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Ezra Sims Interview
About Ezra Sims’s Scale
In some cases the differences between the intervals of the harmonic series (the “natural” or “just ” intervals) and the twelve traditional equal-tempered intervals are almost imperceptible, and in other cases they are quite noticeable. For example, a natural perfect fifth—frequency ratio 3:2—is barely 2 cents (2/100 of a semitone) smaller than its equal-tempered counterpart, while the natural minor seventh—frequency ratio 7:4—is almost 31 cents (roughly 1/3 of a semitone, or 1/6 of a “tone”) smaller than the equal-tempered one.
By dividing the octave into 72 equally spaced intervals, one creates a minute chromatic that includes the twelve traditional equal-tempered intervals and adds 1/12 tones (and multiples of 1/12 tones, such as 1/6 tones, 1/4 tones and 1/3 tones). Using this 72-note palette, one is able to approximate the natural intervals very closely. For example, one can produce a minor seventh that is exactly 1/6 of a tone smaller than the traditional equal-tempered minor seventh, and will resemble very closely the natural minor seventh mentioned above. (The difference between these two minor sevenths is just about 2 cents.)
In the early 1970s Ezra Sims began using intervals derived from 72-note equal temperament in order to create a 24-note, asymmetrical, transposable scale. (Some transposition of this scale is in use at any moment of his music, in the same way that some transposition of the diatonic scale is in use at all times in tonal music.) The 24 pitches of his scale were selected to mimic intervals from the harmonic series. Indicated in open noteheads are the “stable” pitches [see Example C]. These are drawn from the lower harmonics, no.’s 1-16 [see Example B], and include the fundamental itself [the pitch C, in this case]. The filled noteheads indicate the “less stable” pitches, and they are drawn from much higher, more remote harmonics of the same fundamental.
To select which of the available less stable pitches he would use for his scale, Sims relied upon a synthesis of his own musical instincts and certain acoustical facts. For example, he wanted two pitches to break up the intervals between the three lowest “stable” pitches of his scale [here, the C, the D and the 1/12-low E], which form a major second and a 1/12-low major third from the bottom. One simple way to find those pitches was to see how another 1/12-low major third within the harmonic series gets broken up, and to use that as a model. He found that the 1/12-low major third formed by the 12th-15th harmonics was broken up by 2/3 tones [see Example B, harmonics no.’s 12-13], so he used these intervals, and then split them into 1/3 tones. This is how he arrived at the sequence of 1/3 tones which comprise the bottom seven notes of his scale. (Later on he was hearing quarter-tones splitting up the same three stable pitches, and found a model for that in the harmonic series as well. These pitches create the alternate form of the bottom notes of the scale shown in Example C.)
One more feature of Sims’s music which is important to mention in an introduction such as this is his special treatment of “summation” and “difference” tones. These are pitches perceived (though not actually sounding) as the result of the mind’s adding or subtracting the frequencies of two simultaneous notes. For example, an E (660 Hz) and an A (440 Hz) imply a summation tone of 1100 Hz (the C-sharp above the E) and a difference tone of 220 Hz (the A below the 440 A). (A practical example of difference tones is the telephone receiver, which is too small to produce the fundamental tones of the voice, and transmits only clusters of “overtones” from which the mind intuits the resultant fundamentals.)
Sims’s accidentals for 72-note equal temperament:
1/12 tone high
|1/12 tone low|
|1/6 tone high||1/6 tone low|
|1/4 tone high||1/4 tone low|
(A font with these symbols was created by cellist Ted Mook, and may be found here.)
The first 16 pitches of the harmonic series, in Sims’s notation
Ezra Sims’s scale
Interview by Julia Werntz
Originally published in The Micro-Tome
Vol.1, Issue 2
W: Are the stable tones of your scale (marked in whole notes) classified according to their closeness to the fundamental, so that the third harmonic (a P5), for example, would be treated in your music as more stable than the fifth harmonic (a M3)?
S: To try to put it into a nutshell: going by what my ear has demanded in my own compositions, I have this suspicion that our concern now, for the next little while (at least my concern), will be for the harmonics 6-12 as our basic chord, so to speak, in the way that 3-6 used to be our basic chord. Just as you might, in C major, end on a G and an E and it won’t be quite as final as a C and a G, or a C, E and G, but it will establish itself as the home harmony, I suspect the same thing happens with the other ones: I could end (again in C) on a C, D, E and quarter-low F-sharp, (the eighth, ninth, tenth and eleventh harmonics) and that will not be quite so solid an ending as the lower harmonics would be, but it still will be a consonant tonal ending.
What I suspect is the least stable among them, in any case, is no. 13 (in C, the raised A-flat). That’s because 72 notes won’t quite describe it as accurately as it will the others.
Summation and Difference Tones
W: Are the “filled notehead” pitches the only dissonances you want to use?
S: For a while that was the case. Now I’m using different kinds of dissonance, such as summation and difference tones. But there’s one thing: those notes are not inherently dissonant; they’re less stable, they’re somewhat stable, somewhat unstable.
W: How are summation and difference tones felt and treated in the writing? Are they “special” notes with a specific musical effect or structural function?
S: Any two notes from the scale can imply a summation tone, say. Another voice may have a note that is close to it but is not the summation tone, and it will want to resolve to the summation tone. And that, of course, is the definition of dissonance.
Once in a while I’ve been in the position where I had to go outside the scale to get the consonance that’s needed because some very strong pair of voices implied a summation tone that was not in the scale. (I’ve known what it is, and I’ve written it, it sounds right, it obviously has a theoretical implication that I’ve never quite explored.)
W: Is the fundamental, scale-generating tone of a work perceived and portrayed as “home”? If so, how is this established on a “liminal” level in the writing?
S: Take the clarinet quintet, first section. It opens with the violin playing two notes: a D and a sixth-low C. This implies the key of D. Then the clarinet comes in on a quarter-low C-sharp. This configuration will only happen in my scale of G. The key of G becomes even more clear when the clarinet moves to a sixth high D-flat. That makes it certain that we are in G.
Each measure has a idiosynchratic and obvious cluster that could only come from some scale or other.
W: But you prefer not to actually give the fundamental, in most cases.
S: Well, because that would pin it to the ground and it would be rather dull.
It’s nice to have it… not ambiguous, but less weighted.
In diatonic music, particularly the late stuff, it’s not always confirmed what key you’re in, but there are implications of melodic line and what intervals are chosen that now tell us where we are. I’ve been working with my method so long that the same thing happens in these more complicated intervals. What gives me hope is that naïve listeners seems to hear it very well. Trained ones sometimes have more trouble, because they’re professionally deformed to expect only the classic twelve notes.
W: Are performers informed, in their scores, of “parent keys” and modulations, so that these keys will affect their intonation?
S: Well, I put them in partly for my own comfort in rehearsing and the like. I started doing it and it pleased me, but I don’t do it always now. The new piece will not have it. It’s so rich in the matter of keys and chromaticism that I don’t know whether there will be much point in it.
I’ve always remembered a time when Janet Packer was playing one of my pieces, I think it was an ensemble piece. She’d been practicing and a note struck her as wrong. She’d noticed what key it was supposed to be in and went to the chart at the back of the piece, and found that I’d made a mistake.
W: Is distinction between the “true” just intonation and the 72-note, equal-tempered version significant in the final product?
S: The thing is, I can play every piece that I have in the synthesizer either in equal or just. I can’t tell the difference. I couldn’t tell the difference if you sprung one or the other on me. When I’m working on it I begin usually to feel that the just has a little stronger tonal quality, character, or it might be just a little prettier.
My concern for the overtone relations between the notes I use—what some people would call just intonation—is theoretical. It’s not to coerce the performers into the uncomfortable production of some Procrustean set of frequencies. It’s for me to use as a touchstone to help me understand and to inform the harmonic shape of the piece. As such it acts an armature to my composition.
But when we get to actual performance, lots of other things simply have to happen. Nobody ever plays in tune, exactly. No wind instrument can play a sraight, absolutely accurate chromatic scale. Each individual instrument has its own little odd spots. The clarinet gets louder, its pitch drops, and a flute gets louder and its pitch rises. All I ask is that people make it sound right to me. I’m sure that if frequency counters were ever enough to be able to isolate a single line, or really figure out what’s happening in an ensemble, you’d find that they were not playing the note that’s written down, exactly. That they are playing notes that, given the context, sound like the notes I’ve written down. That’s all I want.
I think that any musician is going to try for pure intervals—just, harmonic intervals—but any musician also is going to have, I hope, the intuition to not let it lead him astray. Not let it get in the way of expressivity, of making the piece sound right, of cooperating with his instrument so that it works best, all that kind of thing.
For more about Ezra Sims, click here.