Combatting Anti-Just-Intonation Propaganda

By Kyle Gann

Many of the best known and loved pieces of microtonal music are written in just intonation. Despite this, it has become somewhat the fashion in recent years, among advocates of equal divisions of the octave and Regular Temperament Theory, to disparage and discredit just intonation and the composers who work in it. The statements they make about it are repeated so unvaryingly, in virtually the same words, that I can only consider them talking points, devised initially by some savant or group with the intention of driving just intonation out of serious consideration in the microtonal world, and subsequently parroted by others who wish to do so. The complaints are these:

1. Just intonation requires too many pitches.

2. Just intonation composers go to extreme lengths to avoid beats, which are actually beautiful.

3. Just intonation composers shy away from dissonance.

4. Just intonation is only for people who want to use a lot of math.

Allow me to take up these arguments one by one:

1. "Just intonation requires too many pitches": One of the most famous works in just intonation is La Monte Young's The Well-Tuned Piano. It is for a piano with twelve pitches to the octave. Likewise Ben Johnston's Suite for Microtonal Piano: twelve pitches. Likewise Terry Riley's The Harp of New Albion: twelve pitches. Since Taylor Swift, Prince, and Jimmy Buffett managed to use twelve pitches, there is no universe in which twelve pitches is too many. One of my just intonation works contains only eight pitches. La Monte Young wrote just intonation works using only four pitches. I suppose you'd have to have at least two pitches before you can call it just intonation, but JI imposes no requirements on the number of pitches.

There is a half-truth from which this argument derives: if you went back and tried to tune rather elaborate tonal works from the past in just intonation, you could indeed find that the number of pitches required escalates rather quickly. Even so, I have written out tuning ratios for Renaissance mass movements and movements of Beethoven string quartets, and not found the number of additional pitches unduly burdensome. Some of us do like to use a lot of pitches, because we enjoy small intervals - microtonality - but not because just intonation requires it. The works I mention above are so well known that anyone informed enough to make the argument probably knows them, and is thus deliberately lying; or else has been misinformed by someone else's lies.

2. "Just intonation composers go to extreme lengths to avoid beats, which are actually beautiful." A just intonation interval of 40/27, played in isolation, will produce beats. To avoid beats, you would have to restrict yourself to the simplest possible ratios, which no well-known just intonationists do. La Monte Young's sine tone installations, tuned in just intonation to many octaves of pitches close around octaves of the fundamental, beat furiously: that's all they do. The battle scene of my Custer and Sitting Bull, in just intonation, is structured around fiercely beating "out-of-tune" intervals that finally resolve to a perfect fifth. My piece Pulsars is composed solely of clusters of pitches within less than a half-step and allowed to beat; the opening sonority consists of pitches at ratios 98:99:100, three pitches within a third of a half-step, held beating for fifteen seconds. Here's the beginning of it:

Riley, in The Harp of New Albion, tunes the keyboard to C#, and then plays in the keys of B# and D, so the intervals will beat. Anyone who thinks that just-intonation intervals can't beat is utterly ignorant of tuning math, and shouldn't be listened to on the topic. Or else is lying.

3. "Just intonation composers shy away from dissonance." Johnston's Suite for microtonal piano builds up gnarly complexes like 9:16:19:26:30 and 9:14:17:21:27, which are messily dissonant. Harry Partch declared that "just-intonation dissonance is a whole different serving of tapioca than equal-tempered dissonance," and he was absolutely right. Toby Twining's Chrysalid Requiem heaps up nested 7/6 ratios into fearsome complexes. The Liquid Mechanisms, Star Dance, and Orbital Resonance movements of my Hyperchromatica are couched entirely in dissonances, sometimes with three keys being played in just intonation at once. Here's an excerpt from Liquid Mechanisms:

Anyone who tells you that just intonation music doesn't use dissonance is lying, or has been misinformed by someone else's lies.

4. "Just intonation is only for people who want to use a lot of math." Any kind of alternate tuning can take up about as much math as you want it to. The simple, five-limit scale of The Harp of New Albion could have come straight out of a tuning textbook, and, once the piano was tuned, it did not require Riley to do any math to improvise a two-hour piece in it. The 33-pitch scale of my Hyperchromatica, once I thought of it, took me about five minutes to compute, with cents. Just intonation even at its most intense is basically multiplying and dividing fractions, with sometimes a quick logarithmic conversion to cents. Using Johnston's just-intonation notation makes pure intervals as intuitive to use as any normal musical notation.

Meanwhile, the proponents of Regular Temperament Theory have, in general, taken the theory's math to a frighteningly complex level, with their elaborate formulae for "optimizing" intervals, their changing S-to-L ratios in moving one temperament among different EDOs, their thirteenth root of the tritave, and all that. Many internet pages on RTT are full of mathematical equations too byzantine for my skill set. As Partch aptly wrote on page 105 of Genesis of a Music, "I strongly suspect that men of scientific and mathematical bent show a partiality to temperaments because these offer them teasers for their arithmetical intellects. Just intonation is too laughably simple. It takes them back to seventh grade."

The objections to JI listed at the top are all lies, not just misunderstandings or overgeneralizations, because there is no body of evidence from which these assertions could have originally arisen through observation, no repertoire of just-intonation music to which they truly apply. The question as to what kind of person deliberately lies in order to discredit or marginalize their colleagues in the field is one you are as qualified to answer as I am.

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If you find any of this not clearly enough expressed, e-mail me.