Six American Composers on Nonstandard Tunings

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Six American Composers on Nonstandard TunningsAuthor(s): Douglas Keislar, Easley Blackwood, John Eaton, Lou Harrison, Ben Johnston, JoelMandelbaum, William SchottstaedtSource: Perspectives of New Music, Vol. 29, No. 1, (Winter, 1991), pp. 176-211Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833076Accessed: 05/05/2008 05:06

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Six AMERICAN COMPOSERS ON NONSTANDARD TUNINGS

DOUGLAS IEISLAR

T HIS ARTICLE IS BASED on individual telephone conversations with six American composers who work with microtonal scales or other non-

standard tunings: Easley Blackwood, John Eaton, Lou Harrison, Ben Johnston, Joel Mandelbaum, and William Schottstaedt. These six represent only a sampling from the list of interesting composers in the field. Although their remarks are interleaved here for comparison, none of the interviewees was aware of the others' responses to the same questions.

-Douglas Keislar (italics in the interviews)

Six Composers on Nonstandard Tunings

I. TUNING SYSTEMS

What tuning systems do you use?

Blackwood:Mostly I've explored the equal tunings from twelve to twenty- four notes per octave. The choice of which tuning to use depends largely on the desired style. Certain tunings are more versatile or prettier than others. Twelve, seventeen, nineteen, twenty-two, and twenty-four contain recognizable diatonic scales. If random dissonance is what you want, then the worst of all tunings is twelve-note equal, because it contains a greater concentration of relatively consonant intervals and harmonies in a smaller number of notes. The most effective one for random dissonance is eleven notes. There aren't two notes in that tuning that make any kind of a consonance. Certain others tend toward modal arrangements that coexist in twelve-note equal. For example, if the number of notes is divisible by four, you always have families of octatonic scales. If the number of notes is divisible by six, there are always families of whole-tone scales that can arise as altered chords, as they normally do in twelve-note tuning. If the number of notes is divisible by three, there is a symmetric mode that alternates minor thirds with minor seconds, creating a chromatic world all its own.

Eaton: Most of my pieces involve quarter-tones, but I'm not after rigorous twenty-four-tone equal temperament. Quarter-tones become a field of action for the performers. I want to engage their ears in an adventure and have them explore. Performers will inflect the pitches as the music requires, depending for example on the position of the note in a phrase. They already do so with chromatic music. This is the whole point of music-making; you're not working in a vacuum, but with performers who are very sensitive. After I've worked with a singer or instrumentalist for a couple of hours, they're already hearing the microtonal functions and sonorities in the same way that I do.

I generally work with quarter-tones rather than smaller intervals because every instrumentalist and singer can hear a quarter-tone as a distinct pitch. I've tried smaller intervals, but the performers had a great deal of difficulty. My attitude toward microtonality is that I'll use whatever works.

The other thing that performers can hear is just intervals, where the beating is removed. I used just intonation in one of my most important compositions, the opera Danton and Robespierre. The music of Robespierre is based on a twelve-note just intonation that has just primary triads and a perfect seventh overtone. As Robespierre gets more inhumane, the music becomes more dissonant. On the other hand, the music of Danton is based on quarter-steps, with all the ambiguity of function they permit. For instance, Bb quarter-flat or A quarter-sharp can move in so many different directions.

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I was interested in combining these two generative principles: on the one hand, generating microtones by pulling down the overtones from the harmonic series to construct a scale, and on the other hand, dividing the standard intervals, to preserve and augment the richness of highly chromatic music. When I wrote Danton and Robespierre, the two microtonal

camps-those who base things on the overtone series and those who use divisions-hardly spoke to each other. I thought that was absurd, like the old argument between musique concrete and synthesized sound. Both approaches represent audible acoustical facts and both have a great deal of

capacity for musical expression. What is doctrinaire in theory doesn't matter in music-making at all.

Harrison: I've used many different tunings. I started by getting involved with Asian music. I played the cheng, a Chinese stringed instrument whose pentatonic scale can be tuned two different ways. The first is a subset of the ditone diatonic (also called Pythagorean tuning), with the major third being 81/64. The other one is a subset of the regular just intonation syntonic diatonic, with 5/4 for the third and 10/9 for pitches five to six.

For gamelan, I've used not only the usual tunings, but also just intonation versions that are approved both by those interested in just intonation and by Indonesians. I have three just tunings of slendro that are acceptable to both parties. The fundamental ratios are 8/7 and 7/6. You can pile those up in two or three different ways with a resultant to make the octave, or you can introduce a 9/8 so it's all in superparticular ratios, which is what I like. My pelog tunings lie in the overtone series. The one I've used the most is a seven-note pelog for the Central Javanese style, based on the overtones twelve, thirteen, fourteen, seventeen, eighteen, nineteen and twenty-one.

In my keyboard music I prefer well temperament, specifically Kirnberger number 2, which I used in the Piano Concerto. But when I write for Western instruments with gamelan, for example the Concerto for Piano with Javanese Gamelan, the Western instrument has to be tuned in the intonation of the gamelan. I've also done work for solo strings, French horn, and saxophone, all with gamelan, and they adjust. The brass players can adjust their valves; the string players do it by ear.

Johnston: I've developed a system of extended just intonation. There are two main approaches to just intonation: you can use the overtone and inverted overtone series, or you can approach it from the early music standpoint, where a C major scale in just intonation has its tonic, dominant, and subdominant triads each tuned as 4:5:6. In the first case, extended just intonation means pushing beyond one overtone series into a multiplicity of overtone series with common tones, used analogously to chords in ordinary music. From the point of view of early music, extended

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just intonation would mean pushing first into ordinary chromaticism, and then into the use of seventh-partial and eleventh-partial relationships, and on into higher prime numbers to generate the vibration ratios. Each new prime number yields a characteristically different musical sound.

The highest prime number I've used is thirty-one, in one movement of the Ninth Quartet. In that movement I treat the high partials simply as variants of the lower partials, but I'm sure they could be used in a more extended way. In several pieces I've used the seventeenth and nineteenth partial to get the C# and Eb in the overtone series of C, as part of a twelve- tone set of pitches that could be realized on a keyboard instrument. It's difficult to use any higher overtones systematically, because not only do they generate a huge number of pitches, but it's harder to zero in on the

unique expressive quality of each overtone.

Mandelbaum: I use thirty-one-tone equal temperament, which gives the best approximation to just intonation through prime seven and prime eleven. I started in nineteen-tone equal temperament, using Yasser as a

starting point, along with a bit of the golden-tone theory of Thorvald Kornerup. I might go back to nineteen for a piece or two, but I'm quite happy with thirty-one.

I also use just intonation itself, especially when using higher partials, as on the French horn. Although I often tune my keyboard instrument to thirty-one-tone equal temperament while working on a piece, my results are mostly intended to simulate the upper partials in just intonation, and the theoretical basis of my system is always just. The advantage of the equal- tempered version is that it makes all the music available to the hand all the time. I can find out instantly what an approximate just intonation chord will sound like on any degree. For my purposes, the seventh partial and even the eleventh are sufficiently in tune in thirty-one that I can evoke them in any key. It's the same advantage for a prime seven system that twelve-tone equal temperament had for a prime five system.

Schottstaedt: I use Pythagorean tuning all the time, eleven- and thirteen- tone (equal-tempered) quite often, twenty-four- and forty-eight-tone occasionally, and others from time to time. The most elaborate was the 144- tone equal-tempered system used in You're So Far Away. In that piece, the intervals were basically those of normal twelve-tone tuning, but warped slightly in a consistent direction causing the entire piece to move almost imperceptibly up a tritone, then down an octave. To decide the direction and amount of "warp," I developed a complicated procedure based on Fibonacci numbers, but I'm not sure all the machinery made any audible difference. When I use twenty-four- and forty-eight-tone tunings, the extra pitches show up mostly as melodic coloration or inflection. In terms of harmony, one of the most exciting moments for me is the passage in the

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first movement of Water Music where the main eleven-tone tune climbs up through a descending background of forty-eight-tone chords. Even now, years later, I think it is really beautiful. In computer music you can find

yourself writing long passages in no particular tuning-sounds with an

ambiguous pitch (metallic clangs for example), or no obvious pitch (various kinds of noises), or rapidly changing pitch (bird calls, doors creaking, and so on)-and yet there is a sense of melody and harmony. Busted Pipes and Wait For Me! contain such passages.

Do you use existing tuning systems, or do you tend to invent your own?

Blackwood: I use equal divisions, which are simply there to be discovered; you can't say you've invented them.

Harrison: I've invented a lot of tunings. I've thought up some very beautiful ones, only to discover that they were in fact invented in, say, the seventh century B.C. It's hard to think up something new! I tend to

explore a new system in each piece, and that's true for every aspect of my music.

Johnston: I've greatly extended Harry Partch's system. I had formed some conclusions about just intonation by reading Helmholtz and other Helmholtz-influenced writings before I encountered Partch's writing, but Partch influenced me a lot; it was the first time I had encountered anybody trying to apply these ideas to composition. I generally explore a new aspect of extended just intonation with each piece, but what I've been working on for the last two years is so complex that I could never exhaust its possibilities in one or two pieces. With the kind of scale construction that I've used, I would have over one hundred notes in a chromatic scale. It's very unlikely that I'll get jaded with that kind of a palette.

Mandelbaum: Others have already worked in both just intonation and

thirty-one-tone. I did invent a tuning system similar to Valotti's, but that was just in fun.

Schottstaedt: I use known tuning systems. The only dubious case was Forensic Toxicology, where I chose a bunch of frequencies at random, then stuck to them throughout the piece. I lost that piece when the Stanford Artificial Intelligence Laboratory's seven-track tape drives died, and now I can't remember the details.

Do you compose exclusively with nonstandard tunings? Why or why not?

Blackwood: No. I have a long tradition of writing in standard tuning, and I think the expressivity associated with it is far from exhausted. There is no doubt in my mind that of all equal tunings, twelve is the most versatile and most expressive. It's no accident that we have twelve instead of thirteen.

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One might then ask the question the other way: If that one is the best, why do you use the others at all? The answer is that if the price of gold is high enough, it's worth your while to go looking at the mines that produce a lower quality ore-there's still gold in those hills.

In particular, some of the equal tunings contain chromatic substructures that you cannot duplicate with twelve notes. The most interesting ones in that category involve the equal division of the octave into five equal parts, as in fifteen-note tuning. The resulting progressions seem halfway between diatonic and chromatic. Sixteen-note equal, like twelve, has octatonic scales. Twenty and fifteen have ten-note symmetric modes that are analo- gous to octatonic scales, but they bring about a diatonic rather than chromatic substructure.

Eaton: I haven't written any non-microtonal music since 1964. I'm a very intuitive composer and I just don't hear phrases anymore without microtonal sonorities. It sounds wrong to me if a section of a piece is simply chromatic and then the microtones are added as a spice or coloring, an embellishment. It's just as wrong as it would be for a Bach fugue to suddenly go into modal counterpoint. My very first microtonal piece, a piano piece from 1964 called Microtonal Fantasy, contains no sonorities that are not microtonal. Every single sonority in my music contains at least one microtonal interval.

Harrison: I just finished a string trio and the piano had to be in equal temperament; that was part of the commission so they could perform it around. But I can't stand equal temperament. I compose more easily if I can hear some real intervals. So I composed it on my own piano, which is tuned in Kirnberger number 2. I'd prefer never to compose for standard tuning; in fact it's extremely difficult to do so. I have a little electronic keyboard out in the trailer and I test on that, but finally I come screaming inside to my piano.

When I write for full orchestra it's a compromise, because the orchestra is a compromise anyway, and I take that into account. I find that when I write modally in any kind of mode, the orchestra will tend to get it more or less right.

Johnston: I've written pieces in standard tuning, even fairly recently, but I don't like to. I did the music for an off-Broadway production, and I didn't want the theater people to have to cope with another tuning. But I recently refused a commission that stipulated that the pieces were not to be in any unusual tuning.

Mandelbaum: About twenty percent of my pieces are heavily weighted to alternate tunings, and some of the works I'm most pleased with use alternate tunings for special passages, but for the most part I use conventional tuning. I'm especially hesitant about using keyed instruments like

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woodwinds for playing tunings they were not designed for. I'm going to

experiment with Johnny Reinhard's material on woodwind fingerings for alternate tunings.

Schottstaedt: I like twelve-tone equal temperament. I seem to have fluctu- ated over the years-some years every piece uses unusual tunings, and other

years I work almost entirely in standard tunings.

How systematic are you in your use of microtonality? Could your composition be described as being theory-based?

Blackwood: Yes, I think in my case that is true. I find the theory very useful in arriving at results more rapidly than I otherwise could. I can work at an accurately tuned keyboard, but I find it much faster if I look at the

patterns that are associated with equal tunings, and particularly if I can relate unfamiliar tunings to a familiar one.

Eaton: I certainly don't work from a theoretical premise, but I could give instances of my using microtones systematically. In my opera Myshkin, which was based on The Idiot by Dostoyevsky, I used synthesizers in sixth- tones when Myshkin is in an irrational state. On the other hand, when he's

observing events, I've used an orchestra tuned in quarter-steps to represent reality. The two things weave in and out of each other, depending on

Myshkin's state of mind. It's systematic in that sense.

Harrison: My music isn't theory-based. Having set up an intonational

system, my fun is to explore it in every way imaginable. For example, the main theme of the first movement of the Piano Concerto is in C major in just intonation, with a slightly raised A. In the development section I wanted a variation of the main theme in the minor, so I chose F minor, and in the

Kirnberger that's Pythagorean intonation. Playing around with the intonation this way is fun and very effective.

Johnston: It varies from piece to piece, and even within the same piece I use different techniques. My Sixth Quartet is an extremely systematic piece. The Fifth Quartet, written around the same time, is a through- composed piece without any conscious system. It has a nonstandard tun-

ing, but the way in which it's applied was not worked out. The Duo for Flute and String Bass was almost entirely coloristic; as in seventeenth- and

eighteenth-century music, I used ornaments to get melodic expression and coloration. The ornaments were produced by bending the tone according to pitch curves that were notated like neumes.

Mandelbaum: Certain compositions of mine are heavily theory-based, like the studies on the Euler genera that I wrote under Adriaan Fokker's

tutelage in Holland in 1963. If a piece with microtones that are engendered by the consonance of the seventh partial can be called theory-based, then a

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lot more of my microtonal music is theory-based, but most of the rest of it is simply playing with the intervals empirically to get what sounds best, given what I want to express.

Schottstaedt: I hope I'm not systematic. I avoid theories like the plague. I like keeping my options open-I want to write good music, not test theories. Theory-based music is very boring to me.

What effect, if any, does the tuning system have on theform and structure ofyour pieces?

Blackwood: In my case, a great deal. If there are two distinct modal substructures found in a tuning, sometimes they'll be contrasting and sometimes not. If they're very contrasting, that suggests a bi-thematic form in which one theme is in one mode and the other theme is in another. That's certainly the case where fifteen is concerned. You can make a bi- thematic piece in fifteen-note tuning by making one theme diatonic and the other chromatic.

In other cases there is only one modal substructure. When the number of notes is a perfect square there is a strange disadvantage. Sixteen is divisible by four only, so there are complex arrays of octatonic scales. But that's the only modal substructure that produces any sensation of coherence, so getting a contrast is difficult.

Eaton: I don't think you can separate the form from the tuning system. The way I write operas, which are my most important pieces, is to write a lot of chamber music using specific kinds of materials, and then find the subject for the next opera. The form of the piece always comes out of the material, or the idea and the material come into being at once.

Harrison: The tuning system does affect the structure. One finds new and interesting relationships that don't exist in equal temperament.

Johnston: Sometimes the tuning absolutely determines the structure. In my Fourth Quartet, the variations on "Amazing Grace," the timing, the note durations and the relative tempi are affected by the same integer ratios that govern the pitch. The variations go from a very simple tuning to a much more complex one. Everything other than the decision to have a theme and variations was very much a product of the technique I was using. On the other hand, that piece is one of my most accessible. It really is art concealing art, because listeners have no idea how complex it is.

Mandelbaum: The tuning can affect the form by determining where modulations end up. One of my Dream Songs, for thirty-one-tone instrument plus two violins and a soprano, begins and ends in the same key. I then did a version in twelve, and the equivalent modulation wound up in a different key.

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Thirty-one-tone tuning increases the number of ways to add tension, the

presentation and resolution of which determines the structure of the piece. There is a far richer variety of "artificial" scales that can do battle with a "natural" scale built on the hierarchy of consonances from the overtone series. In twelve, the "artificial" scales are ones like the octatonic and whole-tone scales or the hexatonic scale C Db E F Gt A C. There are

infinitely more in thirty-one.

Schottstaedt: I sometimes put different portions in different tunings, so the tuning system might help delineate the form, somewhat like a traditional key area; at other times I mix two tuning systems, each carrying a different idea (sort of like polytonality). Water Music contains many exam-

ples of these techniques. In terms of overall form, I don't think the tuning system has any effect.

What is it about composing with nonstandard tunings that you find the most interesting?

Blackwood: The aspect that intrigues me most is finding conventional harmonic progressions, or at least coherent progressions found by extension to their analogues in the more familiar tunings.

Eaton: Microtones permit a greater variety of harmonic and melodic motion, which in opera helps delineate drama and define character. My interest in microtones came from three directions. First, I wrote some of the very first pieces that involved woodwind multiphonics in the early 1960's, and I was intrigued by the "out-of-tuneness" of the multiphonics. Secondly, I was interested in cluster music. After a while, though, it seemed like a lot of sound and fury signifying absolutely nothing. But by changing the tuning between or within clusters, I could again generate harmonic and melodic motion and have events of some significance occur. Finally, during this period of my life I was making my living as a jazz musician. With jazz I could get involved immediately with microtonal intervals.

Harrison: The reason for my interest is very simple. Real intervals-the ones with whole number ratios-grab you; they're beautiful; they draw you into the music; whereas fake intervals like those of equal temperament don't do much.

Johnston: I love extending my vocabulary and trying to imagine unfamiliar sounds. You can generally imagine a melodic line, but it's very difficult to imagine what a combination of strange intervals will sound like. And when your instrumentation contains a lot of winds, the timbral changes make the piece an interesting box of surprises. To get the intonation, the players might use alternate fingerings, lip the notes high and low,

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Six Composers on Nonstandard Tunings 185

or pull out the barrel of the instrument, all of which change the timbre. You get a flute that sounds more like a shakuhachi, or instead of an oboe

you get different colors of oboe.

Mandelbaum: I find that extending the consonances to the seventh partial provides a fascinating means of enrichment. It retains traditional consonance and dissonance, unlike atonal music, which has to abolish the old in order to arrive at the new.

Schottstaedt: I like the unusual sounds, the intense dissonances in particular, such as the squeezed minor seconds and stretched fourths in Dinosaur Music. I've never been much interested in getting cleaner consonances; beats don't offend me.

II. INSTRUMENTS

For what media do you typically write?

Blackwood: For the Twelve Microtonal Etudes I used a Polyfusion synthesizer, and I've also written for a refretted guitar in fifteen-note equal tuning. There are other instruments that have the capability of playing microtonal intervals, but often the timbre of an instrument is all wrapped up in the tuning. I don't advocate tuning the piano in other ways than twelve equal. Whereas harpsichords and organs work well in meantone, on a piano the meantone fifths have a terribly hard nasal sound, and the pure thirds don't seem to resonate right. Likewise, the violin sounds bad if you make any change to those pure perfect fifths. Particularly for single lines, the best tuning of the violin is the Pythagorean, which is what violinists

prefer unless they're playing slow double stops. As for brass instruments, they sound very bad with out-of-tune fifths or thirds, especially in the high register.

Eaton: I've already mentioned my writing for opera. I've written a lot of chamber music, and the intonation usually works out; often I divide the instruments into two groups, one tuned a quarter-step below the other. In Sonority Movement, the nine harps are divided into three groups of three and tuned in sixth-tones, and the flute plays in quarter-steps. I've written orchestral music, and I feel that's the most difficult problem, because orchestras simply don't have the time to really get it together.

Harrison: I've used so many instruments, both from East Asia-Korea, China, and Java-and from Northwest Asia (which is what I call Europe). I've also built new instruments for special tunings, which is fun; it doesn't have to be done with electronics.

Sometimes I use a selected orchestra to get the tuning I want. For


the Piano Concerto, I selected instruments that could play in tune with the piano. The three slide trombones, which can play any pitch, only had to listen to the piano once and they got it. The two harps are each tuned to different aspects of the Kirnberger tuning. There are also strings and some

percussion. Similarly, I used a selected orchestra back in the 1950's with

my Four Strict Songs for the Louisville people. I used a chorus and only instruments that could be retuned, throwing out the woodwinds and so on.

Johnston: Recently I've had some opportunities to write for orchestra.

Obviously the most flexible media for intonation are strings and voice. However, small intervals in the higher register of the violin force your fingers close together, so in some rapid passages you have to play an articulated glissando. Also, typical vibrato is too large for some of these intervals, so you have to decide what kind of vibrato to use and how much, if any. As for the voice, it has no limitation in principle; your ear is

everything. I've found that choral music doesn't take exceptional musicians, if I'm kind in my writing.

Mandelbaum: First I would mention the thirty-one-tone keyboards, which I usually use for composing my microtonal music. These have included Fokker's pipe organ, a portable organ called the archiphone, and a version of the Scalatron that has a thirty-one-tone keyboard. (The Scalatron is a tunable electronic keyboard instrument that Motorola manufactured in limited quantities in the 1970's.)

I've written some microtonal music for specific performers: the cellist Janet Holmes and the violin duo of Bouw Lemkes and Jeanne Lemkes-Vos. I rarely use the French horn without writing seventh or eleventh partials, since they come so naturally on the instrument and sound so good. Occasionally I use flutes tuned about a third of a semitone flat, simply to be available for the seventh partial of other instruments' notes. My choral Iaddish and my opera The Dybbuk include microtones. In The Dybbuk, two singers sing in simultaneous parallel just sevenths, supported by a thirty- one-tone keyboard instrument, flattened flutes, and horn harmonics.

Schottstaedt: In the last twelve years, I've only written tape music. I started several pieces for tape and instruments, but the instrumental parts dropped out during composition. For example, in Daily Life among the Phrygians, which was originally intended for cello and tape, I had worked out a cello part, but since the tape part by itself seemed satisfactory, I ended up flushing the cello part. Most of my work has been done using a mainframe computer, CCRMA's custom digital synthesizer (the "Samson Box"), and Pla, a compositional language I wrote in 1979 or so. The musique concrete pieces were done entirely in software, without the use of the Samson Box.

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How well do peformers realize your intentions with respect to intonation?

Blackwood: I would be reluctant to try anything other than fretted

stringed instruments or recorders, especially if the tuning had a large number of notes. Perhaps the flute would work, but there's not enough intonational variation possible in the low register.

Eaton: To me, music is a matter of the expression of the human spirit. It

really doesn't concern me if there are imperfections here and there; what concerns me is whether the performers have the same musical image as I have. If they understand what I'm after, they can realize it. Microtonality, like any musical technique, is simply a means to an end. Music comes from the fact that people need to sing, purely and simply, just as whales and wolves do. All these issues have to be seen in the proper perspective, which is that we're human beings trying to communicate.

If I have two pianos tuned a quarter-step apart so there is some fixed pitch reference, people can have an adventure, and they begin hearing the intervals. I remember one piece, for Syn-ket synthesizer and orchestra, written in 1966. In the first rehearsal the orchestra was in uproar over the intonation: "We've worked all our lives to play in tune, and now you want us to play out of tune." But then they began hearing. I had people from the cello section say, "This piece was fun to play."

With singers there's much less difficulty than with instrumentalists. Jack Beeson, who was an opera coach at the Met, amazed me by singing a perfect sixth-tone scale. They train their singers to add excitement to

perfect intervals by inflecting them a sixth-tone flat or sharp.

Harrison: Sometimes performers do quite well. For example, I've had music played in Korea on the piri, a reed cylindrical-bored instrument that's really the aulos alive and well in East Asia. The piri can do anything with pitch. I've had very good performers for saxophone, which is also a very malleable instrument. William Trimble plays my piece for pelog gamelan and sax, A Cornish Lancaran, beautifully.

I wrote a violin piece in slendro for Dan Kobialka, and he's played it flawlessly with two gamelan, each with a different tuning of slendro. But in England I had great difficulty with my Double Concerto for Violin and Cello with Javanese Gamelan. It apparently never occurred to them to use their ears. They'd see a note and it would go straight from the eye to the finger.

Johnston: Usually they do fairly well, although I've heard some bad performances. I did a big choral/orchestral piece for the Springfield Sym- phony, in Illinois. It was really quite beautifully done and the intonation was impeccable. The Cleveland Chamber Symphony commissioned another piece for tenor and string orchestra, and it only took them about six hours of rehearsal, which means it's not too difficult.

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Performers can play in just intonation more easily than in any kind of temperament, if they don't constantly play with the piano. String players play as near to just as they can. Singers sing in just triads because it's easier. Brass players also have some feel for it. The woodwinds have the most problem, because ordinary fingerings don't work, especially on the oboe. I got good players to edit my parts and provide me with fingering, but then I discovered that it varies widely across instruments and even across different players using the same instrument. So I decided that all I can do is to call for an inflection and let the performer figure out how to get it.

Mandelbaum: Some performers are remarkable; others memorize their fingering in a way that makes microtones out of the question. There is very little correlation between a performer's skill with conventional music and how well the performer can handle the microtones.

I find the exact intonation of the dissonances really doesn't matter. You can be off from any given pitch by as much as you can be in twelve. Consonances, on the other hand, need to be as close to just as possible.

Schottstaedt: None of my instrumental music used nonstandard tunings. It's hard enough to get performances without adding dubious difficulties.

How has technology influenced your musical directions?

Blackwood: Having available an electronic device that will give very accurate and reliable approximations to equal tunings has made possible things that I couldn't do otherwise. I still work with the Scalatron. It's very handy to be able to sit before a keyboard instrument and actually hear complicated harmonies. Also, I think having a synthesized version for reference is the best way for a performer to learn a microtonal piece. That technique worked well for my guitar piece in fifteen equal.

Eaton: I've used electronic keyboards from early on because their pitches are accurate and defined. I think I gave the first live performance on an electronic synthesizer, in 1964 in Italy. I made my living as an electronic troubadour for about six years, during which I gave about a thousand concerts. I've worked a little with computers, but only when I wanted the answer to a specific problem-for example, to hear the precise pitches of a scale I envisioned.

But technology can become a terrible trap, because it can generate a whole series of rather meaningless scales and possibilities. Music never comes from possibilities; it comes from necessities. We sing because we need to sing and we need to find the particular sound that fits the aural image we have. The generation of possibilities can be a real dead end, a real detriment to musical progress. On the other hand, if something sounds good to you, use it.

188


Harrison: I don't like the sound of CDs; I prefer analog. I don't use electronics. When asked why not, I say, "I don't want to be unplugged." As Larry Polansky has said of me, with every advance I take a giant step backwards. More electronics, and I go to flowerpots and tin cans.

Johnston: The computer helps a lot. I've never written computer music, but I know about that from Lejaren Hiller and others. I've used the computer to check my derivation of microtonal scales.

Mandelbaum: My gut reaction to technological developments is suspicion that they will take away the spontaneous interaction between performer and audience. But I do have a tunable synthesizer that I use sparingly.

Schottstaedt: Without the computer, I'd have gone in some entirely different direction, perhaps not even music composition. I was never very happy with available notations, so I was ecstatic when I realized the musical possibilities of computer programs. Common music notation steers you in the direction of using simple rhythms, conventional melodic gestures, and fewer notes (because you get tired of writing them by hand!). With the computer, I could generate very complicated passages-complicated in the sense that they would be a bother to notate, even though they may be musically simple.

III. NOTATION

How do you notate your music?

Blackwood: I use a traditional staff and various accidentals depending on the tuning. Any equal division that contains what I call recognizable diatonic scales, such as twelve, seventeen, and nineteen, can just use the normal accidental symbols, including double sharps and double flats. In nineteen-note tuning the enharmonic equivalent of Fb is El; in seventeen- note tuning the equivalent of Fb is DO.

Sixteen and eighteen can be notated in a coherent way if you use the same enharmonics as in nineteen. Since diminished seventh chords coexist in twelve notes and in sixteen notes, the rule for notating sixteen is that if it sounds like a diminished seventh chord, it should look like one. Similarly, in eighteen, if it sounds like a whole-tone scale, it must look like a whole- tone scale.

It is necessary to introduce new accidental symbols with fourteen, fifteen, and twenty through twenty-four. You can notate fifteen as three intertwined pentatonic scales, each with the same note names but with up or down arrows for accidentals. For twenty you need double arrows, which is cumbersome. I use an arrow that has a circle drawn through it to locate

189


the appropriate line or space. The arrow also serves to notate the quarter- tones in twenty-four.

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At Z 4/ . ?

EASLEY BLACKWOOD, "21 NOTES" FROM 12 Microtonal Etudes, MM. 1-6, AND TWENTY-ONE-NOTE SCALE

Eaton: For a quarter-tone flat I use an open flat, but with a check on the stem. Without the check people confuse it with a regular flat. For a quarter-sharp I use one vertical line and one across. I don't like arrows on accidentals because performers interpret that to mean just a slight inflection. In Myshkin, which uses some sixth-tones in the orchestra, I indicate a sixth-tone flat or sharp with a 6 or a 9. If you use a wholly different system like just intonation or meantone tuning, defining the tuning very carefully at the beginning generally takes care of it.

Harrison: I think I'm one of the few people in the world who has written in free style, by which I mean the joining up of precise expressive intervals without choosing any set arrangement of pitches in advance. You might end up with twenty-three Fs and four Fbs. I've only written a few such pieces, for example At the Tomb of Charles Ives. For these pieces, I usually use staff notation and then put the ratio involved between each of the notes. I do the same thing for vertical combinations. So it's all charted out in terms of ratios, with the noteheads vaguely showing where you are. If it looked like a

190


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Lou HARRISON, At the Tomb of Charles Ives, PERFORMANCE NOTES

major third from D to F#, I would write a sharp in front the F, but I would also have to put a 5/4 or whatever; the ratio is what determines it.

For pieces [or instruments] not in free style, I indicate the ratios at the top of the score, which uses staff notation.

192


Johnston: I was very dissatisfied with Partch's solution to the problem of notation. He used the ratios in place of traditional notation, which is a cumbersome and difficult approach. Tablature is no good either; you can't assume that all your readers know each of the instruments that well, especially if they've never seen them, as with Partch's instruments!

My premise is the C major just intonation scale. A note with no accidental is part of that scale. The inflection that changes C major into C minor is a flat. It's 70-71 cents, which gives you a 6/5 minor third from C to Eb, rather than a 5/4 major third. The sharp that changes A minor to A

major is the same amount, 70-71 cents. In addition to the sharps and flats there are pluses and minuses, which

give the difference of the syntonic comma, about 21-22 cents. For exam-

ple, in C major, the A that's in the dominant of the dominant is a comma

higher than the A that's in the subdominant triad, so I write the former as A+.

There has to be an inflection for each new prime number that you use.

Generally I use the numbers themselves for the symbols. The seventh

partial is forty-nine cents lower than the 9/5 minor seventh. I use a 7 to lower the pitch, and an upside-down 7 to raise the pitch. The eleventh

partial is fifty-three cents, almost exactly a quarter-tone, above the perfect fourth. For this alteration, I use an arrow up or down, since that's com-

monly used by composers to indicate a quarter-tone. I use a little 13 and an

upside-down 13 for the thirteenth partial, which in C is about twenty- seven cents above A flat. There's a pair of those symbols for every new

prime number you introduce.

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BEN JOHNSTON, STRING QUARTET NO. 9, MOVEMENT IV, MM. 24-25

193


Mandelbaum: I use Fokker's notation system, which is traditional except for the addition of new accidentals. In thirty-one-tone music a whole tone is divided into five units, called dieses. A semisharp raises by one diesis, a

sharp by two, and a sesquisharp by three. The semisharp symbol has one vertical line and the sesquisharp has three. Similarly, there's a semiflat, which is a flat sign that doesn't close, and a sesquiflat, which is like a semiflat with an extra hook. A sesquisharp is the enharmonic equivalent of a flat, and a sesquiflat is the enharmonic equivalent of a sharp.

As a supplement, I use symbols that look like 7, 11 or 13, according to which partials I use. To specify a very in-tune major third, I usually don't write a 5 over it, but rather use an asterisk with an explanation.

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JOEL MANDELBAUM, Four Miniaturesfor Archiphone, "ON THE FIFTH RANK," MM. 1-9, AND THIRTY-ONE-TONE SCALE

Schottstaedt: The score for my music is a computer program. I start with a text file containing the Pla procedures that generate another file, a note list containing parameters for the synthesizer. I use the Pla algorithms to generate some basic material, and then mold that into a piece of music by editing the note lists. I never create the note list directly, as some composers of computer music do.

Although traditional music notation is easier to read, I can tell from looking at the note list what the music will sound like. It can be very difficult to do the same by examining the algorithm itself. I don't use

194


COMMENT this is an example of Pla code used in "Pastorale";

DEFINE Lim4-256; DEFINE Time4-90; INTEGER ARRAY Mode[0:12]; INTEGER i; FOR i -0 STEP 1 UNTIL 12 DO Mode[i)]-[0,0,2,4,5,11,7,9,9,0,7,0,0]; COMMENT this is our scale;

REAL ARRAY Rats[0:12]; FOR i+-0 STEP 1 UNTIL 12 DO Rats[i]i-[1.0,256/243,9/8,32/27,81/64,4/3,1024/729,3/2,128/81,27/16,

16/9,243/128,2.0]; COMMENT this is our tuning scheme -- look familiar?;

PROCEDURE Tune(INTEGER x); BEGIN INTEGER Oct,Pit; REAL Base; Pit+-x MOD 12; Oct4-INT(x/12); Base-Rats [Pit]; RETURN((2Ôct)*Base); END;

SEG Bell 0.0 0.0 0.4 10.0 0.8 25.0 1.0 40.0 1.0 60.0 0.8 75.0 0.4 90.0 0.0 100.0;

PROCEDURE RBell(REAL x); RETURN(Bell[x*100]);

INTEGER ARRAY Pits,Octs,Rhys,Begs,Amps[0:Lim]; FOR i--0 STEP 1 UNTIL Lim DO

BEGIN Octs[i]+-2+4*RBell(RAN(597)); Pits[i]-Mode[12*RAN ]; Rhys [i]+4+6*RAN; Begs [i]--2+6*RBell(RAN); Amps [i]1-l+8*RBell(RAN); END;

Pars: Name,Beg,Dur,Freq,Amp,Ind;

FOR i+-l STEP 1 UNTIL 2 DO VOICE "Violin"; BEGIN

INTEGER CellBeg,CellSiz,CellCtr; REAL NextBeg,MyTempo; I ONLY:

BEGIN CellBeg+-0; CellSiz+-8; CellCtr-0; MyTempo+-l/4+i/24; NextBegS-0; END;

Beg+-Beg+NextBeg; IF Beg > Time THEN BEGIN PRINT("overtime..."); KILL(SELF); END; NextBeg+-MyTempo*Begs CellCtr] /8; Dur4-((4*MyTempo*Rhys[CellCtr]/8)*(.9+.2*RAN)) MAX .15; Freq--16.351* (2^ (Octs [CellCtr]) )Tune (Pits [CellCtr] Amp+-Amps [CellCtr]/100; Ind-"0.2, RevSet:.01 pizz"; CellCtrn-CellCtr+l; IF CellCtr2Lim THEN BEGIN PRINT("Hit end at ",pl); KILL(SELF); END; IF CellCtr > (CellSiz+CellBeg)

THEN BEGIN INTEGER i,j; CellBeg- (CellBeg+2); CellCtr+-CellBeg; j4-Pits(CellCtr]; IF CellCtr < (Lim-Cellsiz*2) AND RAN>.975

THEN FOR i'-0 STEP 1 UNTIL CellSiz*2 DO

IF Pits[CellCtr+i] = j THEN Pits(CellCtr+i]l-Pits[CellCtr+l];

END; END;

COMMENT that piece of code generated a zillion notes. These were then edited by hand and by Pla, to create a portion of the final note list. An example of the note list is:

FrqD+-810/348; IndX+-.1; Violin, pld+.000,1.323, 348.123*FrqD, .080, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+.182,.335,87.031*FrqD, .090, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+.636,1.595,138.153*FrqD, .080, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+.726,.386,34.538*FrqD, .090, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+.908,1.470,103.497*FrqD, .060, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+1.419,2.633,206.995*FrqD, .080, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+1.884,.352,58.086*FrqD, .090, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+2.253,.346,87.031*FrqD, .089, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+2.695,1.674,138.153*FrqD, .079, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+2.781,.380,34.538*FrqD, .089, 2'IndX, RevSet:, .1, PIZZ; Violin, pld+2.968,1.390,103.497*FrqD, .059, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+3.473,2.304,206.995*FrqD, .079, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+3.904,.346,58.086*FrqD, .089, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+4.256,1.969,46.103*FrqD, .069, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+4.256,1.663,138.153*FrqD, .079, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+4.347,.323,34.538*FrqD, .089, 2*IndX, RevSet:, .1, PIZZ; Violin, pld+4.517,1.413,103.497*FrqD, .059, 2*IndX, RevSet:, .1, PIZZ;

WILLIAM SCHOTTSTAEDT, PLA CODE FROM Pastorale


graphical or pictorial notations at all. Around 1983, I added a common music notation display to the text editor, so that composers could display their note lists in a more familiar fashion. However, composers at CCRMA didn't seem to make much use of it.

I don't even use the traditional pitch or rhythm names anymore. I work entirely with scale degrees, and the resulting pitches depend on whatever tuning has been specified at that point. In the note list that gets generated, everything is in Hertz and seconds. The rhythms are complicated; I try to avoid simple divisions of the beat. The raw material usually includes a set of rhythms, which changes for every piece.

Is a general-purpose microtonal notation system possible, or is a multitude of notations inescapable, given the multitude of tuning systems?

Blackwood: I can't find a general-purpose notation, but the equal tunings do tend to fall into groups, as I described.

Eaton: I'm sure it's going to come, but gradually. I don't think you should decide these things in advance because invariably you cut off possibilities. Notation is an awkward process of evolution.

Harrison: Seeking a general notation is part of a whole package that I'm not attracted by, which I call nineteenth-century system-building. Nineteenth-century theorists wanted to build a system by which you could do everything. But I have no interest in large-scale intellectual exercises of that sort. I use what I want when I need it and make do, inventing a new way if necessary.

Johnston: I doubt that a general-purpose notation is possible, but I don't know for sure. Easley Blackwood has notations that work extremely well for the equal divisions of the octave, but they wouldn't transfer to just intonation any more than just intonation would transfer to them.

Mandelbaum: Most of the wide variety of microtonal notations start with what's already there, namely, standard notation. If we can refine the agreed-upon notation beyond one hundred cents to smaller intervals, that would be very helpful. It's desirable enough that even people with unique needs should start with a general notation with agreed-upon diesis and comma signs, and then add their own individual special-ticket items. If you specify the tuning, there is no reason why the the semisharp and semiflat symbols cannot be used for both quarter-tone and diesic music.

Schottstaedt: For computer music, a general notation is a possibility, though not one that interests me much. For instrumentalists, there are ways to use five-line music paper for other tuning systems (for example, you can get thirteen-tone tuning by assuming that BO isn't C, and so on).

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IV. AESTHETICS

Does a nontraditional system of tuning imply a nontraditional aesthetic? What happens when a nontraditional tuning is applied to a traditional musical style?

Blackwood: Some people find it delightful; others find it confounding. In

my experience, most people think that my Microtonal Etudes are intriguing because of the way they make new organizations of familiar-sounding harmonies.

Eaton: I don't like sprucing things up with microtones. It has to be a much more organic process than that. As I said before, music has to come from necessities, not from possibilities. On the other hand, there have been

composers who have put new wine in old bottles, or old wine in new bottles, and yet made a valuable contribution. If something is genuine, you know it. The most traditional composer in some ways was Arnold

Schonberg.

Harrison: A given tuning system can support widely divergent aesthetics. The tuning period of twelve-tone equal temperament has witnessed everything from Scriabin and Schonberg (who had the same ideas actually) through John Adams and Steve Reich.

Johnston: I don't like applying a nontraditional tuning system to a traditional style. What bothers me about the music of Alois Haba and Julian Carrillo is that the pieces don't seem unusual at all, just the intonation. The notes sound wrong, because the gestures, structures, and idioms are familiar from a different tuning.

I have used traditional structures in my music, but they are transformed by the logic of the tuning system. In my Duo for two violins, for example, I wrote a Bach fugue to show what would happen to the traditions of the fugue if they were subjected to this prism. I once studied with Milhaud, who said, "Don't ever use sonata-allegro or a fugue or any of the traditional forms unless you have something new to add." In a way that's what Haba tried, but it seems to me there's a failure of transformation there.

Mandelbaum: In my view, a nontraditional tuning helps to empower a traditional aesthetic. By adding to the available consonances, it permits the overtone series to continue to be the basis for harmonic structure in music. Otherwise this basis might be exhausted, if the consonances were limited to those that are well represented in twelve-tone equal temperament.

Schottstaedt: Putting something written in a completely traditional style into a nonstandard tuning might be an interesting experiment from a musicological point of view, but it's not what I call composition. I consider myself a traditional composer in the sense that I'm consciously working

197


within the Western musical tradition, but I hope I take a more speculative or creative approach to these materials.

Does agiven tuning suggest a certain musical style, or even a certain affect?

Blackwood: In the broadest sense, yes, at least where equal tunings are concerned. It is hardly possible, however you try, to write pretty chords in eleven notes. It would be awfully difficult to go I-IV-V-I in sixteen notes. If you use the octatonic modes in sixteen, you'll sound like Ernest Bloch, or certain pieces of Scriabin or Stravinsky.

Harrison: I don't think a given tuning implies any particular aesthetic. The tuning system does affect the musical materials, however. By the time

equal temperament was fairly well accepted (and it only started around 1850, being an artifact of the iron piano), Schonberg wisely observed there was no tonality in it. What happened in twentieth-century music was the

rejection of the triad, and simultaneously the adoption of the fifth and

second, both of which are not bad in equal temperament, whereas the

major third is terrible. Schonberg was piling up fourth chords. Debussy and Ravel heard a gamelan at the fair in Paris and used that influence in their music. These are instances of a change in the fabric of music due to

composers' rejection of materials that couldn't be done well in the tuning system.

Johnston: Definitely the affect is unique with each tuning. Each overtone is a unique rasa. The third partial, which generates perfect fifths and fourths, contributes stability and strength. The fifth partial, which is the third and sixth, contributes warmth of emotion, ordinary human warmth. The seventh partial creates a sensuality, for example in vernacular music like the blues. The eleventh partial introduces ambiguity, because the intervals of 12/1i and "1/o, which are the overtone intervals surrounding the eleventh

partial, are neutral seconds, squarely in between major and minor. The 1/9 is a neutral third. The "/8 is in between a perfect fourth and augmented fourth. The thirteenth partial has a melancholy, dark quality. Nearly every time I've used it, it has something to do with death, which would square with the meaning of thirteen in numerology. The seventeenth and nineteenth don't really bring anything new, because seventeen is almost exactly a tempered half-step and nineteen is close to a tempered minor third.

Mandelbaum: I note with some interest the writings on this subject by Ivor Darreg, who has made some important contributions to the field. Darreg says each equal division of the octave has its own mood, and I think he's probably right. Tunings that stay close to just intonation, such as thirty-one, with pure thirds and sevenths, tend to provide an aesthetic that permits the expression of sweet, loving and world-embracing feelings. That's why I like them. I'm sure there are other microtonal systems that would make raising revolutionary hell easier.

198


Schottstaedt: In most cases, I don't think the tuning system suggests a particular style. Just intonation, however, has always struck me as bland and lifeless; it's ideal for background music. I think this is caused by the flat major third, which has an unassertive feel that can lead to unmotivated

voice-leading, and eventually to aimless doodling and strumming.

Do you draw upon non-Western influences in your music?

Blackwood: I found that the slendro and pelog modes of Indonesia have greatly aided my understanding the operation of twenty-three notes. The number of steps between the notes of the pelog in this tuning is 7-3-3-7- 3, and the slendro goes 4-5-5-4-5.

Eaton: I've been influenced by sounds I've heard, but I've never deliber- ately set out to write non-Western music. I have too much respect for those musicians. I did learn from a Turk that a singer can get a three-quarter-step trill, which is a very characteristic and interesting sound, by smiling while trying to sing a semitone trill. It works!

Harrison: At least half of my music is based on non-Western influences.

Johnston: I've been influenced some by Indian music, particularly North Indian. I've listened to it a lot, and I'm aware that it uses just intonation; the ragas are organized that way.

There's an interesting scale that Partch used in one of the two ancient Greek studies that are part of the Intrusions. It's a variation of the enharmonic Greek genera, and if you omit one note in each tetrachord it's very close to the most familiar Japanese scale. I use that scale in one variation of the "Amazing Grace" Quartet, and John Sherba of the Kronos Quartet plays it very Japanese, in a real kabuki style.

Mandelbaum: I've never methodically studied non-Western music, but I've listened to a little Indonesian, Chinese, Japanese and Indian music. Once in a while a melodic turn will reach me and something similar will come up in my music. Some of my experimental music has representations that approach Oriental scales.

Schottstaedt: Part of SandCastle was inspired by the "thumb piano" music of West Africa; part of the third movement of Water Music was an attempt to imitate a Nigerian march that I heard on a Folkways record; Pastorale uses a gamelan scale. I doubt that anyone listening to the music would notice these influences, though. Does microtonal music run the risk of sounding out of tune? If so, how do you address this concern in your composition?

Blackwood: It does. There's no getting around that whatever. In some cases it sounds out of tune in an agreeable way, and in other cases just out

199


of tune. With fourteen notes, there is no way to conceal the fact that it's out of tune. It's so dissonant I couldn't bring myself to close that one of the Microtonal Etudes on any kind of harmony. It just closes on a

single note.

Eaton: I don't think you can do anything about it. I remember playing my Microtonal Fantasy for a famous American composer, who said, "It's a wonderful piece, but it just sounds to me like it's out of tune." What could I do? That's not the way I or most people hear the piece. Some people will

always hear it that way.

Harrison: I don't have any problem. I did have one reviewer speak of "the acrid dissonances of just intonation." He should have known better. On occasion I've had to point out to people that I was using a different tuning system, because it sounded so natural and normal to them. That's my pride and joy, when it sounds normal.

Johnston: I address the problem by using just intonation. I didn't start out by being interested in microtones; they were a by-product. I started out by being interested in getting the music in tune. But if you use some of the

higher partials in the wrong way, they do sound out of tune. In fact, sometimes I want them to; sometimes that's what I'm playing with.

Mandelbaum: Yes, microtonal music can sound out of tune. All we can do is train our audience's ears as quickly as possible. At the same time I think this concern is exaggerated. Since I tend to use pure consonances as my microtones, critics have written of their disappointment, after reading my program notes, that nothing sounded out of tune.

Schottstaedt: I like out-of-tune sounds. What sounds in tune is very dependent on context. An interval or chord that initially sounds out of tune may come to sound in tune in the course of a piece. It's a matter of setting up expectations. One obvious example is the first movement of Water Music, where the eleven-tone intervals sound right by the end of the piece.

Does exposure to microtonal music tend to reduce the sensation that it's out of tune?

Blackwood: Up to a point, but there are certain ones that always sound out of tune. I can't put my finger on why certain new aspects are easily and readily learned. Others you learn, but not readily; and others sound alien and weird forever. We're dealing with very complex psychoacoustic phenomena.

Johnston: Probably exposure helps. It's quite possible that my difficulty with Haba is simply that I haven't listened enough.

200


Mandelbaum: The out-of-tune sensation can disappear very quickly if the microtones are consonant. It's playing with fire to intentionally use "out- of-tuneness" for a certain emotional reaction. I carefully used those just sevenths in The Dybbuk to represent the possession of the girl by the Dybbuk, who had been in love with her and who was predestined for her, sanctioned by nature. I thought it was a nice idea to symbolize this by the pure sevenths, since they should sound strange to people "outside of nature," trained in a societal artifice, as it were. Instead, the sense of

strangeness that I wanted (even though it was to sound fundamentally right) disappeared far too quickly, after one or two hearings.

Schottstaedt: I think that the perception of "in-tuneness" is a matter of what you're used to, not an absolute. I was pleased to discover that after

working for a long time in eleven-tone music, twelve-tone music sounded strange.

What is the relationship, if any, between "out-of-tuneness" and dissonance?

Blackwood: I draw a distinction that I think is perhaps original on my part between dissonance and discordance. A discordance is a rough sound. In twelve-note tuning most discords are dissonant, but some of the dissonances are not very discordant. The roughest sound we have in the twelve- note scale is a minor second. On the other hand, a diminished seventh chord is not a discordant harmony, yet it's dissonant. A discordant consonance is a very disagreeable sound to my ear-for example, the very bad major triad that you find in seventeen-note tuning. A discordant dissonance, by contrast, is not a disturbing sound.

The level of discordance varies depending on the register the chord is played in, and the tone color. Anything can become discordant if you play it in a high register and loudly. The roughness is caused mostly by the beating of the harmonics, but also by the timbre if it's very shrill.

Eaton: "Out-of-tuneness," meaning "out of tune with accepted positions of notes within the chromatic scale," doesn't necessarily involve dissonance. The problems that the famous composer I mentioned had were probably problems of "out-of-tuneness" in that sense: not being in conformity with the pitches of the chromatic scale.

Harrison: Dissonance is something within a tuning system that is tighter or closer in quality than other intervals. To me, "out of tune" means that the interval or pitch is inaccurately played or tuned, regardless of whether the intent is a consonance or a dissonance.

Johnston: It's a matter of extremes. I think dissonance is a mild version of what you mean by being "out of tune." Ordinary listeners would give you that reaction. Listening to an out-of-tune piano they would be bothered,

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but they would be just as bothered listening to Schonberg on an in-tune

piano, because they don't like those intervals.

Schottstaedt: "Out-of-tuneness" and dissonance are different, but both cause you to expect some musical explanation. At the start of a piece, I assume that the "out-of-tuneness" will be unsettling. I try to keep in mind what the normal audience is expecting-not everyone is Harry Partch. I don't think that musical language is something I can invent; I don't see a

piece of music as a self-contained structure of arbitrary interrelationships. So I treat "out-of-tuneness" somewhat in the same way as dissonance.

Are consonance and dissonance more or less constant across tuning systems, or do

they take on different definitions with each tuning system?

Blackwood: I have found them to be fairly constant. There are certain

types of dissonances or chords containing combinations of tendency notes that are very badly represented in twelve notes. In some cases you find more accurate ones in some of the other tunings, especially certain families of altered chords. Diminished seventh chords vary all over the map, especially if the number of notes is odd.

Eaton: I find that I redefine consonance and dissonance with every piece. In a certain sense they're absolutes, but they're also dependent upon the music we've experienced. For listeners, consonance is what puts one to sleep and dissonance is what wakes one up.

Harrison: I don't have any terms of reference for consonance and dissonance anymore. I think in terms of the ratio. Dissonance corresponds to the complexity of the numbers in the ratios.

Johnston: I think it's a continuum, and where you draw the line between consonance and dissonance is arbitrary. There are different kinds of dissonance: the dissonance of complex ratios and the dissonance of higher prime numbers, which is really very different. For example, the ratio 25/24 is a chromatic half-step in just intonation, C-Ct. It's a fairly harsh interval, that everyone would consider dissonant, about seventy-one cents. But 26/25, although its numbers are about the same size as 25/24, involves that high prime number thirteen, making it audibly much more dissonant.

Mandelbaum: Consonance and dissonance can be redefined fairly successfully in a new tuning system. One could condition listeners by using other invervals at the points where the music sets up the expectation of rest. But with our cultural history and the natural tendency of the beatless fifth to produce calm, I think the composer using a microtonal scale that includes traditional consonances might as well use them as such, if resolution is part of the desired emotional language.

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Also, anything beyond what is already possible as dissonance in twelve seems like overkill and not any more dissonant. Playing thirty-one tones at once sounds more like an agreeable noise than does playing twelve tones at once. Microtones certainly give you more ways to avoid consonances, but the least reason to use microtones is to try to make dissonances more dissonant.

Schottstaedt: I'd like to think that "consonance" and "dissonance" are purely a matter of musical context, so that outside of any context, nothing is consonant or dissonant. In my music, however, I do tend, for example, to treat very small intervals as dissonant and fifths as consonant.

V. EDUCATION

How should music education deal with nonstandard tunings?

Blackwood: When enharmonic equivalents are introduced in a basic theory class, the instructor might point out that other enharmonic equivalents are possible. One of the more complex but accessible equal tunings, such as nineteen, could be given at least a brief introduction. I'm not sure about microtonal ear-training. But listening to microtonal intervals is harmless to the musical ear. You simply learn them in addition to the standard intervals, although it may take a bit longer.

Eaton: People will write microtonal etudes and microtonal instruction books. But the main thing is to create more microtonal music, one piece at a time, solving a problem in each as it comes along. I don't think a general catch-all approach has much musical relevance.

Harrison: I've complained about music education for a long time. Kids learn their fractions in fourth grade, and at that point they could use a monochord, which is still a superb instrument for instruction, to hear the fractions as well as do them. They could learn the modes of their own culture, and how to add and subtract intervals. Carl Orff had a wonderful idea about teaching the modes, as is done in many parts of the world, but he didn't tune them, alas.

Johnston: People should be made aware from the very beginning that there are many different ways to tune music. If they were exposed to different tunings and given the corresponding ear-training, it would be very useful. Joe Maneri has done some microtonal ear-training at New England Conservatory. It would have been wonderful to have been exposed to that when I was learning.

Mandelbaum: Music educators should be careful in their introduction of

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Partch. If students start reading Partch's nonmusical writings-he was very anti-school, like Ivan Illich-they will probably be influenced to quit school and never go back!

More seriously, any school with the budget can invite Johnny Reinhard to talk, and every student in the school will be turned on to microtones. He's a one-man microtonal education committee.

Schottstaedt: Introductory classes in "music appreciation" should include non-Western music; I would urge that students be exposed to Indian, Chinese, and Indonesian music. In standard music education, I'd ignore nonstandard tunings until they've proven themselves to be more than a

curiosity.

VI. OTHER COMPOSERS

In your opinion, who are the interesting composers using nonstandard tunings?

Blackwood: Most of the composers I know of in this field, such as Ezra Sims and Ben Johnston, compose with just intervals. Most of the successful pieces in just intonation use the just intervals to create unusual sonorities.

I do know a few equal-tuning enthusiasts, but most tend to fasten onto one equal tuning rather than being interested in the whole family. They're usually interested in the very consonant tunings; nineteen, twenty-two, and thirty-one are very common. Paul Rapaport, Rudolf Rasch, and the Fokker people in the Netherlands are names I think of. Historically, there's Nicola Vicentino; I'm persuaded that his archicembalo was in thirty-one- tone equal.

There is a substantial body of existing quarter-tone repertoire, such as Alois Haba's, but if you examine it, it's not very encouraging. I don't find the Ives quarter-tone piano pieces to be very compelling, either. All the quarter-tones do is add an array of extremely discordant sounds to the standard tuning, and they can serve as inflections.

People interested in microtonal music are a very mixed bag, and there is a tendency to form what one might characterize as cults that proclaim the one right way to use microtones. I don't find such dogmatism very profitable. One reason people get interested in just intonation is that they look up tuning theory in the library and find writers who state that just intonation is the best tuning. But I cannot retreat from the conclusion drawn in my book, The Structure of Recognizable Diatonic Tunings, that just intonation is of no use for any portion of the standard repertoire. It is certainly possible to use just intervals to create a new music that would be even more minimal than the current minimalism. There's too little known about the whole subject, and the only way to learn more is to explore it and create a substantial repertoire.

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Eaton: I find a lot of composers interesting. I like Ben Johnston and Ezra Sims very much, and Easley Blackwood. What's great is that, in contrast to the closing down of music that happened in the serial years, there are so many different approaches. The important thing is that it doesn't become too doctrinaire, because it's downright silly to insist that a certain approach is the only approach. There are all sorts of ways of generating interesting microtonal materials.

I can truthfully say I haven't been influenced by other microtonal composers. My first microtonal piece was the piece for two pianos tuned a quarter-tone apart, the Microtonal Fantasy. At that time, someone told me about the Ives pieces. That was the first I had heard of them, and I had already written my piece.

Harrison: The origin of my interest in all of this, outside of Asian music, is that Virgil Thomson gave me the first edition of Harry Partch's Genesis of a Music, and said, "See what you can make of this." So I studied it, and within a day or two I bought a tuning hammer for the piano and began exploring, and I haven't looked back. And of course I knew Partch; we had a very close relationship for a number of years in his later life. I've always enjoyed his music.

I'm very fond of Terry Riley's works. It seems to me he's doing more and more beautiful work. I heard some of his pieces at Telluride a couple of years ago that are just gorgeous. He's thoroughly knowledgeable. Larry Polansky, Ben Johnston; there are many others whose music I like.

Two theorists influenced me early-Henry Cowell (in his New Musical Resources) and Joseph Yasser. I learned in Yasser's A Theory of Evolving Tonality that you don't necessarily have to get more and more complicated. In his book he harmonized a Tchaikovsky passage in quintal polyphony, which I thought was marvelous. It set me off on quintal polyphony, which I still use today.

Johnston: Of the previous generation, one of the most important was Partch. Even though there's only one composition with unusual intonation, Ives has to be mentioned; his quarter-tone pieces are intuitively very important.

As for people who are living and working now, I think James Tenney's work is very interesting and probably of great value in the long run. Lou Harrison is an important figure. Ezra Sims's work I like very much. He usually notates using quarter-tones, but he told me he's actually using higher overtone relationships; he uses arrows to indicate the approximation and expects the player to make the adjustment. Of course I like my approach to notation better. Among younger people, I like Larry Pol- ansky's work very much. He's really got a point of view, which is one of the things that's hardest to come by.


Of the people using quarter-tones, the most interesting music is Gyorgy Ligeti's. He also says he uses quarter-tones to approximate the overtones; he expects the player to make adjustments by ear. His Ramifications for

string orchestra has the instruments tuned a quarter-tone apart. It's fas-

cinating, wonderful texture music. He's very sensitive to the nuances of these textures and their meaning. Manfred Stahnke, who studied with

Ligeti and came here to study microtones with me, has written very interesting music, especially stage music-a couple of operas on Edgar Allen Poe texts. There's a composer named Sergei Slonimskii, in Leningrad, who writes Bartok-like music, using inflections that evoke folk music. That's not all the people I know who are writing this kind of music, or even all the ones I have respect for, but they come to mind first.

Mandelbaum: Blackwood is important; the fifteen-tone study for electronics was one of his best. Henk Badings is no longer alive, but his body of works in thirty-one is superb, among the finest in his oeuvre. Hans Kox in Holland did some fine work also. I admire the work of Partch. Mordecai

Sandberg did some beautiful settings of the Jewish liturgy. His microtones tend to fall into two categories: either to provide upper partials, especially the seventh, or to provide modal or intervallic ambiguity, for example by putting a note between the major and minor third. I've heard far too little of the present generation, but what I've heard of Ben Johnston and Lou Harrison I like very much.

Fokker is an important influence as a theorist. He was a relativity physicist who had some major discoveries and was a junior colleague of Einstein at one point. He belongs to a long tradition of great mathemati- cians who have made important contributions to music theory.

Schottstaedt: I like some of Partch's music, and Ives. I don't follow

contemporary music very carefully, so I don't know much about other

composers working in this area. Some of Lou Harrison's music is very pretty.

Why do you think more composers haven't gotten involved with nonstandard tuning systems?

Blackwood: First, it's difficult except under limited conditions to get a live

performance. I don't think concerts of taped music make a good impres- sion on audiences. Secondly, this field is in its infancy and there are no big bucks there. Finally, there are considerable problems involved in writing in the new tunings; they're harder to write in than twelve equal. There are fewer choices.

Eaton: Practicality; fear. It amazes me that more composers haven't gotten involved. There's such a rich world there.

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Harrison: For a number of them it would probably represent a departure from the profession in which they're so earnestly working to earn a living. As I grow into my late years now I realize it's quite a battle. I'm being invited to do everything, and I have now developed a formula for gently refusing commissions.

Johnston: It's a little frightening from a standpoint of relationships with the performer. It's hard enough to get a new work performed when there aren't any performance problems of that magnitude. Also, if you use a retuned piano, you have to tie it up for several days at least, making it unavailable for anything else. That is quite sufficient to make performances of such works very rare. Another reason is that performers are afraid it will be hard to retrain their own ear. They're wrong. People overestimate the

power of habit and underestimate their own flexibility.

Mandelbaum: I've just looked at the work of fifty relatively young com-

posers applying for a position at Queens College, and I find they write very similarly to their teachers. People from Illinois, where Ben Johnston was, used microtones. Composers from other places hadn't. So at least at this

point, change is very slow.

Schottstaedt: It's partly inertia; instruments and performers expect standard tunings, and it's a major bother to try something new. Also, there's an unfortunate association between nonstandard tunings and tiresome cranks

spouting small integers.

Will more composers start using nonstandard tunings?

Blackwood: I hate to say this, but the most advantageous use for new

tunings now would be popular music. You would get a lot of people hearing them on television or the radio. I can imagine some cute jingles in fifteen equal.

Eaton: I'm sure things will change. Maybe the change is going to come, as so many things have in this century, from vernacular music, jazz, popular music. All the music of the world, except for a very brief period in Western music, has involved intervals which are not part of the white and black keys of the piano keyboard. There's a whole reservoir of microtonal melody to discover and seize upon.

Harrison: Many young people are interested in intonation; whether they do it electronically or with real instruments is neither here nor there. They find themselves going outside the "gray veil" of equal temperament. There is a change in every department, both in and out of the academy. The early music people have spread the idea of using different instruments for different periods and in different intonations.

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Johnston: There's a trend that has gone farther than I would have pre- dicted, but I don't know how far it will go. I hope it does continue, of course. I believe this trend is happening because the world is getting smaller, in the Marshall McLuhan sense, and we are aware that music is very different in different places. We aren't so terrified of a whole new pitch system. If you've heard Balinese music or African tribal music, you know it's altogether different from ours.

Mandelbaum: Many well-known European composers, for instance Henri Pousseur, are starting to use microtones. The trend is definitely upward in this country, too. I'm not sure that's entirely a good thing for microtones. It's been nice not having the company of hangers-on and chasers after fashion. In certain ways, the field will be less enjoyable when we get our dose of it.

What role do you see microtonality and nonstandard tuning systems playing in the future development of music?

Blackwood: I think it's a rather independent direction, and the most advantageous way seems to be through recordings. Given recent advances in technology, I'm sure that someone could make a better version of my Microtonal Etudes, for example. For me, unlike some electronic composers, the recording is not definitive; what's written on the page is the piece.

In terms of music theory, much of the algebraic theory that's come out recently is too locked into twelve-equal. Theories involving sets or patterns ought to be generalized to other tunings, although I'm not interested in doing that myself.

Eaton: I think microtonality is going to become general. We're in a wonderfully adventurous, expansive period right now. It's true that there's a certain sleaziness in the music that's usually performed today, which has little to do with what composers are really doing and thinking. The great adventurous spirits in American music now are being somewhat sup- pressed, but that can only be a passing thing. All changes in the melodic and harmonic structure of music have occurred because people were tired of hearing what they had always heard. Very little is generated by theory.

Harrison: Northwest Asian music will change. It will absorb from other Asian sources. Tuning periods don't last forever. We've seen a lot of changes within this one tuning period, and I think the tuning period will change. We'll find ourselves with a much richer variety.

Johnston: We're training our ears and expanding our abilitities, and that won't stop. The field will probably expand for some time. We're a long way from having a homogeneous global music, in spite of the media. The media have already latched onto pop music as their thing, and I hope that this will

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never have the effect, Republican administrations notwithstanding, of kill-

ing the arts. It would seem that the arts are in more danger from economic causes than from technological ones. The technology tends to enhance what happens. Japan, which is so omnivorous, devours everything, and it all comes out in a special way Japanese, even jazz.

I think there's also going to be much more effort to perform seventeenth- and eighteenth-century music, not to mention earlier music, in the

right intonation, and audiences will enjoy the difference.

Mandelbaum: There will be a good cross-fertilization between present-day microtonal composers and people interested in reclaiming the properties of the different keys for seventeenth- and eighteenth-century music. The nature of the different keys plays an important part in music as late as Beethoven, and this is tied to the history of what Mark Lindley calls "elastic" tunings, which actually made the keys acoustically different.

What future directions will you be taking in your own music?

Blackwood: I'll continue writing for standard tuning and standard instruments in a variety of styles. I found from writing the Microtonal Etudes that I feel perfectly at home in a completely traditional tonal style. I'm presently working on a big orchestral piece in a slightly different style. One could say it's the radical piece that Sibelius didn't write in 1916.

There are two possibilities for microtonal pieces that would interest me now. One is a larger piece in twenty-one-note tuning, an electronic piece with a lot of orchestral-style effects. The other is an ensemble piece in fifteen notes, for either guitar and recorder, or some combination of guitars and recorders, conceivably with other fretted instruments as well.

Harrison: I intend to retire after the two commissions I'm presently working on. I'm going to get a motor home, travel around, and do some artwork and writing. Someone recently asked me, "Retire from what?" When I said "composing," she acted as though I had committed both treason and heresy. So I said to her, "Madam, I have all the rights of an

ordinary citizen!" I'm not going to be locked into equal temperament or the profession. If I do compose again, it won't be on commission; it will be because I damned well want to.

Johnston: I'll just go on trying to explore the sounds that I'm so fasci- nated by. I would like to do it with the kinds of ensembles I haven't been able to use before. If the opportunity arises, it would be interesting to write more orchestra music, or even an opera. I've done a chamber opera, and a rock opera so to speak, but not a real opera.

Mandelbaum: I hope to work successfully in larger forms, pitting the overtone series against artificial scales in thirty-one-tone equal temperament, to express some of the big issues of the human condition.

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REFERENCES

Blackwood, Easley. 1985. The Structure of Recognizable Diatonic Tunings. Princeton: Princeton University Press.

Cowell, Henry. 1930. New Musical Resources. New York, London: A. A. Knopf.

Partch, Harry. 1974. Genesis of a Music. 2d. ed. New York: Da Capo Press.

Yasser, Joseph. 1975. A Theory of Evolving Tonality. Reprint. New York: Da Capo Press.

SELECTED DISCOGRAPHY

Easley Blackwood:

Twelve Microtonal Etudesfor Electronic Music Media (LP), 1980. Available for $9.95 from the composer at 5300 S. Shore Drive, Chicago, IL 60615.

John Eaton:

The Music of John Eaton, Indiana University Press (CD), 1990. Includes Ajax, Fantasy Romance, Sonority Movement, A Greek Vision, Ars Poetica, The Cry of Clytaemnestra (excerpt).

Danton and Robespierre, IUS-421, distributed by CRI (3 LPs), 1980.

Microtonal Fantasy, Decca DL-710154 (LP), 1966. Includes Songsfor R P. B., Piecefor Solo Syn-ket no. 2, Microtonal Fantasy, Prelude to Myshkin.

Concert Piece for Syn-ket and Symphony Orchestra, Turnabout TVS-34428, 1971 (LP).

The Music of John Eaton, CRI SD-296 (LP), 1971. Includes Mass, Blind Man's Cry, Concert Music for Solo Clarinet.

Electro-Vibrations, CRI SD-296 (LP), 1971. Includes Thoughts on Rilke, Soliloquy, Vibrations, Duet.

Lou Harrison (a small sampling of his recordings):

Piano Concerto; Suite for Violin, Piano, and Small Orchestra, New World NW366-2 (CD; also LP and cassette), 1988.

La Koro Sutro, Varied Trio, Suite for Violin and American Gamelan, New Albion NA 015 (CD; also cassette), 1988.

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Double Concerto for Violin and Cello with Javanese Gamelan, TR Records TRC-109 (LP), 1983.

At the Tomb of Charles Ives, Gramavision GR 7006 (LP), 1983.

String Quartet Set, Main Bersama-sama, Threnodyfor Carlos Chavez, Serenade for Betty Freeman and Franco Assetto, CRI SD 455 (LP), 1981.

Gending Pak Chokro, Cambridge 2560 (LP), 1977.

Concerto in Slendro, Desto DC-7144 (LP), 1972.

Four Strict Songs, Louisville 582 (LP), 1955.

Ben Johnston:

White man sleeps, Nonesuch 79163-2 (CD), 1987. Includes Amazing Grace (String Quartet no. 4).

String Quartet no. 6, CRI SD 497 (LP), 1983.

String quartet no. 4, Gasparo GS 205 (LP), 1980.

Music from the University of Illinois, CRI SD-405 (LP), 1979. Includes Duo for Flute and Double Bass.

Soundformsforpiano, New World NW 203 (LP), 1976. Includes Sonata for Microtonal Piano.

String quartet no. 2, Nonesuch H71224 (LP).

Ci-Git Satie, Ars Nova-Ars Antiqua AN-1005 (LP).

William Schottstaedt:

Music with Computers, Wergo WER 2023-50 (CD), 1989. Computer Music Currents, vol. 3. Includes Leviathan.

Dinosaur music, Wergo WER 2016-50 (CD), 1988.

Wait For Me!, Perspectives of New Music PNM 28 (CD), 1990.

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Documents

Six American Composers on Nonstandard Tunings