On Interval Discrimination

LMY—The way I like to think of tuning, I tend to follow the Indian classical approach to theory, which is that there is only one octave and there is only one fifth degree of the scale. And, by analogy, I feel that there is only one perfect fourth degree of the scale and only one major second degree of the scale, and that all of the other fourth and second degrees are intervals unique unto themselves. And with the filth degree of the scale there are no variations, and with the octave there are no variations. [In other words, the fifth is always 3/2 and the octave is always 2/1, the perfect fourth is 4/3 and the major second is 9/8—Ed.] With the perfect fourth degree there are no variations, simply you have all the other sharp forms. Then you have some flat forms of the fourth degree of the scale, such as 21, which is obviously the seventh partial of the dominant, although surprisingly it's in that area of the third degree. But without doubt it's not a third degree of the scale, it's a fourth degree of the scale.

DD—Right. This relates to something we were speaking of earlier on the phone, to the notion of false consonance.

LMY—What does false consonance mean? You'd better fill me in.

DD—It's more of a question as to what, indeed, it does mean, and is it important? For instance, you say, for instance, that there's only one octave, and there's only one fifth degree ... the theory is that if anything else falls close into the fields of attraction of those two intervals, because they're so strong, you won't hear them as a true something-else, you'll hear a false octave or a false fifth. [For a more coherent exposition of this theory, see "Heavenly Harmony," 1/1 Vol.2, No.3—Ed.]

LMY—So that's the theory. I see. My feeling is that anything less than an octave is not an octave, and anything less than a fifth is not a fifth, but in the case of the fourth degree, there's clearly this case of 21 which is 21... its not a false ... I don't find the terminology "false" helpful.

DD—In other words, a 21/16 will stand on its own.

LMY—21/16 is 21/16.

DD—It's not a bad imitation of 4/3?

LMY—I don't think so, because my entire theory has developed around intervals being precisely the intervals. Of course, when you set up a modality of tones or a constellation of tones, and these are well defined tones ... you define those tones ... O.K., you're singing ... you come close, as long as you're not introducing a new pitch that is clearly well defined, everybody knows that you were trying to sing that same tone, and that's really what it was about and you didn't do as good a job that time. Nobody imagines for a moment that you introduced a new tone. That's really how I think it happens in common practice.

Conversely, when you set up a situation where you have some very, very subtle relationships with some very close tones, then you write the composition or improvise the composition in such a way that that is clear: that you have some frequency relationships that are very close to other frequency relationships, and that sometimes there is even a very subtle interplay between those where it could take years of listening to the piece to understand how one is actually not the other, but at times they might sound the same. I think it's very important to admit early on that the ear is not infallible, that we are students of sound, that we are learning about sound, and that our ears get better and better, and we hear finer and finer relationships, and that we don't have to pretend that we can hear something we can't hear. I think its perfectly legitimate to write something for an instrument that's capable of playing something that we couldn't, perhaps, sing. A great deal has been learned in the entire history of music theory from being able to tune up some strings and make a tuning stand there that you could listen to and study.

DD—When you look, for instance, at some of the Greek tunings, particularly the enharmonic tunings, that involve very small intervals with ratios like 52/51 or 32/31, those are obviously not intervals that someone arrived at, in the first place, by tuning. They had to arrive at them through theoretical speculation first and then hear them.

LMY—I think so, and its not to say that some people don't have very sensational ears, and its not to say that we shouldn't develop our ears, and its not to say that we shouldn't be able to sing very fine relationships, but it is to say that we have to admit that—not just in this lifetime, but over all history—we're developing our ears to be able to hear and sing finer relationships, and that wherever we are at this point in time is where we are. It's wonderful, for instance, for me to be able to work with the Rayna synthesizer. [See 1/1, Vo1.2, No.3] I can punch up intervals with really sizable numerators and denominators, and be assured that they are exact. And I can listen to them, and study them. It's really fantastic to be able to listen to those and think about do I like it and how does it make me feel, what is it doing to me ... how will I use it in a composition or will I use it at all, and what's it all about.

DD—So you would generally concur with the notion that there's a historical evolution up the harmonic series, in being able to appreciate progressively more complex relationships?

LMY—I think without doubt. In fact, I think I touched on that in my notes to The Well-Tuned Piano [See 1/1 Vo1.3, No.3], that I feel that we're developing over time an ability to understand, use, explore, and further refine intervals which are evolving through an expanding threshold of complexity. I think its becoming apparent with the strong movement in tuning that's developing that there's a much greater practical knowledge of tuning... Sure there have been particular societies that have advanced the art of tuning to quite a remarkable degree. But I think now, with the shrinking of the globe, with modern-day electronics, which give us communications, travel, recordings, all the media ... Think back to the days when Debussy had to wait for the gamelan to come to Paris! What a big experience it was for him to hear that. Who knows how long he had to wait again to have an experience like that. And today, you know, minute by minute, second by second, we're having that experience every day of our lives if we want it. We can walk down to the library, we can turn on the radio, we can go to the record store, we can hop on a plane. The opportunities that are available to us to know what world musics are and what scholarship has been down through the ages—we're in a unique time as far as that's concerned. We have the opportunity to really absorb and adjust and finally to turn this material into something that is really much greater than the sum of the parts, and which is, I think, capable of giving humanity of today and the future information that will help them be able to elevate their lives to a new level of understanding of universal structure and time.