my idiosyncratic reasons for using just intonation

7/28/2019 My Idiosyncratic Reasons for Using Just Intonation

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My Idiosyncratic Reasons for Using Just Intonation by Kyle Gann

Definitions:

Just Intonation: the practice of choosing pitches according to whole-number ratiosbetween frequencies, almost necessarily resulting in scales with unequal scale steps.

Equal Temperament: the practice of dividing the octave into an equal number of parts,or of making up a scale from equal-sized steps.

Im a great fan of both just intonation and various equal temperaments. Personally, Ivastly prefer composing in just intonation, but I am thrilled by the sound of a lot of musicthat uses equal temperaments of more than 12 pitches per octave. Artists have to usematerials with which they can feel comfortably creative: for me, thats the ratios of justintonation, but for many other people, equal scale steps are easier to negotiate. Bothare valid, and the results can sometimes even be practically indistinguishable.

However, microtonal musicians who use equal temperaments often express anunfortunate assumption about composers who use just intonation: that justintonationists 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, suchas is found in 19-tone equal temperament, is close enough to a pure 5/4 major third of386 cents to be indistinguishable in normal contexts. So they think that nature-worshipping just intonationists go to absurd lengths to be mathematically accuratebeyond the ears capacity to care, and that we do so in search of pure, beatlessconsonances - and that consequently we apparently like our music all simple and prettyand full of major triads and uninteresting. (Just intonationists have no complementarycomplaint about equal temperaments, as far as I know.)

These ridiculous fallacies come up so frequently that I, as a composer associated withjust intonation, have decided to post an answer to them here (originally written for thetuning list), in hopes that equal-temperament microtonalists will have to think twicebefore tarring us all with the same brush.

For anyone, no matter whom, to make the assumption that composers who use justintonation do so from a desire to hear pure, beatless intervals, and only for that reason,would be presumptuous and naive. For instance, I use just intonation with synthesizers,and not very sophisticated ones at that. I am under no illusion that I am going to getbeatless consonance. I usually cant even get a single beatless tone. Ive written just-

intonation pieces on an Akai sampler with only a 6-cent resolution and been happy as aclam. I think the only composer who is really looking for perfectly beatless consonancesis La Monte Young, and he has an extreme synthesizer, extreme ears, and extremepatience. I dont.

But while I dont insist on pure beatless consonances, I do prefer composing in justintonation to any equal temperament, no matter how finely divided, for the followingreasons:


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1. To give me approximations of the harmonics I want, an equal-tempered scalewould have to have more pitches than I can handle. I have never succeeded infinishing a piece with more than 31 pitches in it. I dont see how Partch kept 43pitches in his head. To get the accuracy I need for 7th and 11th harmonics, Ineed to be able to have pitches as close as 15 cents apart. To use an equal-

tempered scale that would give me pitches that close would require more than 60pitches per octave, and I only have 128 pitches in my MIDI controls and 61 keyson my keyboard. Just intonation gives me criteria for choosing only the pitches Ineed and leaving out all the rest.

2. I like, and in fact compose according to, the harmonic implications of fractionsand ratios. I like knowing, when I use a 21/16 interval, that the upper pitch is animplied seventh harmonic of the dominant of the lower pitch. I like the way a 7/6minor third not only has a different flavor than a 6/5, but also a different impliedset of related pitches, so that it suggests ways to harmonize it. I like the way thenumbers keep every pitch related to every other one in the system via a series ofimplied, interconnected harmonic series. The higher the numbers, the moreexotic the pitch seems. Thats an interesting thing to work with compositionally.No matter how dissonant and atonal you get, the gravitational pull of 1/1 keepsyou oriented to a fixed point in the universe.

3. I have never liked the concept of transposability, which is considered by manythe primary virtue of equal temperaments. I dont like the way (and noticed thiseven as a child), in some of Mozarts piano sonatas, the second theme soundsso perfectly placed as to register in the exposition, and then when its transposeda fourth up or a fifth down in the recap, it doesnt sound as good. Ive alwaysinstinctively agreed with Dane Rudhyar that to transpose a sonority is to diminishits 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 veryimportant to me to remember the pitch of the music at its first appearance: if Itranspose it for some reason I am in danger of losing the freshness of firstcontact and I will have difficulty in recapturing its attractiveness. Even within theclassical tradition, I tend to prefer composers who do not transpose material(Satie) to those who transpose all over the place (Schoenberg). Therefore, theuniversal transposability of sonorities in an equal-tempered scale holds nocharms for me. It is actually a deficit. I trust I will not be begrudged a position thatStravinsky 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 Im carving a gnarly piece ofwood instead of in smooth, mass-produced plastic. The material gives mefeedback: I run up against things I cant do, keys I cant modulate to, andcomposing becomes a dialogue between me and the scale. I enjoy that. (In fact, Ifind that if I can set up an elegant, asymmetrical scale to begin with, the piecealmost writes itself.) Perhaps I would also enjoy a nonequal, non-just-intonationscale, but I wouldnt know how to start making one. And why would I try?


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5. For me the great thing about just intonation is not that everything is consonantand beats dont exist, but that you have a tremendous range from having nobeats at all to extreme WOWOWOWOWOW beat conglomerations. Its not that Idislike the buzziness of out-of-tune intervals, but I want to be able to control thatbuzziness, 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-tunemajor thirds and sixths of the normally tuned piano. I frequently use intervals like40/27 to get beats, deliberately. Ben Johnstons music is often based aroundmoving gradually from extreme consonance to extreme out-of-tuneness, and itsan amazing effect - I try to get the same thing in, for instance, the Battle sceneof my Custer and Sitting Bull. Nevertheless, the fact that even my simpleconsonances are not exactly perfect on my synthesizers has never oncebothered 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 ashame to waste it. I warn my students that if they dont have a good head forfractions and logarithms they should leave just intonation alone. Its not foreveryone.

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 LaMonte Young. All of them use(d) just intonation (although Lou and Jim arevariable, sometimes using equal or historical temperaments). I dont know of anyother microtonalists working in any other kinds of scales whose music I lovenearly so much. Im fond of the 19-tone, 24-tone, 34-tone, 36-tone, and 72-tonemusics of Ivan Wyschnegradsky, Julian Carillo, Alois Haba, Ezra Sims, NeilHaverstick, and others, but while I get a kick from the pitch relationships, I donthave as deep an affection for the music itself - I thrill to its frisson of weirdness,

but dont find it as moving as Johnstons Fourth String Quartet, or PartchsBarstow, or Youngs The Well-Tuned Piano. I harbor no theory as to why all myfavorite microtonal music seems to be in just intonation - possibly just acoincidence. But I wouldnt start working in 72-tone or any other equaltemperament unless I first heard some music in that scale that blew me away, inemotional as well as technical terms.

8. Also, Ben Johnston developed a very logical, harmonically meaningful notationfor just intonation, and I find it an easy notation to think in. Equal temperamentnotations Ive seen (Easley Blackwoods, for instance) have less harmonicrelevance, and contain an element of arbitrariness; besides which, one has to

switch among different notations for different divisions of the octave. In Bensnotation I can have five pitches to the octave or 500, and use the sameaccidentals either way.

Beats, schmeats - its not so much the purity of sound I get from just intonation as thecreative influence of thinking in ratios that I treasure (along with the variety of intervalsizes, of course). Some hot-shot whos figured out that 137 pitches per octave is theperfect equal division will harangue me that my music could be redone in a 137-equal


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scale and Id never be able to tell the difference, and maybe hes right - but I wouldnever 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 Ive alreadygot exactly.) You cant just ignore the impact that how you define your materials has onthe 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 thatinterconnectedness, but the ultimate sonic manifestation does not have to be pure forthe composing process to have the intensity I love about it. As Ben always says, Betterto have a perfect model and get an imperfect realization of it, than to have an imperfectmodel to begin with. Or as Charles Ives asked, What has sound got to do with music?

I dont proselytize for just intonation. Everyone who likes working in equaltemperaments should continue doing so. I have nothing against equal temperaments 19and over - theyre just inefficient for my purposes. I dont imagine I could be verycreative in an expanded equal temperament, just as I imagine a lot of composers wouldhave trouble being creative within masses of fractions. Im glad other composers areexploring equal temperaments, and I follow their results with eager curiosity. May ahundred thousand scales flourish. And may the equal temperament people leave us justintonationists to our preferred way of composing without further caricature.

Kyle Gann

June, 2004

my idiosyncratic reasons for using just intonation

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