To test the hypothesis that chromatic scale intervals are specifically embedded in the frequency relationships in voiced speech sounds (i.e., phones whose acoustical structure is characterized by periodic repetition), we analyzed the spectra of different vowel nuclei in neutral speech uttered by adult native speakers of American English, as well as a smaller database of Mandarin.In other words, the 12-note scale isn't so arbitrary after all. Interestingly, there's preference for tuning systems in speech as well:
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... [We calculated] the distribution of all F2/F1 ratios derived from the spectra of the 8 different vowels uttered by the 10 English-speaking participants (i.e., the relationships in 1,000 utterances of each of the vowels). Sixty-eight percent of these ratios fall on intervals of the chromatic scale (red bars), and all 12 chromatic intervals are represented over a span of 4 octaves.
In so far as the observations here inform this argument, the observed ratios in speech spectra accord most closely with a just intonation tuning system. Ten of the 12 intervals generated by the analysis of either English or Mandarin vowel spectra are those used in just intonation tuning, whereas 4 of the 12 match the Pythagorean tuning and only 1 of the 12 intervals matches those used in equal temperament. The two anomalies in our data with respect to just intonation concern the minor second and the tritone.That minor-second/tritone anomaly brings up a good chicken-egg question, given that composers who work with more chromatic than diatonic sounds tend not to explore alternate tunings so much: does a preference for crunchy dissonance mean that just intonation sounds "wrong"? Or is it that, in our predominantly equal-temperament world, it's those clashing seconds that sound the most "natural," so that's where the preference comes from? As someone who likes the sound of diatonic music in pure ratios, but opts for equal-tempered dissonance in my own, I'm inclined towards the latter, but I would imagine this is a highly personal impression.
Anyway, turns out Harold Hill was right: singing is just sustained talking.
6 comments:
What's even more interesting is the recent research that turned up a genetic link between tonal and non-tonal language speakers.
Maybe there is a divinity that shapes our ends.
More likely, the divinity is too busy to bother, though.
The paper jodru refers to is here, if you're curious. (Cool stuff.)
I'm with you on the divinity. I always picture God sitting in a club chair, reading the Financial TImes, checking the caller ID every time the phone rings, and deciding it's just not worth picking up.
"...composers who work with more chromatic than diatonic sounds tend not to explore alternate tunings so much..."
My experience suggests exactly the opposite. Many, many of us who work in just intonation do so in search of a more seamless chromaticism than a paltry 12 pitches can provide.
Kyle: Mea culpa for the stupid generalization. I was primarily thinking of the historical moment when just intonation and microtonality started sneaking back into Western classical music—the 40s and 50s. Hardly an excuse, though—I've been spending a fair amount of the past months with music of varying degrees of non-equal-temperedness, from Ben Johnston to Kaija Saariaho. Sometimes my brain just turns off.
I would be curious to know whether composers who work with just intonation came to it through diatonicism and then realized how cool it would be to adapt it to chromaticism, or whether they were chromatic from the start and just continually dissatisfied with the equal-tempered results. I'd bet there's varying paths—for me, I like the sounds of natural horn partials and string harmonics interacting with triadic sonorities, but I'm still unconvinced by my tentative efforts to integrate them into the dense crunches of harmony I seem to always come back to.
Well, there's no generalizing about microtonalists, because their motivations and methods thoroughly cover a tremendous range. But Partch was driven partly by an extremely micro-chromatic voice-leading he called Tonality Flux:
http://en.wikipedia.org/wiki/Tonality_flux
David Doty and I have followed a similar path, creating harmonic progressions my moving voices less than 70 cents where possible. (I was a Max Reger fan pretty early in my development.) Ben Johnston cites pure consonance as a motivation, but much of his JI music, from the first examples, is 12-tone, and even when it's not it tends toward scales of 22 or 32 steps. The closest I can think of to a major diatonic microtonalist is Terry Riley, and I'd have to heavily qualify that. There's a common myth that just intonationists are attracted to JI by a love of pure harmonies, and therefore write simply diatonic music. I address it here:
http://www.kylegann.com/JIreasons.html
Anecdotal evidence suggests to me, rather, that developing one's perception of tiny increments is a more common motivator, but you'd have to survey a lot of people to be able to generalize.
That should have been "*by* moving voices," of course.
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