My Idiosyncratic Reasons for Using Just Intonation
By Kyle Gann
Just Intonation: the practice of choosing pitches
Equal Temperament: the practice of dividing the octave
according to whole-number ratios between frequencies,
almost necessarily resulting in scales with unequal scale steps.
into an equal number of parts, or of making up a scale
from equal-sized steps.
Just Intonation: the practice of choosing pitches
Equal Temperament: the practice of dividing the octave
I'm a great fan of both just intonation and various equal temperaments. Personally, I vastly prefer composing in just intonation, but I am thrilled by the sound of a lot of music that uses equal temperaments of more than 12 pitches per octave. Artists have to use materials with which they can feel comfortably creative: for me, that's the ratios of just intonation, but for many other people, equal scale steps are easier to negotiate. Both are valid, and the results can sometimes even be practically indistinguishable.
However, microtonal musicians who use equal temperaments often express an unfortunate assumption about composers who use just intonation: that just intonationists have some kind of quasi-religious faith in the "purity" of whole-number-ratio-based intervals. They point out that, for instance, a major third of 379 cents, such as is found in 19-tone equal temperament, is "close enough" to a pure 5/4 major third of 386 cents to be indistinguishable in normal contexts. So they think that nature-worshipping just intonationists go to absurd lengths to be mathematically accurate beyond the ear's capacity to care, and that we do so in search of pure, beatless consonances - and that consequently we apparently like our music all simple and pretty and full of major triads and uninteresting. (Just intonationists have no complementary complaint about equal temperaments, as far as I know.)
These ridiculous fallacies come up so frequently that I, as a composer associated with just intonation, have decided to post an answer to them here (originally written for the tuning list), in hopes that equal-temperament microtonalists will have to think twice before tarring us all with the same brush.
For anyone, no matter whom, to make the assumption that composers who use just intonation do so from a desire to hear pure, beatless intervals, and only for that reason, would be presumptuous and naive. For instance, I used to make just intonation music with synthesizers, and not very sophisticated ones at that. I was under no illusion that I was going to get beatless consonance, and I didn't care. I usually couldn't even get a single beatless tone. I've written just-intonation pieces on an Akai sampler with only a 6-cent resolution and been happy as a clam. I think the only composer who is really looking for perfectly beatless consonances is La Monte Young, and he has an extreme synthesizer, extreme ears, and extreme patience. I don't.
But while I don't insist on pure beatless consonances, I do prefer composing in just intonation to any equal temperament, no matter how finely divided, for the following reasons:
1. To give me approximations of the harmonics I want, an equal-tempered scale would have to have more pitches than I can handle. I have not yet succeeded in finishing a piece with more than 37 pitches in it. I don't see how Partch kept 43 pitches in his head. To get the accuracy I need for 7th and 11th harmonics, I need to be able to have pitches as close as 15 cents apart. (I have devoted my career as a microtonalist to exploiting commas - the tiny intervals resulting from the collision of intervals based on different prime numbers - and the thought of "tempering out" my beautiful commas would give me nightmares.) To use an equal-tempered scale that would give me pitches that close would require more than 60 pitches per octave, and I only have 128 pitches in my MIDI controls and 61 keys on my keyboard. Just intonation gives me criteria for choosing only the pitches I need and leaving out all the rest.
2. I like, and in fact compose according to, the harmonic implications of fractions and ratios. I like knowing, when I use a 21/16 interval, that the upper pitch is an implied seventh harmonic of the dominant of the lower pitch. I like the way a 7/6 minor third not only has a different flavor than a 6/5, but also a different implied set of related pitches, so that it suggests ways to harmonize it. I like the way the numbers keep every pitch related to every other one in the system via a series of implied, interconnected harmonic series'. The higher the numbers, the more exotic the pitch seems. That's an interesting thing to work with compositionally. No matter how dissonant and atonal you get, the gravitational pull of 1/1 keeps you oriented to a fixed point in the universe.
3. I have never liked the concept of transposability, which is considered by many the primary virtue of equal temperaments. I don't like the way (and noticed this even as a child), in some of Mozart's piano sonatas, the second theme sounds so perfectly placed as to register in the exposition, and then when it's transposed a fourth up or a fifth down in the recap, it doesn't sound as good. I've always instinctively agreed with Dane Rudhyar that to transpose a sonority is to diminish its absolute value as a sonic phenomenon and reduce it to a set of relationships. Igor Stravinsky said something nearly identical in his Conversations: "It is very important to me to remember the pitch of the music at its first appearance: if I transpose it for some reason I am in danger of losing the freshness of first contact and I will have difficulty in recapturing its attractiveness." Even within the classical tradition, I tend to prefer composers who do not transpose material (Satie) to those who transpose all over the place (Schoenberg). Therefore, the universal transposability of sonorities in an equal-tempered scale holds no charms for me. It is actually a deficit. I trust I will not be begrudged a position that Stravinsky and I hold in common.
4. Relatedly, I like having different-sized intervals available on different scale steps. It makes the scale have a "natural" feel to me, like I'm carving a gnarly piece of wood instead of in smooth, mass-produced plastic. The material gives me feedback: I run up against things I can't do, keys I can't modulate to, and composing becomes a dialogue between me and the scale. I enjoy that. Sometimes, if I design the tuning system elegantly enough, the piece practically writes itself. Perhaps I would also enjoy a nonequal, non-just-intonation scale, but I wouldn't know how to start making one. And why would I try?
5. For me the great thing about just intonation is not that everything is consonant and beats don't exist, but that you have a tremendous range from having no beats at all to extreme WOWOWOWOWOW beat conglomerations. It's not that I dislike the buzziness of out-of-tune intervals, but I want to be able to control that buzziness, and have it only when I intend it as part of the musical effect - not pop up quasi randomly and without expressive intent, as it does in the out-of-tune major thirds and sixths of the normally tuned piano. I frequently use intervals like 40/27 to get beats, deliberately. Ben Johnston's music is often based around moving gradually from extreme consonance to extreme out-of-tuneness, and it's an amazing effect - I try to get the same thing in, for instance, the "Battle" scene of my Custer and Sitting Bull. Nevertheless, the fact that even my simple consonances are not exactly perfect on my synthesizers has never once bothered me. I live in the real world, where nothing is perfect.
6. I have a tremendous natural talent for fractions and logarithms. It would be a shame to waste it. I warn my students that if they don't have a good head for fractions and logarithms they should leave just intonation alone. It's not for everyone.
7. Not least, I am building on the work of six composers whose music I deeply love: Harry Partch, Ben Johnston, Terry Riley, James Tenney, Lou Harrison, and La Monte Young. All of them use(d) just intonation (although Lou and Jim are variable, sometimes using equal or historical temperaments). I don't know of any other microtonalists working in any other kinds of scales whose music I love nearly so much. I'm fond of the 19-tone, 24-tone, 34-tone, 36-tone, and 72-tone musics of Ivan Wyschnegradsky, Julian Carillo, Alois Haba, Ezra Sims, Neil Haverstick, and others, but while I get a kick from the pitch relationships, I don't have as deep an affection for the music itself - I thrill to its frisson of weirdness, but don't find it as moving as Johnston's Fourth String Quartet, or Partch's Barstow, or Young's The Well-Tuned Piano. I harbor no theory as to why all my favorite microtonal music seems to be in just intonation - possibly just a coincidence. But I wouldn't start working in 72-tone or any other equal temperament unless I first heard some music in that scale that blew me away, in emotional as well as technical terms.
8. Also, Ben Johnston developed a very logical, harmonically meaningful notation for just intonation, and I find it an easy notation to think in. Equal temperament notations I've seen (Easley Blackwood's, for instance) have less harmonic relevance, and contain an element of arbitrariness; besides which, one has to switch among different notations for different divisions of the octave. In Ben's notation I can have five pitches to the octave or 500, and use the same accidentals either way.
Beats, schmeats - it's not so much the purity of sound I get from just intonation as the creative influence of thinking in ratios that I treasure (along with the variety of interval sizes, of course). Some hot-shot who's figured out that 137 pitches per octave is the perfect equal division will harangue me that my music could be redone in a 137-equal scale and I'd never be able to tell the difference, and maybe he's right - but I would never have written the piece the way I did thinking in 137 equal steps. (I do, however, enjoy being told that by adding lots more pitches, I could approximate what I've already got exactly.) You can't just ignore the impact that how you define your materials has on the creative process. Just intonation, for me, represents the ability to use every note with an intense awareness of its harmonic interconnectedness with every other note. The theoretical harmonic purity of numerical relationships is the basis of that interconnectedness, but the ultimate sonic manifestation does not have to be pure for the composing process to have the intensity I love about it. As Ben always says, "Better to have a perfect model and get an imperfect realization of it, than to have an imperfect model to begin with." Or as Charles Ives asked, "What has sound got to do with music?"
I don't proselytize for just intonation. Everyone who likes working in equal temperaments should continue doing so. I have nothing against equal temperaments 19 and over - they're just inefficient for my purposes. I don't imagine I could be very creative in an expanded equal temperament, just as I imagine a lot of composers would have trouble being creative within masses of fractions. I'm glad other composers are exploring equal temperaments, and I follow their results with eager curiosity. May a hundred thousand scales flourish. And may the equal temperament people leave us just intonationists to our preferred way of composing without further caricature.
June, 2004; slightly updated September, 2016
Copyright, Kyle Gann, 2004
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