones are (as much as possible) eliminated, as with electronic sine-wave oscillators? Does an augmented fourth really sound consonant if the overtones are removed?
Falls Church, VA
To the Editors:
Norman Cook's excellent article helped immensely in my own arguments regarding the idea of relationals and their successively higher-order role in evolving man's speech and music. Virtually all successively higher-order evolution has been marked by successively higher-order capability for response to successively higher-order relational properties of the environment. Frequency and rhythm, then, were principals of such relationals in the eventual registration and use of sound as generally manifest from first cold-blooded vertebrates upward. Therefore, the successively evolving, frequency-sensitive cochlea was principal to its co-evolution of meaning—howls, purrs, grunts and so on. The registration and use of the higher-order relationals, such as birdsong, identify successively higher-order responses to relationals in complexes of sound. In hominid evolution, marked by the evolution of distinctly human deliberative capability, it was only a matter of time (for music) before successively higher-order response to relationals in sound was manifest in individuals being able to "hold a note" and others holding different notes at the same time. These still-higher-order relationals—discordant or otherwise—are precisely the half-tones, triads and so forth identified in the article.
San Pedro, CA
Dr. Cook responds:
I still run lots of rather simple harmony experiments and will think about an "emotional similarity" experiment for the future. But is my current work a theory without experimental support? Not really. The starting point of my own obsession with triadic harmony specifically is that the rather successful models used to describe interval perception completely fail to explain harmony. Some argue that the typical perception of the augmented chord as being low on "tonalness" is learned, a purely cultural effect. I do not believe this view. If there isn't something acoustical in the augmented chord that gives it its unusable sonority, then what is the point of any kind of auditory psychophysics other than to demonstrate what people in different cultures have learned? What we know both from laboratory experiments and from the incidence of chord usage in classical/popular music is that some chords sound relatively stable (sonorous, beautiful, tonal, strong, resolved) and others less so. There are lots of ways of measuring that and tabulating their incidence as chords or short melodies in classical and popular music. There are of course influences from musical training and culture, but I take that sequence to be an empirical fact in need of explanation. My general conclusion is that the strongly reductionist "summation of interval effects" approach to harmony is too simple. Three tones is not too complex to do controlled experiments with, so, before jumping to the conclusion that everything is context dependent, I think there is a world of three-tone psychophysics that needs to be addressed.
Regarding Mr. Hutton's query about overtones, we have done experiments using different types of tones (sine-wave, grand piano and others) and do not find big differences due to upper harmonic structure. Some problems remain, however, in so far as it is technically difficult to deliver a pure fundamental frequency without some overtones generated in the musical instrument or amplifier. But probably a bigger problem is that, since all musical sounds from real instruments do indeed have upper partials, the typical human listener probably has a strong association between the fundamental frequency and a set of upper partials that usually accompany it. So, even if the signal is "pure," the perception is probably muddied by that kind of inevitable association. I'm not sure how to get around that problem to find out what the perception of pure fundamentals really is. It seems to me that this is a problem for psychology, because we want to reduce stimuli to their simplest form, and yet there are all kinds of contextual cues that do have effects.
From the perspective of human psychology, I think Mr. Bezanis is onto the main issue. The terminology is still debated and uncertain—and worth spending our time on—but it is certainly higher-order relations of some kind. What is amazing to me is that a number of researchers in psychology prefer to rely solely on quite low-level phenomena in trying to explain higher-level phenomena. I am convinced that three-body or three-cue effects need to be specifically addressed and cannot be explained as the sum of multiple two-body effects. I think we have shown that in the realm of harmony perception, but there are many other topics of higher-order perception/cognition that still need to be addressed in a similar manner.