Since his death the American composer Harry Partch has had a profound impact on contemporary music, at least in academic and intellectual circles. His main contribution has been that he got people seriously thinking about tuning systems. He wasn’t alone in this, but he was arguably the strongest voice at a time when such a voice was much needed. There’s no need for me to say much about Partch, as he’s much written-about and celebrated elsewhere. But I will comment on one incongruity in his work.

Partch’s concern about tuning systems was grounded in the idea that just intonation systems most accurately reflect the ways our ears and brains respond to music. Just tunings are those that, unlike the equal-temperament system in wide use today, are built around the ratios between the fundamental frequencies of the notes in play. This reflects the fact that our ears do naturally seem to interpret musical intervals on the basis of the frequency ratios involved. Partch was quite rigorous in his approach to these things – rigorous in his math, and rigorous in his insistence on accurate tuning. But here’s the odd thing: Partch was also known for his explorations with unusual instruments, and many of his instruments were percussion instruments which produce prominent inharmonic overtones. That means that, for all his concern with getting the pitches of his music just right, the music was filled with overtone pitches that were, as often as not, way out in left field someplace.

Our ears are amazingly adept at recognizing a single pitch, usually the fundamental, as the single defining pitch within a musical tone, even when that tone may have a lot of other frequencies present in the form of overtones. The process occurs effortlessly and unconsciously. In the end result the listener is much aware of the fundamental pitch and its musical meaning, but almost entirely unaware of the overtone frequencies present except insofar as they contribute to the listener’s sense of the tone quality or timbre. Thus it’s easy to see how someone thinking about just intonation could obsess over getting the fundamental pitches just right, all the while remaining oblivious to the other pitches present in the form of overtones.

Harmonic overtones are overtones whose frequencies line up with the frequency of the fundamental in specific simple arithmetic relationships. Inharmonic overtones are overtones that don’t line up that way. When the overtones are harmonic, the most prominent overtone frequencies typically are, for the most part, not in serious conflict with the scale in which the music plays. For the majority of music and the majority of scales, most of the prominent harmonic overtones align themselves nicely with the intended pitches and harmonies. (The alignment isn’t perfect for the equal tempered scale; this is a commonly-cited argument against that scale and in favor of just scales.) But when the overtones are inharmonic, those overtone pitches represent a lot of pitch information that, in all likelihood, is unrelated to the intended scale.

Does this matter? After a lot of listening and thinking about this, my sense is that those unaligned overtones do affect the listener’s sense of tonality. At the same time, I think that most listeners are pretty good at unconsciously masking this irrelevant harmonic information so as to be able to focus on the intended fundamental pitch information. I think we can say that the tonal meaning of any given piece of music is likely to be clearer when the overtones align with the intended pitch information of the fundamental tones. Stated differently, when there’s a lot of unintended and unacknowledged pitch information flying around in the form of prominent inharmonic overtones, the overall effect of the music is less clear. I hasten to add: this need not be seen as a bad thing. The added complexity may just as well enrich the effect as detract from it.

The most interesting work in this area has been done by William Sethares. In various articles and in his book Tuning Timbre Spectrum Scale, he discusses the idea that if you think of timbre as the tone quality of a musical sound as manifest in its particular overtone recipe, then scale and timbre are intimately related. If the frequencies of the overtones align with the frequencies of the scale, then the resulting music has a quality of integrity and clarity. If they do not, then the overtones introduce a lot of irrelevant pitch information into the mix, and integrity and clarity are compromised. Working with computers and synthesized tone qualities, Bill did some really fascinating investigations based on this idea. He constructed odd scales and odd timbres to match, such that the overtones within the timbres bore coherent relationships to the intervals of the scales. Music played in these matched scale-and-timbre systems indeed sounded remarkably coherent, even when they might seem on paper to be very peculiar scales and timbres indeed. As one example, he created stretched scale-and-timbre combinations. For example, he made scales constructed much like a just major scale, but with all the intervals proportionally enlarged so that the octave was substantially larger than the 2:1 octave that seems natural to our ears. To play these scales, he created timbres analogous to harmonic timbres but correspondingly stretched. Such a stretched scale, played with conventionally harmonic timbres, sounds bizarre and discordant. Likewise, the timbre with stretched harmonics, when used with a standard just major scale, sounds definitely off. But as a matched scale-and-timbre system, the two together sound unusual yes, but remarkably natural and coherent.

A while back I built a big, multifaceted instrument that I call bands and bars. One thing about it is relevant to the current discussion. The instrument includes several sounding elements in the form of metal bars long enough to make their fundamental frequencies subsonic – well below the hearing range, thus inaudible. That leaves many of the overtones in the heart of the hearing range, and the relationships among those overtones are thoroughly inharmonic. The instrument, multifaceted as it is, also includes other sounding elements in which the fundamentals sound quite clearly and for which the ear easily recognizes the fundamental as the defining pitch. So when it came time to decide on the tuning of these various elements, I found myself thinking about the Bill Sethares question: could the peculiar relationships of the audible overtones in the long bars inform my thinking about what sorts of scale to tune the other elements to? My approach was entirely non-mathematical. It was influenced by that fact that the instrument was already odd and esoteric in both construction and sound. To counterbalance this, in the tuning I wanted to create something that listeners could effortlessly relate to. So I engaged in a kind of meditation: I played the long bars, listened to their peculiar inherent tonal blends, and let them suggest to me what the tuning for the remainder of the instrument might be. I allowed those bars to create a tonality in my mind. I helped the process by sort of humming along. From what might have seemed like a wilderness of arbitrary tones I looked for relationships that seemed to have musical meaning. Somehow out of this I arrived at a feeling for a particular tonality, and I built the tuning for the instrument as a whole around that.

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