Author: Kyle Gann

From Folk Song to the Outer Limits of Harmony—Remembering Ben Johnston (1926-2019)

A Caucasian man with his head titled, glasses and a white beard

I first saw Ben Johnston when I was a student at Oberlin, maybe 1976. The composers at the big Midwest music schools were in continual rotation as each other’s guest composers, which in itself was an amazing education. Ben lectured and played a recording of his Fourth String Quartet, based on the song “Amazing Grace.” He was a Quaker-bearded, good-humored, gruff, not very talkative fellow, and there was a peculiar contradiction, I think we all sensed, in this composer who had invented his own pitch notation and 22-pitch scale and written a score nearly black with ink using all these crazy polyrhythms of 35 against 36 and 7 against 8, 9, and 10 – all at the service of an old folk song anyone’s grandmother could sing. Conservative versus avant-garde was how we divided the music world up at that time. Where the hell did this fit?

Ben Johnston sitting and writing on a piece of music paper.

Ben Johnston in 1976.

Forty-odd years later, several of them spent working with him, I still think there’s an essence to Ben that in the current musical climate can only be seen as a paradox: he was a down-to-earth, populist visionary. I truly think that he thought there were no limits to what pitch and rhythm relationships musicians could learn to play, as long as the approach to the difficulties was gradual and intelligible. Famously, the third movement of his Seventh String Quartet contains more than 1200 pitches to the octave. It is structured around a 176-note microtonal scale that glacially traverses one octave over 177 measures, and, written in 1984, it remained on the page until the Kepler Quartet recorded it a couple of years ago. But it is carefully written so that if the players can get their perfect fourths and seventh harmonics in tune, they can creep securely, interval by interval, through this free, gridless, infinite pitch space – astronauts of harmony, floating beyond the gravity of A 440. The conceptual achievement leaves Boulez and Stockhausen in the dust. Moment by moment, the music can sound as mild as Ned Rorem.

The conceptual achievement leaves Boulez and Stockhausen in the dust.

Ben had a strange mind, and I say that up front only because he often frankly said so. He thought he had some kind of mental disorder, possibly caused by being taught to meditate wrong by the Gurdjieff cult in the early ‘60s – this is what he repeatedly told me, even in interviews. He was always trying various remedies. When I studied with him privately in 1983-86 (post-doctorate), he was on medication that made him very quiet. He would look at my score for fifteen minutes without speaking, and then say something incisive and profound. A few years later he was controlling his problems via diet. I went to a conference with him, where I was going to interview him onstage: the night before, he kept me up until two in the morning, talking nonstop. His Catholic priest in Champaign-Urbana recommended he go to a Zen temple in Chicago, and so for a couple of years that’s where he and I met, and I started going through the Zen services with him. Those were wonderful, and the lessons afterward took place in a blissful haze.

Ben Johnston in 1962

Ben Johnston in 1962

I do think that, whatever was strange about Ben’s mind, it was what made his music possible. At age twelve, attending a lecture on Debussy, he was introduced to Helmholtz’s On the Sensations of Tone, the foundational treatise on acoustics that first appeared in English in 1875. He spoke about it as though it confirmed for him what he already sensed: that the music we play has something wrong with its tuning. At age 17, after a concert of his music, he was interviewed by the Richmond Times Dispatch (where his father was managing editor, admittedly), and predicted, “with the clarification of the scale which physics has given to music there will be new instruments with new tones and overtones.” This was 1944. Harry Partch’s Genesis of a Music wasn’t even published yet. By 1950 Ben was in grad school at Cincinnati Conservatory, and someone gave him a copy of Partch’s then-new book, with its outline of his 43-tone microtonal scale and perceptive history of the vicissitudes of tuning over the centuries.

Thrilled to find another musician who shared his misgivings about tuning, Ben wrote to Partch asking to study with him. Partch, who once wrote that he would “happily strangle” anyone who claimed to have been his student, took him on as an apprentice and repairman instead, and so Ben went to live for six months on Partch’s ranch in Gualala, California. Partch liked to have only young men in his orbit, and was affronted when Ben’s wife Betty arrived in tandem, but Betty Johnston was a powerhouse, and eased her way into Partch’s reluctant affections. Ben later wrote that Partch

could have wished for a carpenter or for a percussionist… But he had one thing he had not counted on: someone who understood his theory without explanation, and who could hear and reproduce the pitch relations accurately.

Ben Johnston, wearing a jacket and tie, sitting outside with Harry Partch in 1974

Ben Johnston with Harry Partch at Partch’s home in 1974.

Ben’s preternatural ability to hear and reproduce exotic intervals was the one intimidating thing about studying with him. My brain not being strange in the same way, I spent years training myself to hear eleventh harmonics and syntonic commas using primitive digital technology, and to this day I would never attempt to coach an ensemble to play one of his string quartets. When I came to his house he liked to play me whatever he was working on. Once, in the early weeks, it was a piece for trumpet and piano called The Demon-Lover’s Doubles, of which he played me the piano part. His piano was tuned for maximum consonance in G major with some peculiar pitches outside that diatonic scale, and as he started, it seemed like an oddly homespun, tuneful little piece. Then, magically, his piano started going sourly out of tune and got weirder and weirder, and I was thinking, “Man, you’d think Ben would tune his piano.” Finally, of course, he returned from his modulations into distant keys, and in G major the piano sounded fine again. I just remember sitting there thinking, “Huh.”

In that experience is the alpha and omega of Ben’s vision. What fascinated him, I think, was how vastly just intonation and the higher harmonics expand the range of consonance and dissonance, in both directions. You can have so many flavors of harmony: triads purely in tune, edgy Pythagorean triads, chords with exotic upper harmonics, dark chords from a subharmonic series, excruciating chords specifically out of tune by a comma here or there, bell-like chords related by higher harmonics, grating seventh chords with deliberately mismatched ratios, tight clusters – the route from purity to noise is no longer a line but a large three- or four-dimensional space.

One of Ben Johnston's pitch charts.

One of Ben Johnston’s pitch charts.

Many, many microtonal composers, I think, are looking for a total alternative to our tuning system, total exoticism, experimenting with how far we can adapt to new intervals, adding new complexities beyond what twelve-tone music provided. Ben wasn’t. Ben was never disappointed in the major triad. For Ben, the tonal music system that we’d developed over the last few centuries was a template, a first draft, a worthwhile approximation, but only a fragment of the universe he could hear. Seventeenth-century theorists like Marin Mersenne and Christiaan Huygens had argued for including the seventh harmonic as a consonance; Giambattista Doni (c. 1594-1647) wrote music using the eleventh harmonic. Theoretically, Ben goes back to that era and accepts those arguments. Keep the system, but add back in what was prohibited. Thus, unlike the general run of modernists, he could envision a brave new world without ever having to reject or exclude anything.

Cage and Xenakis may have wanted to reinvent music, but Ben saw a way to keep the foundation and keep building.

And so we have “Amazing Grace,” which so anchors one of the most avant-garde works of 1973 that the audience can hum along with it the first time they hear it. Also the sentimental old tune “Danny Boy,” which gradually emerges from the last-movement variations of Ben’s Tenth Quartet, and the folk song “Lonesome Valley” which is the subject of his Fifth Quartet, and the folk tune in The Demon-Lover’s Double. Cage and Xenakis, whom he knew well, may have wanted to reinvent music from the ground up, but Ben saw a way to keep the foundation and keep building.

Ben Johnston with The Kepler Quartet in 2015

Ben Johnston with The Kepler Quartet in 2015 (Photo by Jon Roy).

What’s amazing about his use of old folk tunes is how devoid of nostalgia it is. He’s not like Charles Ives, with “Beulah Land” faintly heard above the dissonant chords below; there is no modernity with which the songs’ innocence is contrasted. His “Amazing Grace” grows step-by-step from five pitches to twenty-three as though all those pitches were implicitly in there to begin with – which I imagine to his ears they were! It is difficult, probably, for most of us new-music types to take “Danny Boy” as seriously as he did, but for him it was simply a familiar item of our culture from which new implications could still be drawn. He didn’t have to renounce the naïve perspective on music to see through to the other side of the musical universe. And this is why some of Ben’s works will always appeal even to people who don’t like abrasive modernism.

That’s certainly not to deny that Ben’s music could be thorny. He kept writing twelve-tone music, in just intonation, and I once asked him why. He replied, “Well, I had learned all that theory, and I didn’t want it to go to waste.” Since he said almost everything with a slight smile, I’m not sure I ever knew when he was kidding. His Sixth Quartet draws the principle of endless melody from a twelve-tone row that consists of the first six non-repeating harmonics of D and the first six subharmonics of D#. The row matrix for the piece contains 61 different pitches. Even though it uses a twelve-tone row, though, each hexachord is actually a tonality in itself, so you do hear the harmony shift back and forth between major and minor – or between otonalities and utonalities, as we microtonalists say. At the time I wrote a rave review of the Sixth Quartet for the Chicago Reader and Ben said, “I think you like that piece better than I do.”

One piece I analyzed had some repeated pizzicatos in the cello that didn’t fit into the structure, and I asked him where they came from. He looked, and said, “Oh, that was to give the audience something to listen to while I worked out this contrapuntal problem.” That was a lesson: that the composer and the audience could want different things from a piece, and that both could be satisfied.

The composer and the audience could want different things from a piece, and both could be satisfied.

As with Partch, I also insist that Ben should get credit for his rhythmic innovations as much as for his microtonality. In the Fifth Quartet “Lonesome Road” floats above a bobbling sea of polytempos, and in the Fourth Quartet there’s a long rhythm of 35 against 36 (analogous to what we call the septimal comma), involving different meters in the various instruments. Back when I was younger and smarter, I once successfully parsed it, but I’ve never figured it out again since. He was a great proponent of Henry Cowell’s theories that pitch and rhythm, both being number based, could be developed analogously and in the same directions – that was the principle, of course, of his first hit tune, Knocking Piece, which became a percussionist’s standard. That he was focused on extending musical language in terms of both pitch and rhythm has limited his influence among the mass of composers who think there’s nothing new to be done in those directions, but when we’re ready he’s left us a foundation for a radically new music.

Ben never proselytized for microtones or just intonation. He imposed no stylistic dogma. Like so many American experimentalists, he himself was stylistically multilingual: he wrote chance music, twelve-tone music, conceptualist works, a musical, and a surprising amount of his output is in a neoclassic vein, with standard forms like sonata-allegro and variations. Neo-romanticism, I think, is the only idiom he avoided, which is not to say his music couldn’t be deeply moving; he just wasn’t sentimental. In 1983 I asked to study privately with him because I loved his music (I never attended the University of Illinois where he taught for 35 years), but I didn’t want to get into microtonality, which seemed like too much work. That was fine with him, but at my first lesson he looked at a chord I’d written and remarked how beautiful it would be if tuned properly, and he reeled off the ratios. With a shock I realized I understood just what he was saying. It was as if a huge iron door had slammed shut behind me. I was in his world and couldn’t go back.

I didn’t need to. The microtonal notation he invented opened the universe to me, and I learned to think in it fluently. My own microtonal music, more single-minded and homogenous than his (not to mention more cautious – god, that Seventh Quartet!), inherited his worldview of microtones as an extension of tonality rather than an alternative. I would be remiss here if I failed to mention another of his microtonal students, Toby Twining, who, in his Chrysalid Requiem (2002), developed Ben’s ideas into one of the most impressive feats of musical architecture ever perpetrated, incredibly complicated yet unearthly beautiful. That’s a legacy.

Ben Johnston as a child driving a toy car.

A 10-year-old Ben Johnston in 1936. He was already eager to explore.

I remember once in Ben’s medicated days we had him over for dinner, and he played solitaire obsessively while we were preparing dinner. After he retired we visited him in Rocky Mount, where Ben and Betty, equally strong characters, practically barked at each other, but clearly with no lack of affection. He was a crucial link between me and several other people I didn’t meet until later, all of whom were devoted to him: Bill Duckworth, Neely Bruce, Bob Gilmore. I last saw Ben in 2010 at a microtonal conference. He could barely get around. After I delivered a paper about his music he tottered up to say “thank you,” and I replied, “No, thank YOU!” He looked up from his walker with a big grin and gruffly growled, “YOU’RRRE WELCOME!” That meant the world to me: I needed him to acknowledge how much he had done for me. A few years later I called to tell him that he appeared as a character in Richard Powers’s novel Orfeo, about the University of Illinois’s music department in the 1960s. His mind was deteriorated by Parkinson’s, and the next day his caretaker called me saying Ben was under the impression that some kind of copyright infringement had taken place and he needed a lawyer. I set his mind at rest and assured him it was a compliment.

And once when I was a young, new home-owner with a lawn to keep up, I was driving Ben somewhere and we passed a vacant lot covered with blooming dandelions. I made a slighting reference to the plant, and Ben just said, “But they’re awfully beautiful, aren’t they?” That was a lesson too. He was a lovely soul, and a caliber of musical mind we will not see again.

Ben Johnston and Kyle Gann c. 1994 (Photo by Bill Duckworth)

Ben Johnston and Kyle Gann c. 1994 (Photo by Bill Duckworth, courtesy Kyle Gann)

Intuition and Algorithm in Einstein on the Beach

[Ed. Note: The following paper was presented at the Einstein on the Beach conference of the University of Amsterdam, January 6, 2013. The present version is slightly expanded based on questions and comments from that session. All score excerpts from Einstein on the Beach by Philip Glass ©1976 Dunvagen Music Publishers. Used by Permission.]

Some of us are old enough to remember the public impression that minimalist music made before the premiere of Einstein on the Beach. Minimalism in its first manifestation was a strict, objectivist style. We thought of it, pretty much, as gradual-process music. Philip Glass’s Music in Fifths and Music in Contrary Motion offered us perceptual exercises in additive process, and taught us to hear the gradual expansion of a time frame. Steve Reich’s out-of-phase tape loops amplified microscopic phenomena of the human voice. The similarly phasing 12-note pattern of Piano Phase created its own objective geometry, as did the change-ringing patterns of Jon Gibson. La Monte Young’s sine-tone installations were comfortingly based in mathematics. Charlemagne Palestine’s piano improvisations conjured up overtones. Only Terry Riley seemed a little loopy, pardon the pun, but even in In C we heard the echoes of melodies as a strict canonic process.

It is odd to remember at this distance how important this criterion of objectivity seemed at the time. We had come out of a period of serialism and strict chance processes, glorifying mathematics and the natural world. In the conditioned milieu of 1960s avant-garde music, mere expression of emotion seemed at the time unworthy of serious study; subjectivity was distrusted. The worship of science was rampant, and music had become scientific. For many musicians involved in the avant-garde it accelerated the acceptance of minimalism, I think, that it seemed to be about natural and or logical phenomena. Some of us weren’t yet ready to return to intuition, art, shading, eccentricity, and the unsteady foundation of personal preference.

There were enough hints of gradual process in Einstein on the Beach, I think, that it was accepted as fitting this objectivist paradigm at the time. The use of numbers and solfège syllables as text facilitated this impression. So did Glass’s liner notes to the original Tomato recording of the work. Of the lightning fast patterns in the Building scene, Glass states that “the repeated figures form simple arithmetic progressions,” and he refers to a figure in the Trial scene which, he writes, “slowly expands and contracts […] through an additive process.”[1] While this is arguably true of the Trial scene, I will show that the progressions of the Building scene are far from arithmetically simple, and also that many of the other scenes are devoid of predictable algorithmic thinking. Looking back in retrospect, Einstein seems a far more intuitively written work than we thought at the time. For several decades the score wasn’t available, and to transcribe these lightning-fast patterns would have taken a lot of patience; we thought we had a pretty good idea what we were hearing. Eventually a score became available via links on Glass’s website, and I bought it in 2008. Upon opening it I was immediately struck by how much more unpredictable the music was than I had remembered it, how circuitous its forms were, how difficult it often was to pinpoint the musical logic. I was struck by how compositionally playful the piece is. In particular it offers some striking examples of recomposition, of writing through the same parallel succession of motives and harmonies several times within one piece and doing it a little differently each time. It is this playful, intuitive technique of recomposition in the composed musical scenes of Einstein on the Beach that I plan to focus on here.

Let me begin, almost pro forma, by reviewing the recombinant elements that make up Einstein, since I’ll be referring to them later. First of all are three recurring chord progressions, one with three chords, one with four, and one with five.
(Glass’s notes also refer to ideas of two chords and one chord, but these don’t appear as frequently.) The famous five-chord progression modulates from F minor to E major, and is the basis of the Spaceship scene, appears in the Train and Building scenes, and is the basis of the internal Knee Plays. Glass refers to it as “cadential,” but the three-chord progression heard in the first and last Knee Plays seems cadential as well: a simple vi-V-I. The four-chord progression appears in the Trial and Bed scenes, always in the kind of slowly arpeggiated motion seen here. In addition, there are a few other features found from scene to scene. The upward A-minor triad with a variety of continuations serves as a prelude to the four-chord progression. A la-fa-la-si-do-si motto in A-flat appears as a kind of section marker in the Train and Night Train scenes, and the following figure of four modules appears in both those scenes and constitutes almost the entire notated material of the Building scene.

Many movements of Einstein seem to be written in a kind of stanzaic form, wherein a movement is divided into stanzas which are parallel in their function and similar (though varied) in their progress through the same harmonies and motifs. Sometimes the beginnings are marked by introductory motives which I will call incipits: such as the three perfect fourths in the saxophones at each new section of the Train scene, the two four-note patterns of Night Train, and the reduction of the Building scene to a 6/8 pattern:
Likewise, some of the stanzas end in signalling characteristic figures that I will call envois, after the medieval poetry term. These include a quick F-minor triad in the Train scene, the solo violin playing A minor scales in Trial 1, and, again, the la-fa-la-si-do-si motive in Night Train. Not all stanzas in the various scenes are marked by these devices, but in those that are the incipits and envois are quite clear in their framing intent.

There are moments in Einstein at which a more stereotypically linear minimalist logic prevails. The most obvious is the bulk of the Bed scene, where the soprano sings over the four-chord progression. As this chart of the rhythms for each chord shows, the length of the rhythmic cycle expands in a fairly predictable manner with each iteration.
The voice part, however, is a more intuitive element, drawing lines that use only notes from the four triads. Out of 81 possibilities (not counting octave displacements), Glass chooses only seven of the available such lines and repeats three of them, creating a mild climax by using sevenths in the 7th and 8th cycles. (Each voice line is repeated once before proceeding to the next.)
Likewise, the violin part of the Trial 1 scene does, as Glass says, go through a process of expansion and subtraction, though not in a completely linear manner.
The chorus doubles the low C and A in the first part of each pattern; thus, once the music begins leaving this part of the phrase out of each repetition, the chorus disappears and only the violin continues.

At the other extreme is the Building movement, in which only the two organs are notated, as the voices and other instruments drone and improvise. As notated, the piece is entirely in eighth-notes in contrary motion, much like several of Glass’s minimalist works of the late 1960s. (It should be kept in mind that all of these patterns repeat 2, 4, or 8 times before proceeding to the next one.)
The move from one pattern to another, however, is not at all predictable. The following chart of the right-hand Organ 1 part shows all the pitches for the first 30 (out of 37) cycles, lined up vertically to show easily what notes are added or subtracted to get from one repetition the next (here the lower-case “e” denotes the E-flat in the upper octave, and there is a key signature of three flats).
What making this chart clarifies is that the movement is made up of only four modules whose changing combinations make up the form:
The movement’s seeming micro-complexity is due to the fact that module A is contained in module B, and likewise module C in D. The following chart shows the deployment of these four modules throughout the entire section:
At each step one can see a kind of additive or subtractive logic: the 3/8 modules start out with a 6/8 feel, and then the A module is added to give kind of a quarter-note bump to the repetition of BD, then another A is added, then steps 2 and 3 are added together, and so on. After expanding via additions of the A module, the music strips back down to just B and D, after which module C starts to be added in. Towards the end the music begins to emphasize the ten-note pattern ABCD, and finally resolves to the opening BD with which it began. The musical continuity here is not illogical, but neither is there any place where one could look at two or three successive phrases and guess (with any confidence of accuracy) what the next one will be. Glass’s comment about “simple arithmetic progressions” notwithstanding, this is a very unpredictable sequence. And, it must be said, this is all background structure anyway, since in this scene the pentatonic drones and improvisations tend to greatly override the subtlety of the organ patterns.

The Train

The Train scene, one of the most musically complex movements, is made up of three recurring sections, structured in the form ABABCABC. The B sections, which seem to serve a connective function, are instrumental (without voices), using the same four modules from the Building scene that were just identified. The C sections are based on the five-chord cadential progression that is the basis of the Spaceship scene. The A sections are unique to this scene. The first two B sections are identical, the third one considerably expanded. The two C sections are identical except that the chorus is added in the second one; the rhythmic patterns here follow those at the beginning of the Spaceship scene. What is illustrative of Glass’s approach to form in Einstein, though, are the three A sections.

The diagram here outlines the three A sections in a kind of shorthand that isolates an abbreviated set of features, namely the length of the repeated phrases and the notes of the soprano solo (once again in a key signature of three flats).
A three-note drone ostinato in the saxophones runs throughout all the A sections, imposing an underlying 3/4 meter. The voices sing repeated patterns of various lengths, entirely in quarter-notes except for a recurring refrain which I will identify in a moment. When the number of quarter-notes in the voice pattern is not divisible by three, the voices and saxophones run through a brief out-of-phase pattern, and the number of their repetitions must be divisible by three to make the phrases come out evenly at the end of the measure. The numbers on each left-hand column indicate the number of quarter-notes in each voice phrase. A number given as 4×3, 5×3, and so on, indicates that the phrase goes out of phase with the saxophone ostinato. A number given as 6+4+2 or 5+4+3+2+1 points to a subsidiary rhythm within the phrase suggesting an additive or subtractive rhythmic process; note that these occur only in the second A section. In each right-hand column are given the pitches in the solo soprano voice part, and since there are three flats in the key signature, A should be read as A-flat, B as B-flat, and so on. As in earlier examples, all these melodic fragments are stated in quarter-notes except for a recurring refrain in 8th-notes on Ab-F-Ab-Bb-C-Bb, sung on the solfège syllables la-fa-la-si-do-si, which recurs both here and in the Night Train scene as a kind of motto. One can see that here it appears twice at the beginning, and then at the end of each A section.

Other points that could be made here are even clearer in the following example. This comparison of the three soprano parts (and the tenor is always either a perfect fourth or major third below, in parallel) shows that the soprano begins each section alternating between Ab and Bb, gradually making her way up to Eb and then F, then descending back to Bb before concluding with the la-fa-la-si-do-si motto.

Einstein Train melody

click image to enlarge

Notice, however, that the melodic and rhythmic character of the route is quite different in each A section. The first section reaches the high F relatively quickly, the second takes a long time to get there, and the third stays on F and Eb for a long time as a kind of climax. The second section, as previously noted, contains more patterns which contain an internal subtractive or additive process, and the third section contains the only additive process among phrases, and one additional subtractive process. At the end, each of them finally goes into a subtractive rhythmic process of 5-4-3-2 before lapsing into the la-fa-la-si-do-si motto. What is evident, then, is how many rhythmic and melodic options were open to Glass to get him from the Ab up to the F and back to the closing refrain, and how carefully he recomposed this process for three parallel sections achieving the same function through different routes. This possibility of intuitively recomposing a section is far removed from the typical concept of early minimalism as being something logically predetermined. We’re not just listening to nature here; we’re listening to variations in a large-scale melody conceptualized as rhythm.

Dances 1 and 2

One of the most fascinating views of Glass’s compositional process in Einstein is the subtle contrast between Dances 1 and 2. Many of the materials are identical from one dance to another, but the second is somewhat transformed in consequence of its use of the solo violin representing Einstein. Both dances contain a trio of drone notes that sound throughout: the pitches A, D, and E. These pitches are heard in the solo voices, the saxophones, and the left hand of Organ 1 in every measure. In addition, a fourth pitch, F, appears in the culminating repetitions of each large section. These drone pitches are recontextualized by the changing harmonies around them. In Dance 1, the arpeggios in the organs and piccolo move among chords of F major, A major, Bb major, G major, and C major, the constant D, E, and A being reinterpreted in each new harmony.
(Actually, Glass describes it in his program notes as always returning to D, which is justifiable if you consider the F major as part of a D minor 7th chord; but which isn’t the way I hear it.) The singers and saxophones use only the pitches D, E, F, and A, voiced either as quarter notes, dotted quarter notes, half notes, or, at one arguably climactic point, dotted half notes. A listing of the chord progressions and the rhythms in each repetition throughout Dance 1 reveals a clear division into three parallel parts, though these are not marked by clear incipits and refrains as in the Train scene:
Though there is no key signature, the general tonality of Dance 1 sounds to me to be in F major; the piece begins and ends on an F major chord (with an added sixth D), and the phrase rhythm frequently makes F major sound like a resolution, though it can also sound like a flatted-seventh adjunct to G major. Listing the harmonic progressions of each repetition, we see a clear parallelism among phrases 1 to 17, 18 to 33, and 34 to 50. That is, there are 50 phrases in the dance, divided into three stanzas with lengths 17 + 16 + 17. (By the way, the Nonesuch recording of Einstein omits the second stanza, as did the recent production of the opera in Amsterdam.) As is clear from the diagram, each stanza starts by alternating F major and A major, then adds in Bb major, and finally moves to an alternation of G and F, inserting between them a C major chord to make a kind of II-V-I cadence. Although this pattern is clear, there is some variety in the tonal emphasis: stanza 3 spends less time on Bb than stanzas 1 and 2 do, and stanza 2 has a long middle passage on F major lacking in stanzas 1 or 3. Likewise, in an overview of the rhythms of each repeated phrase one can note rough parallels, but no clear isomorphism. In the first half of each stanza there is one repeated pattern longer than the ones around it; in stanza 1 it’s the fourth, in stanza 2 the third, and in stanza 3 the fifth. In stanza 1, half-notes appear in phrases 5 to 7, in stanza 2 in phrases 1 to 4, and stanza 3 contains no half-note rhythms, but offers dotted half-notes in phrase five.

The last four or five phrases of each stanza are rather climactic. While elsewhere the soprano and soprano saxophone use only the pitches D and E, in these final phrases they use a repeating DEFE, as marked in the diagram. Note that the rhythms here are entirely in quarter-notes, and that in stanzas 1 and 2 there occurs a nine-note pattern of DEFE-DEF-DE, a kind of small 4+3+2 subtractive motif. (By the way, we’ll see Glass using this 4+3+2 pattern 15 years later in his Columbus opera The Voyage, and many of these other patterns as well.) These DEFE motives appear only over the harmonic progressions G-F and G-C-F. All of these features point to an overall form divided into three parallel parts, but the musical continuity is so static, with its endlessly sustained A, D, and E, that the listener does not distinctly experience the piece as sectional, but as a smooth continuum with variations in the symmetry of the rhythm.

Turning to Dance 2, we find many of these same characteristics. Again the pitches D, E, and A are sustained throughout, the DEFE motive appears as a kind of relative intensification, and the rhythm moves among quarter-note, dotted-quarter, and half-note beats. But now the saxophones and piccolo are replaced by Einstein’s violin, and the necessity of writing a playable if still extremely virtuosic part for that instrument seems to suggest quite a few alterations.
Most noticeably, the tonality of F that dominated Dance 1 is replaced with a feeling of A minor, or at least an A natural minor scale (denoted here by a lower-case “a”), a tonality that marks much of the violin solo’s music throughout the opera. The tonality of Bb no longer appears. For the first ten phrases the music merely alternates between an A natural minor scale and an A major triad. The DEFE motive appears only twice in the piece, about a third of the way through and for a long time at the very end. Replacing Dance 1’s middle stanza is a long section (phrases 15 to 25) in which the violin articulates a strict process that is both additive (in terms of adding phrases together) and subtractive (in terms of each new phrase addition being fewer notes than its predecessor): it plays a scale starting on A and going up to G, then another phrase going up to F, then up to E, D, C, and B. After reaching maximum length it then begins subtracting the opening phrases one at a time, and I tried to spell out in the diagram the strict process of addition and subtraction. Later, starting in phrase 37, Glass reinserts this scalar process into larger phrases on the chords of G, C, and A, resulting in repetitive sections far longer than anything in Dance 1. At last the chorus and organ suddenly drop out, and the violin is left to play a solo transition to Knee Play 4.

One of the realizations one draws from such a reading of Einstein, I think, is that it does not much matter whether the progression of patterns follows a strict algorithm, or whether the music moves from pattern to pattern more arbitrarily. An algorithm that is sufficiently complex will prevent the listener from gaining a firm sense of what the patterning is; and, conversely, given a severe restriction of material, a series of similar but nonlinear patterns can be interpreted as probably following some pattern too complex to tease out by ear. The effect can be much the same. The two Dance movements are rather different in this respect without the effect being noticeably formally contrasting. However, I think there is one exception to this in Einstein, and it is the Bed scene with which we started, the opera’s penultimate major scene. Here the rhythmic progression is not only linear and predictable, but proceeds so slowly that it is quite easy to count, and the listener will be tempted to do so. In this case I find something nostalgic about the linearity, as it is the one part of the opera that exposes the underlying process in an audibly discernible way, inviting the listener to step behind the curtain, as it were, and find out how the music works. Given Einstein’s historical appearance just after the repertoire of strict-process minimalism, this mood may even be felt as a nostalgia for the musical period that had just passed. As a kind of retrospective adagio, the Bed scene virtually invites us to remember the minimalist works of the late 1960s and hear how far the rest of the opera has moved away from them.

Aside from the special case of sonata form, in which a composer rewrites the exposition as a recapitulation in order to transpose all themes into the tonic, this idea of using several recomposings of the same passage within one piece does not come up often in the history of music. The composer who wants to get from point A to point B typically figures out the best way to do so, and then proceeds to point C. To find three different and functionally interchangeable ways to get from point A to point B and then use all of them in the same piece, as Glass does here in the Train scene, is rather rare, I think. (After all, had Glass merely repeated three identical A sections, how many listeners would have noticed, how many analysts would have found that anomalous in this context?) And one would have to go to the music of Erik Satie, such as the Gymnopedies or the Pieces Froids, to find a composer writing two large movements of a piece with such similar content as Glass does between these two dance movements. And yet the Dance 2 is quite different in feeling than Dance 1, with its focus on the violin soloist, its incessant running up and down the scale, its greater reliance on additive and subtractive process, and its lack or the comforting F major into which Dance 1 tended to resolve. All the usual jokes about minimalism aside, I find it remarkable that Glass could generate 45 minutes of his opera with so little material, shaping each internal stanza so intuitively, and differentiating the two dances into such different purposes and moods. It is a real piece of compositional virtuosity, and not at all the kind of predetermined logic that we tend to associate with early minimalism.

As my predecessor at The Village Voice Tom Johnson wrote in 1981 about Glass’s Music with Changing Parts, “Yet as I listened once again to those additions and subtractions I realized that they are actually rather whimsical. Composers like Frederic Rzewski, Louis Andriessen, and William Hellermann have written such sequences with much greater rigor. By comparison, Glass is not a reductionist at all but a romantic.” [2] Romantic is not quite the word I would have used—I would be loathe to think that the mere absence of a generating algorithm suffices as evidence of passion or individualism. (In fact, that Tom would use the word on such minor grounds in 1981 is indicative of the atmosphere I began this essay by describing.) But I do think that there is a kind of inherent mystery in Glass’s circuitous, unpredictable paths through extremely circumscribed material, and that Einstein on the Beach would be a less compelling work than it is had he been more content with mere concept and less generous with his subtly-shaping artistry.

1. Philip Glass, “Note on Einstein on the Beach,” Einstein on the Beach, Tomato Records, TOM-4-2901 (1979).
2. Tom Johnson, “Maximalism on the Beach: Philip Glass,” Village Voice, February 25-March 3, 1981; reprinted in The Voice of New Music, Amsterdam (Het Apollohuis, 1989)
Copyright 2013 by Kyle Gann

From No Such Thing as Silence: John Cage’s 4’33”

Reprinted from No Such Thing as Silence: John Cage’s 4′33″ Copyright © 2010 by Yale University Press. Used with permission of the author and publisher.

From Chapter One, 4′33″ at First Listening

John Cage’s 4′33″ is one of the most misunderstood pieces of music ever written and yet, at times, one of the avant-garde’s best understood as well. Many presume that the piece’s purpose was deliberate provocation, an attempt to insult, or get a reaction from, the audience. For others, though, it was a logical turning point to which other musical developments had inevitably led, and from which new ones would spring. For many, it was a kind of artistic prayer, a bit of Zen performance theater that opened the ears and allowed one to hear the world anew. To Cage it seemed, at least from what he wrote about it, to have been an act of framing, of enclosing environmental and unintended sounds in a moment of attention in order to open the mind to the fact that all sounds are music. It begged for a new approach to listening, perhaps even a new understanding of music itself, a blurring of the conventional boundaries between art and life. But to beg is not always to receive.

What was this piece, this “composition” 4′33″? For so famous and recent a work, the number of questions that still surround it is extraordinary—from its lost original manuscript, to its multiple notations, to unexplained deviations in the lengths of the movements, to the peculiar process of adding up silences with which it was composed, to the biggest ambiguity of all: How are we supposed to understand it? In what sense is it a composition? Is it a hoax? A joke? A bit of Dada? A piece of theater? A thought experiment? A kind of apotheosis of 20th-century music? An example of Zen practice? An attempt to change basic human behavior? Let’s try the hoax hypothesis. Here are some definitions for hoax:

1. An act intended to deceive or trick;
2. Something that has been established or accepted by fraudulent means;
3. Deliberate trickery intended to gain an advantage (synonym: fraud);
4. A deception for mockery or mischief.

In what was Cage trying to deceive the audience? Attempting to make them think they had heard something when they hadn’t? The audience was fully aware that Tudor was sitting onstage and neither touching the keyboard nor making any audible sounds. If Cage was trying to fool the audience into thinking he had written a piece when he really hadn’t, who was deceived? One could argue that Cage was mocking the audience, but he wasn’t doing so by deceiving them. There was no attempt to cover up what 4′33″ was: a man sitting at a piano for four and a half minutes without playing. There was no moment following the performance at which listeners learned that what they’d heard was not what they thought.

Perhaps it was trickery intended to gain an advantage? Ah yes, the advantage! And what was that advantage? Why, money, of course! Every time I have ever played or explained 4′33″ to a class, one student has always exclaimed indignantly, “You mean he got paid for that?” According to the common understanding of how musicians lead their careers, the musician makes some music, it gets played, and the musician is given some money through some means or another. But Cage wasn’t paid for writing 4′33″; the piece wasn’t commissioned. The concert was a benefit for a good cause. The money people paid to hear David Tudor play did not go to Cage, or even to Tudor.

And in fact, while songwriters usually get paid for their performances and receive royalties for the use of their songs, classical composers like Cage sometimes compose for commissions, but also often write pieces with no commission at all. Often they compose simply because they have an idea, or they’re building up a portfolio for future performances, or they’re trying to advance their careers by doing something impressive, or—quite often—they compose for the sheer love of composing, which can be an enjoyable and fulfilling activity. At that time, Cage was, as he said, “poor as a church mouse,” and he had been so for many years. He had spent the year 1951 composing his piano piece Music of Changes on the sidewalk and on the subway, and asking friends and strangers to support him by buying shares in his music in case it ever did actually make some money. The year following the 4′33″ premiere, the old Lower West Side apartment house Cage was living in was scheduled for demolition, and he was forced to relocate. Not affluent enough to find another place in the city (even with cheap 1950s rents), he eventually moved with friends to an artists’ collective upstate at the community of Stony Point, where he could enjoy two small rooms for $24.15 a month (about $194 in 2008 dollars).1 Not until the 1960s would Cage gain any measure of financial security. The idea that he might have made any money off an avant-garde gesture like 4′33″ is a raw caricature of a composer’s life. (In the 1960s, however, when he was much more famous, Cage did sell the manuscript of 4′33″ for a large sum of money, much as one might sell any document that had come to have historical significance.)

Or perhaps Cage was just lazy, “writing” a piece that took no work at all and hoping to make some money off it later. Any such impression is belied by the sheer volume of Cage’s lifelong output, the detailed complexity of many of his scores, and the loving care he put into copying his manuscripts. He would later say that 4′33″ took longer for him to write than any other piece, because he worked on it, as a concept, for four years. And in 1951 he had written the tremendously virtuosic and complex Music of Changes, more difficult to conceive and compose than anything a lazy person would have ever contemplated.

In 2004 the BBC broadcast an orchestral version of 4′33″—which meant that the BBC Symphony Orchestra sat onstage for four and a half minutes without making sounds, and people listened to their silence in the hall and over the radio. Some of the comments the BBC received over the Internet played into the “hoax” theme:

I’m sorry, but this is absolutely ridiculous. The rock ‘n’ rollers and the punks were wrongly bashed in their day, but this genuinely deserves a big thumbs down.

This is clearly a gimmick, when he ‘wrote’ this piece he was testing who was stupid enough to fall for it. I think you’ll find he wrote it on 01 April 1952.

I find it quite patronising and disturbing that self proclaimed intellectuals are trying to convince us that this is art—just another nail in the coffin for the world of art!

Is this how our licence fee money is being used? I’ve never heard of such a stupid thing in my life! God rest his soul, but this ‘composition’ by Cage smacks of arrogance and self importance . . .

Emperor’s new clothes anyone?2

Yet for the rest of his life, Cage talked about 4′33″ as his most important work, the one he returned to again and again as the basis for his other new works. He knew what it consisted of and was well aware of the range of receptions it generated.

How about the “joke” theory? Well, Cage was certainly afraid it would be taken as a joke, which is why it took him four and a half years (nice coincidence) from conceiving the piece to actually presenting it publicly. (“I have a horror of appearing an idiot,” he once told a critic.)3 In a 1973 interview he admitted, “I was afraid that my making a piece that had no sounds in it would appear as if I were making a joke. In fact, I probably worked longer on my ‘silent’ piece than I worked on any other.”4 Cage explained the “joke”: “I think perhaps my own best piece, at least the one I like the most, is the silent piece. It has three movements, and in all of the movements there are no sounds. I wanted my work to be free of my own likes and dislikes, because I think music should be free of the feelings and ideas of the composer. I have felt and hoped to have led other people to feel that the sounds of their environment constitute a music which is more interesting than the music which they would hear if they went into a concert hall.”5 For a joke, this is an awfully earnest philosophical program.

How about Dada? Dada was an art movement, or perhaps anti-art movement, associated with the period during and after World War I. Disillusioned by the great world of European culture being plunged into war, artists like Tristan Tzara, Hugo Ball, Hans Arp, Sophie Tauber, Erik Satie, and others dove into a world of nonsensical art that eschewed reason and logic in favor of chaos, randomness, and paradox. In the foreword to his seminal early book Silence, Cage acknowledges a debt to Dada, and Satie was one of his favorite composers. Cage also notes that “what was Dada in Duchamp’s day is now just art,” but on Cage’s own authority the possibility that 4′33″ was a Dada-inspired gesture, even if also more than that, cannot be entirely dismissed.

How about theater? One of the crucial aspects of 4′33″, at least in the first performances, is that there was a pianist onstage, whose presence, and whose behavior in the previous pieces on the program, clearly led the audience to expect that his hands would at some point engage the keyboard, and that they would hear deliberately made sounds coming from the stage. That this did not happen, that the listeners’ expectations were deliberately flouted, cannot be entirely divorced from the sonic identity of the piece, even though the way Cage talked about 4′33″ later in life—claiming, for instance, that he often “performed” the piece while alone—seems to suggest that it can. As New York Times critic Edward Rothstein suggested in a rather unsympathetic obituary of Cage, had Cage simply wanted his audience to listen, he could always have instructed them to do so.6 In fact, following 4′33″, Cage’s music, by his own enthusiastic admission, began tending more and more toward theater, and during the 1960s in particular he became very interested in the physical and cognitive relationship between performers and audience members.

The description of 4′33″‘s theatrical recontextualization can hardly be phrased more delicately and thoroughly, I think, than Douglas Kahn has done:

Ostensibly, even an audience comprised of reverential listeners would have plenty to hear, but in every performance I’ve attended the silence has been broken by the audience and become ironically noisy. It should be noted that each performance was held in a concert setting, where any muttering or clearing one’s throat, let alone heckling, was a breach of decorum. Thus, there was already in place in these settings, as in other settings for Western art music, a culturally specific mandate to be silent, a mandate regulating the behavior that precedes and accompanies musical performance. As with prayer, which has not always been silent, concertgoers were at one time more boisterous; this association was not lost on Luigi Russolo, who remarked on “the cretinous religious emotion of the Buddha-like listeners, drunk with repeating for the thousandth time their more or less acquired and snobbish ecstasy.” 4′33″, by tacitly instructing the performer to remain quiet in all respects, muted the site of centralized and privileged utterance, disrupted the unspoken audience code to remain unspoken, transposed the performance onto the audience members both in their utterances and in the acts of shifting perception toward other sounds, and legitimated bad behavior that in any number of other settings (including musical ones) would have been perfectly acceptable. 4′33″ achieved this involution through the act of silencing the performer. That is, Cagean silence followed and was dependent on a silencing. Indeed, it can also be understood that he extended the decorum of silencing by extending the silence imposed on the audience to the performer, asking the audience to continue to be obedient listeners and not to engage in the utterances that would distract them from shifting their perception toward other sounds. Extending the musical silencing, then, set into motion the process by which the realm of musical sounds would itself be extended.7

Kahn is right: 4′33″ cannot be bracketed as a purely sonic phenomenon. It called upon the audience members to remain obediently silent under unusual conditions. The pianist’s refusal to play calls a whole network of social connections into question and is likely to be reflected in equally unconventional responses on the part of the audience.

How about a “thought experiment,” a kind of “metamusic” that makes a statement about music itself? For many people, including me, 4′33″ is certainly that, if not only that. One story about Cage recounts his sitting in a restaurant with the painter Willem de Kooning, who, for the sake of argument, placed his fingers in such a way as to frame some bread crumbs on the table and said, “If I put a frame around these bread crumbs, that isn’t art.” Cage argued that it indeed was art, which tells us something about 4′33″.8 Certainly, through the conventional and well-understood acts of placing the title of a composition on a program and arranging the audience in chairs facing a pianist, Cage was framing the sounds that the audience heard in an experimental attempt to make people perceive as art sounds that were not usually so perceived. One of the most common effects of 4′33″—possibly the most important and widespread effect—was to seduce people into considering as art phenomena that were normally not associated with art. Perhaps even more, its effect was to drive home the point that the difference between “art” and “non-art” is merely one of perception, and that we can control how we organize our perceptions. A person who took away nothing from 4′33″ but this realization would, in my view, already be taking home something revolutionary.

From a broader perspective, how about 4′33″ as the apotheosis of twentieth-century music? There is something intriguing about the piece’s position as a kind of midpoint of the century. The years just following World War II had seen a resurgence of the twelve-tone music invented by Arnold Schoenberg. Composers like Karlheinz Stockhausen, Pierre Boulez, and Milton Babbitt were expanding the twelve-tone idea from the realm of pitch to include rhythm, dynamics, and timbre, and in the process creating music of unprecedented complexity. Such hyperstructured music began to verge on the realm of incomprehensibility, a kind of perceptual chaos arising paradoxically from rational processes.

It’s true that most of this development appeared in the years just following 4′33″, but in the 1960s it became common to talk about how little different the super-controlled music of Stockhausen and Babbitt sounded from the totally chance-controlled music Cage was writing. And indirectly 4′33″ led to the developments from which grew the simpler and more accessible new style of minimalism. As a locus of historical hermeneutics, 4′33″ can be seen as a result of the exhaustion of the overgrown classical tradition that preceded it, a clearing of the ground that allowed a new musical era to start from scratch.

And how about 4′33″ as an example of Zen practice? This, I think, may be the most directly fertile suggestion. Cage first spoke of the possibility of a silent piece in 1948, and several steps in his thinking led him, over the next four years, to the inevitability of presenting such a work in public. There are many levels on which 4′33″ can be understood, and many simultaneous meanings to be grasped within it—which, after all, is one of the signs by which any great work of art can be recognized as such.9


1. Revill, The Roaring Silence, pp. 179-80.

2. “Radio 3 Plays Silent Symphony,” BBC News, January 19, 2004, (accessed April 9, 2009).

3. Donal Henahan, “Who Throws Dice, Reads I Ching, and Composes?” New York Times, September 3, 1972; quoted in Revill, The Roaring Silence, p. 12.

4. Interview with Alan Gillmor and Roger Shattuck, quoted in Kostelanetz, Conversing with Cage, p. 67.

5. Jeff Goldberg, “John Cage Interview,” Soho Weekly News, September 12, 1974.

6. Edward Rothstein, “Cage Played His Anarchy by the Rules,” New York Times, September 20, 1992.

7. Kahn, “John Cage: Silence and Silencing,” p. 7.

8. Interview with Robin White, quoted in Kostelanetz, Conversing with Cage, pp. 211-212.

9. Philip Gentry has theorized that 4′33″ might have represented for Cage, or for some of the audience, an appropriation or expression of the silence that gay men were forced to maintain (even more than usual) during the repression of the McCarthy era, when gays were being fired from government and institutional jobs—and that the audience’s anger may have had to do with the inherent homosexuality of the gesture, given Cage’s persona. However this may be, the anger does seem disproportionate in a way that begs for further explanation. See Gentry, “Cultural Politics of 4′33″.”

Crash Course: Minimal Music, Maximal Impact

Minimalism began as a movement of the 1960s and ‘70s, but it didn’t die–it evolved. And it’s apparent now that it was the beginning of a new musical sensibility whose worldwide ramifications we’ve only begun to figure out. Join us as we sample from a rich catalog of work beginning with the groundbreaking music of composers such as Steve Reich and Philip Glass up through recent compositions from Michael Gordon and John Luther Adams.

Counterstream OnDemand: Minimal Music, Maximal Impact

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Kyle Gann, photo by Jorgen Krielen

Photo by Jorgen Krielen

About Your Host
Kyle Gann is a composer and was new-music critic for the Village Voice from 1986 to 2005. Since 1997 he has taught music history and theory at Bard College. He is the author of The Music of Conlon Nancarrow (Cambridge University Press, 1995), American Music in the 20th Century (Schirmer Books, 1997), and Music Downtown: Writings from the Village Voice (University of California Press, 2006).

Recommended Listening:
Steve Reich: Music for Mallet Instruments, Voices, and Organ (Deutsche Grammophon)
Ben Harms, Bob Becker, Glen Velez, James Preiss, Janice Jarrett, Jay Clayton, Joan La Barbara, Russ Hartenberger, Steve Chambers, Steve Reich & Tim Ferchen - Reich: Variations, Music for Mallet Instruments & 6 Pianos

Terry Riley: In C (Cantaloupe)
Bang On A Can All-Stars - Terry Riley: In C

Philip Glass: Einstein on the Beach (Sony Bmg Europe)
Michael Riesman & Philip Glass Ensemble - Glass: Einstein On the Beach

Jon Gibson: Two Solo Pieces: Cycles (1973)/Untitled (1974) (Dunya)

Harold Budd: Ambient 2: The Plateaux of Mirror (Astralwerks)

Tom Johnson: An Hour for Piano (Lovely Music)
Frederic Rzewski - Johnson: An Hour for Piano

Eliane Radigue: Trilogie de la Mort (Experimental Intermedium)

Janice Giteck: Om Shanti
Janice Giteck - Home (Revisited)

Daniel Lentz: Wild Turkeys
Daniel Lentz - Wild Turkeys

Elodie Lauten
Waking in New York (4Tay Records)

Michael Gordon: Yo Shakespeare (Argo)

Mikel Rouse: Return
Mikel Rouse - Return

Further Reading:
Gann, Kyle. “Minimal Music, Maximal Impact.” NewMusicBox, 2001.

Gann, Kyle. American Music in the Twentieth Century. Schirmer Books, 1997.

Fink, Robert. Repeating Ourselves: American Minimal Music as Cultural Practice. University of California Press, 2005.

Johnson, Tom. The Voice of New Music. Apollohuis, 1991; currently out of print, available for download here.

Potter, Keith. Four Musical Minimalists. Cambridge University Press, 2000.

Strickland, Edward. Minimalism: Origins. University of Indiana Press, 1993.

Schwarz, K. Robert. Minimalists. Phaidon Press, 1996.

Fairbanks: A Long Ride in A Slow Machine

Kyle Gann
Kyle Gann
Photo by Nicole Reisnour

The immense new wing of the University of Alaska’s Museum of the North is intended, I’m told, to resemble icebergs. It’s certainly towering and extremely white, but for me its out-of-kilter crescent shapes evoke Native American art of the Northwest’s indigenous tribes. Perhaps that’s a chicken-and-egg argument, but it’s a fine building. (“The only piece of architecture-as-art in Alaska,” UA Museum Director Aldona Jonaitis proudly assured me.) And if architect Joan Soranno was aiming, as rumored, at something Frank Gehry-esque, what she achieved was warmer, more inviting, and more snugly fit to its environment than the Gehry buildings I’m acquainted with. This concludes my undistinguished career as an architecture critic; what drew me to Fairbanks, of course, courtesy of the museum, was their new permanent sound installation, The Place Where You Go To Listen by John Luther Adams, which has generated a remarkable amount of national buzz for any work of that genre, let alone one so distantly regional.

The Place Where You Go To Listen is a translation for Naalagiagvik, an Iñupiaq place name on the arctic coast. Jonaitis talked to Adams, Alaska’s most visible composer, about creating a permanent installation for the museum before ground for the addition was even broken. At about twenty feet by nine or so, the space allocated turned out to be smaller than anticipated, but it serves as a meditation room directly upstairs from the main entrance. You walk in, separate yourself from the world directly outside, sit on the bench, and slip into the red-and-violet, or blue-and-yellow, moods of the five glass panels in front of you. A continual hum greets you, and after a moment you begin to sort out the strands of the complex tapestry that the hum turns out to be. There are sustained chords, an intermittent rattle of deep bells overhead, and an irregular boom of extremely low frequencies that you have to focus on to remain aware of. It’s a complex net of heterogeneous sounds, and though the ambiance is relaxing, taking everything in is a challenge for the ears.

What makes The Place—as Adams likes to refer to it—different from other sound installations is that you can’t just drop by for half an hour and take it all in. La Monte Young’s Dream House is a similarly complex acoustic experience, but it doesn’t change from one day or hour to the next. And most installation artists sort of plan around the presumed length of the average gallery visit. The Place changes radically from night to day, from winter to summer, from season to season.

First of all, those sustained chords: one is called the “Day Choir,” the other the “Night Choir,” and the former follows the sun around. Literally: there are fourteen speakers around and above the room, and from the listener’s perspective the day chord is centered on the direction the sun is at at that moment. Relative strengths of the day and night chords vary with the sun’s location above or below the horizon. In Fairbanks, which is less than 200 miles from the Arctic Circle, this means a strong seasonal difference as well, the night chord being far more prominent in winter. Add to this that the Day Choir is based on an overtone series, the Night Choir on an undertone series, and you get an association of light and dark with major and minor, and an eerie blending of the two during Alaska’s leisurely twilights. Nature is not always soothing; neither is The Place.

The Place
Seen but not heard:
The Place Where You Go To Listen at midnight
Photo by Kyle Gann

Another tone, less easy to isolate, follows the phases of the moon through a month-long glissando. The booming low frequencies indicate seismic activity. The computer that controls all this is receiving real-time data from seismological stations around Alaska, which is an unusually earthquake-prone region. There’s something going on almost all the time, and people were speculating that an actual earthquake would create quite a noise indeed.

But the really romantic association, and not only for us lower-48ers, is that between the bell sounds and the aurora borealis. The bells emerge from the speakers in the ceiling, and they’re driven by streamed data from five Alaska geomagnetic monitoring stations, arranged north to south and mirrored that way in The Place. When you see the aurora borealis playing in the sky, as I did on my first night, you know plenty of bells are going to sound in the installation; likewise, if you hear lots of bell activity late in the afternoon, you know that the aurora is revving up for a colorful night. If you walk in and there are no bells, you can be as momentarily disappointed as you might be on an aurora-less night but then pay attention to the subtler harmonies you might otherwise miss. And if it’s cloudy, you can hear the aurora even when you can’t see it. Passing clouds affect the overall sound as well, muting the brightness you’d hear on a sunny day.

So you sit in this room, on the bench, or lie on the floor as some did, and through a kind of conceptual prosthesis you become aware of the earth’s activities, including some things you could see for yourself outside, but many others that you couldn’t see and at a detail not available to human senses. As with many sound installations, there is a left/right-brain split involved, but perhaps one unprecedentedly mammoth in its impact. That split was quite apparent in the reactions of the listeners at the March 21 opening (timed to coincide with the equinox). Some wanted to learn about the scientific workings of the piece in exhaustive detail, and to isolate each sound and know what was caused by what. Others fiercely resisted explanation and simply wanted to soak up the sensuous ambiance.

Of course, neither pure state is really sustainable, a contradiction that is part of The Place‘s charm. Reduce it to the meaning of the seismological and geomagnetic data, and you miss all the months of fine-tuning that Adams and his programming assistant Jim Altieri put into making exactly this complex of scales and harmonies, all tuned to a G that matches the rotation period of the earth. Merely listen as a meditative experience, and you miss the super-large scale of the piece and the logic of its nested periodicities. The poetry exists in-between: savoring the slow-changing forms with their rich detail of surface activity, being conscious of their relation to global processes, and learning to appreciate the time-scale, the lumbering sense of syncopation, of the planet on whose surface you scratch out your humble existence.

Of course, as the eternal explainer of such music I never have ignorance as an option, so Adams opened the hood and let me peer inside. The entire piece is a humongous, multilayered Max patch, augmented by software programs that, for example, chart the relative position of the sun and moon. The starting point for all of the sounds is pink noise, meticulously filtered into minute pitch bands capable of being combined into timbres. Not wanting to fall into what one might call the usual Max sounds, Adams worked out his tones on alternate software, and then assigned Altieri—a former student of his at Oberlin, a double-major in composition and geology, and a programming superwiz—the task of replicating them in Max. Unconventional tuning is a large part of the piece, and the different layers demanded heterogeneous solutions. The Day and Night Choirs fused into mere timbre when tuned to an actual harmonic series (one of the difficulties of writing polyphony in just intonation), and so a tempered tuning was sought, the most flattering of which turned out to be the good old 12-pitch equal scale. The aurora bells, though, are tuned to prime-numbered harmonics from 2 to 31.

By zipping through some time-lapse data in the Max patch, John could zip me between summer and winter, night and day, fine and inclement weather, and show me The Place‘s range. (An internet demonstration by Roger Topp available in the lobby, soon to be marketed on DVD at the museum’s gift store, provided a similar function for the less privileged tourists.) Contrasts were indeed stark—the piece’s center of harmonic gravity, so to speak, shifting over a four-octave range. In real time, most of the drama happens over a languorous time curve, which means that the real audience for The Place isn’t us tourists who fly in through Seattle for a week (imagine getting to hear only ten measures of the Eroica Symphony), but the locals who check in every month on their regular visits to the museum. They’re the ones who’ll get to experience The Place in fair weather and foul, November, March, and July, quiet moonlit evenings and invisible geomagnetic storms. (John’s a little concerned that the midnight sounds won’t get heard much, since the museum is closed, but there are some plans to keep it open for special events like solstices.) They’ll learn and cherish its moods, habits, and anomalies. Perhaps no other sound installation has ever so justified, by vastness of time scale, its permanent place in a museum’s architecture.

In that respect, The Place is the culmination of Adams’s output to date. His long, long orchestra works—In the White Silence, For Lou Harrison, and Clouds of Forgetting, Clouds of Unknowing—work with Morton Feldman’s expansive sense of scale, but also, within that, with a sense of periodicity almost too large to take in. Adams is one of the few composers around who still talks about, and yearns to evoke, that 19th-century attribute called the Sublime, inspiring awe, attraction, and fear all at once. One could surmise that his love of the sublime was inspired by contact with the panoramic harshness of the Alaska landscape, but I suspect that, rather, he was born with a yen for that feeling and moved to Alaska decades ago in search of it. Like Feldman’s For Samuel Beckett, Adams’s 75-minute In the White Silence enwraps you in sensuousness but makes your human attention span feel picayune and inadequate. The Place Where You Go To Listen zooms beyond even that to a potential eternity that you’ll have to go back to again and again to fully appreciate.


Kyle Gann is a composer, music critic, musicologist, and Associate Professor of Music at Bard College. His music, which frequently uses microtonal scales, has been released on Cold Blue, Monroe Street, and New World Records. He maintains a blog on ArtsJournal and is the author of three books: The Music of Conlon Nancarrow (Cambridge University Press, 1995); American Music in the Twentieth Century (Schirmer Books, 1997) and Music Downtown (University of California Press, 2006).

Letter to the Editor: Reluctantly Weighing in on Uptown/Downtown

I am reluctant to comment on the controversy surrounding the use of the terms Uptown and Downtown; as someone who just last month published a book with the title Music Downtown, it might be inferred that I have some vested interest in the matter. However, since I am someone who wrote a book, I hope it might be granted that there are some statements I could make that could not meet with persuasive disagreement.

1. I was hired in 1986 by Doug Simmons, an erudite music editor who did not take his musical terminology lightly, to “cover the Downtown scene.” The Downtown scene was, first and perhaps foremost, a specific group of people who socialized and made music together during a specific period and at specific places. We called ourselves Downtown musicians and referred to our music as Downtown music. Some of us, perhaps regrettably, are still alive, though even the youngest of us are doddering old quinquegenarians by now. Some of us write music essentially similar to the music we made then. You may argue, if you like, that context alters terminology, and that a piece of music written in eighth-notes in a diatonic scale was “Downtown” if it was written in New York in 1980, and “not Downtown” if it was written in upstate New York in 2004. It is an argument.

2. In the institution where I teach, I perennially have composition students who encounter fierce opposition from music professors for writing music that uses repetitive structures, diatonic tonality, and/or steady-state (or unspecified) dynamics. By an eerie coincidence, these are all qualities that were common in what people on the Downtown scene called “Downtown” music back in the 1980s. Randy Nordschow says that he is “a little perplexed as to why these dagger terms, which can still stir bitterness and pain in the over-40 crowd, are perpetuated by the very same generation. You’d think we composers would yearn to close the book on that whole divisive rift of the past.” Personally, I use the term as a convenient shorthand, because, in the heat of the moment, it is quicker to defend one’s beleaguered student by calling her “a victim of a bias against Downtown music” than by calling her “a triple victim of several unrelated biases against repetitive structures, diatonic tonality, and/or steady-state (or unspecified) dynamics.” If I had no need to defend such students, it is doubtful that I would ever bring up the subject at all. In the larger scheme of things, however, my emotional attachment to my students outweighs my desire to make Randy Nordschow’s life more comfortable.

On the other hand, there are questions about the issue not nearly so easily answered:

1. Does the Uptown/Downtown dichotomy still apply to music by people born after 1965? I frankly don’t know. Downtown Manhattan still exists. Performances of new music there are far fewer than they used to be. If there is any cohesion to music performed on what is left of the Downtown scene, I no longer possess the range of recent experience to characterize it. Downtown music, it seems, has splintered into a hundred different and reconverging streams, as has what was originally and neologistically called Uptown music. Other streams have appeared which would be impossible to trace to either sphere. Judging from opinions expressed on the Internet, one could say that, among the infinite rainbow of views, one occasionally encounters a musical sensibility that tends toward complex, highly fixed, detail-inflected musical structures, and another that runs toward simpler, more variable, looser structures. One could call these “conservative” versus “liberal,” “classical” versus “postclassical,” “mauve” versus “puce,” but let’s agree for argument’s sake that they shouldn’t be named at all. Naming leads to discussion, which leads to recognition of differences, which foments hatred and exclusivity. Better to say that Brian Ferneyhough and Brittany Spears cannot be meaningfully distinguished in words. Their music, I mean. To distinguish Brittany from Brian would diminish her, and god knows I don’t want to do that.

2. Why are Mary Jane Leach and I the only people from the old Downtown scene who seem to inhabit the blogosphere? I have no idea. Having been paid to focus on the Downtown scene for 19 years, I have always taken the position that what people outside the scene think Downtown music is is of relatively scant importance; and that the day that composers within the Downtown scene begged me to quit talking about it, I would quit. Since all of the people who have expressed such eagerness for me to quit talking about Downtown music were never part of that scene, I have always dismissed their requests as irrelevant.

But here I am, indulging the worst vice of the aged: yammering on about the good old days, still obsessing about issues and musical compositions that are, by now, ten, fifteen, even twenty years old, and that should have long since been consigned to oblivion. My apologies. It’s a pain to have to hear us oldsters rehash the battles of our long-lost youth, but take heart: I’m not feeling too well lately.

Making Marx in the Music: A HyperHistory of New Music and Politics

“There is no such thing as Art for Art’s sake, art that stands above classes, art that is detached from or independent of politics.”

—Mao Tse-tung

Natalie Maines of the Dixie Chicks and I have something in common: we’re both ashamed to share our home state with George W. Bush. But she’s gotten a lot more attention for having said so. After she dissed the President to a concert audience in London, she and the other Chicks received obscene phone calls, threatening drive-bys, bomb threats, and had their songs blacklisted off of hundreds of radio stations, many of them owned by the right wing-connected Clear Channel Corporation. Meanwhile, John Mellencamp revved up an old 1903 protest song called “To Washington,” refitted it with new 2003 lyrics, and released it provocatively just as the troops were headed for Baghdad:

A new man in the White House
With a familiar name
Said he had some fresh ideas
But it’s worse now since he came
From Texas to Washington
He wants to fight with many
And he says it’s not for oil
He sent out the National Guard
To police the world
From Baghdad to Washington

For that, hundreds of radio listeners called in and said things like, “I don’t know who I hate worse, Osama bin Laden or John Mellencamp.”

No one can doubt that music has a big role to play in the world of political protest. The controversial musicians we read about in the papers, though, are mostly from the pop and folk genres. It’s not only that those musicians are more visible, though that’s certainly true as well. Classical music and jazz seem to have a more long-term, measured, even sublimated approach to political protest, slower to react and more deeply embedded in the structure of the music itself. When John Mellencamp writes a political song, he can use the same old chords and instruments he always uses; political classical composers often feel that the political intention entails a special style and strategy. When Billy Bragg is infuriated by an item in the paper, he can fire off a song that day:

Voices on the radio
Tell us that we’re going to war
Those brave men and women in uniform
They want to know what they’re fighting for
The generals want to hear the end game
The allies won’t approve the plan
But the oil men in the White House
They just don’t give a damn
‘Cause it’s all about the price of oil.

—”The Price of Oil” by Billy Bragg

The classical and jazz worlds, however, generally have a longer turnaround time.

Some composers see themselves playing to such a small audience that they see no point in writing political music, and often they compensate with more conventional types of political activism; Conlon Nancarrow, for instance, didn’t believe in music’s ability to portray anything extramusical, let alone political, but was nevertheless a sufficiently committed Communist to fight in the Spanish Civil War. Others feel, more obliquely and with little opportunity to gather concrete evidence, that through the nature of their music they can encourage perceptions that bring about greater awareness in the general population.

Most problematic of all, perhaps, is classical music’s traditional relationship to established power and wealth. Rock guitarists and performance artists can challenge the status quo without subsidy, but the composer who gets performed by orchestra or chamber ensemble usually does so by the grace of either government grants or wealthy patrons or both. You can write a symphony subtitled “Death to the Corporate Ruling Class” if you want, but think twice about showing up for the orchestra trustee board meeting at which the commission is announced.

Consequently, political controversies involving classical music have been few and far between, and not always attributable to radical intentions on the part of the composers. The few highly visible cases are easy to enumerate. In 1953, Aaron Copland’s A Lincoln Portrait—and how can you get any more innocently American than Copland’s narrated tone poem with Lincoln’s words laced by folk song quotations like “Springfield Mountain” and “Camptown Races”—was abruptly canceled from performance at President Eisenhower’s inaugural concert, because an Illinois congressman, Fred E. Busbey, had protested Copland’s Communist connections of the 1930s. Copland had never actually been a Party member, but had written a prize-winning song for the Communist Composers’ Collective, given musical lectures for Communist organizations, and appeared at the 1949 World Peace Conference to meet Shostakovich. Within months, Senator Joseph McCarthy called Copland to appear before the House Committee on Un-American Activities, a fate that also eventually befell fellow composers Elie Siegmeister, Wallingford Riegger, David Diamond, and the German émigré Hanns Eisler, who was subsequently deported.

A similar situation recurred in 1973, when Vincent Persichetti’s A Lincoln Address, also based on words of the Great Emancipator, was to be premiered as part of Richard Nixon’s inauguration. Lincoln, however, had denounced “the mighty scourge of war,” which threatened to look like a reflection on Nixon’s pet venture, the Vietnam War. Persichetti was asked to make changes. He declined. The performance did not take place. Apparently the words of Abraham Lincoln are too inflammatory for today’s politicians. More recently, John Adams and Alice Goodman had the choruses of their opera The Death of Klinghoffer canceled by the Boston Symphony in the wake of 9-11 for their arguably pro-Arab (or in Adams’ view, even-handed) stance. The words of that opera, such as—

“My father’s house was razed
In nineteen forty-eight
When the Israelis
Passed over our street”

—were to some listeners, it has been charged, “not a simple statement of fact, but rather provocation.” Nevertheless, despite these isolated headline-grabbers, by and large—aside from the perennial attacks on Wagner’s anti-Semitism that constitute a cottage industry—the world rarely takes classical music seriously enough to protest it.

As Marx and Engels wrote in the Communist Manifesto, the bourgeois epoch has simplified the structure of the world’s class antagonisms into two camps: bourgeoisie and proletariat. (In recent years, the [s]election of former CEOs like Bush and Cheney has eroded even the slim, traditional distinction between politicians and the corporate class.) Virtually by definition, “political music” is understood as music that supports the interests of the working classes, and exposes the corporate/governing class as thieves and oppressors. As Christian Wolff—one of the central composers in this area—has pointed out, almost all composers called political are leftist: there have been virtually no composers whose music was explicitly associated with conservative causes, notwithstanding a number of patriotic symphonies and tone poems penned during World War II. In Marxist terms, composers who write for the delectation of the rich and for their fellow professionals are giving aid and comfort to the bourgeoisie, and are by definition counter-revolutionary, no matter what their conscious personal politics. Most non-pop music of the past century that we think of as political has come from a Marxist, communist, or socialist viewpoint—the composers who come to mind are Hanns Eisler, Marc Blitzstein, Frederic Rzewski, Cornelius Cardew, Christian Wolff, Luigi Nono. Even for composers who write from a feminist or gay or pro-Native American or Save the Whales viewpoint, Marxist conditions for political music tend to be assumed: simplicity, relation to some musical vernacular, non-elitist performance situations.

For many people, music can only be political when it has a
text, and for certain composers, the style is immaterial as long as the text makes its point. The latter group, however, seem to be a minority; most political composers feel that music should be understandable not only by musical connoisseurs, but by the working classes whose interest it represents, whereas writing music for new-music specialists and the upper class is regarded as being of little value or point. Therefore, political music tends to be widely accessible, non-abstract, familiar in its basic idiom, tending towards simplicity rather than complexity. There are exceptions; Nono wrote political music in a serialist and rather forbidding idiom, and Wallingford Riegger was a curiously complacent 12-tone Communist. Leftist composers of the Depression Era believed in using folk tunes to represent, and reach out to, “The People.” Analogously, some more recent composers have believed in starting from a pop or rock idiom, as being the “folk” music to which today’s mass audiences are attuned.

However, as Wolff has written, the conditions through which popular music develops are themselves corrupt and exploitative. Those who take pop music as a stylistic basis may already be, by implication, playing into the hands of the corporate world—unless, somehow, they engage to subvert it. Swerve toward popular music and you may be letting corporations dictate your personal expression; swerve too far away, even in the direction of simplicity and accessibility, and you run the danger, as Wolff says, of seeming merely “eccentric.” As he further spells out the paradox, parsing German social thinker Theodor W. Adorno: if music “lets go of (its) autonomy, it sells out to the established (social) order, whereas, if it tries to stay strictly within its autonomous confines, it becomes equally co-optable, living a harmless life in its appointed niche.” The road from classical composition to the working classes is riddled with pitfalls and chasms.

One of the largest fissures, plaguing politically conscious composers for the last eight or nine decades, is that musical progressivism and political progressivism do not go hand in hand, and often are felt to be diametrically opposed. For music to be abstract, complex, difficult to understand—so the argument runs—supports the power structure of the bourgeoisie, since it provides a harmless distraction from the real conflicts of class oppression. This belief has resulted in the seeming paradox of some of the most advanced and forward-looking musicians—most famously Hanns Eisler in 1926 and Cornelius Cardew in 1971—turning their backs on the continuation of what seemed at the time an inevitable musico-historical trajectory.

Thanks to such paradoxes, unanswerable questions run through the background of the present survey:

  1. Can music (without text) express political truths?
  2. Does “concert hall” music with political texts achieve any useful end?
  3. Can political music made by composers in the classical tradition, no matter how simplified or accessible, do anything besides preach to the converted?
  4. Do composers have a social responsibility to attract or address certain audiences?
  5. Does who you get your money from affect your art? Should it?
  6. Is politics the business of only pop music, while experimental music is already too much of an elitist pastime?
  7. Given that the music the working classes are familiar with is exploitatively limited and controlled by commercial and sometimes even right wing corporations, to what extent can the more musically aware composer build on that foundation to reach a wider audience? Is pop music the only possible basis for communication, a contaminated anathema, both, or neither?

There can be no attempt in a survey such as this to definitively answer most of these questions; nor, however, will they be, as they so often are, pessimistically dismissed. For some, answers will forever depend on the consciences of individual composers; others may be clarified as time goes by and our experience of music in differing contexts accumulates. It may be worth keeping them in mind as we discuss individual cases, because I have so often heard composer discussion groups run circles around these questions and get nowhere. If we are to eventually arrive at more compelling answers, the base level of our collective questioning needs to be raised.

The present HyperHistory divides into not historical periods, for the most part, but into strategies for politicizing music. These strategies fall into two clearly differentiated areas: political music with words, and political music without words. Across those two categories does run a rough historical divide: before the 1960s, one’s political views sometimes determined what kind of music one should write, but in the 1960s there was born the relatively new idea of making music a political statement in itself. Of course, this divide does not apply to opera, which has famously been making political statements for most of its history. Hatred of tyranny is implicit in Beethoven’s Fidelio, and an entire economic critique of European society in Wagner’s Ring, albeit one perhaps interrupted and unfulfilled—to accept for a moment Shaw’s view of the case. Interestingly, what seems lacking in today’s operas is political statement, even despite the current trend of historical operas drawn from recent politics. As exceptions one could point to Anthony Braxton’s little-heralded 1996 opera Shala Fears for the Poor, which painted a bitter satire of corporate America—and Conrad Cummings’ Vietnam opera, Tonkin.

In the case of texted political music, there has been a new approach in the last 30 years that scorns the earlier convention of “setting text to music,” speaking or intoning it instead. One political composer closely connected with text, Luigi Nono, can be considered separately as an exception to all rules. The case of non-texted political music diffracts into a rainbow of related concepts, ranging from the denotative technique of direct quotation, to the culturally conditioned but commonsensical reading of music as Social Realism, to the more rarefied approach to musical structure as political analogy. Independently of all this, we should consider the extreme case of Cornelius Cardew, a composer who not only most sharply defined the role of political music by turning his back on the avant-garde, but who also was the clearest and most passionate writer about what was politically wrong with new music.

Inner Pages:

Certainly this survey will be far from complete—by its very nature, political music is typically likely to be, if not censored outright, at least unsupported by the existing power structures, and frequently lost to history, or at least difficult to obtain documentation on. I only hope that I can give a well-rounded list of the various ways in which composers have found to give their music political impact, and bring out the most often-encountered advantages and problems of each. As a movement, political music flourished most during the 1930s and 1970s, the periods of greatest Marxist sympathy in the West, the first spurred by sympathy for Russia, the second by that for China, and both ending in disillusion; the influence of the latter period, though, has convinced a number of younger composers, myself included, to
write the occasional politically motivated work. And as the world continues to change in more ominous directions, it becomes harder and harder for the thinking artist to keep silent—as the Dixie Chicks have realized to their everlasting credit.

Back to Nature: Tracing the History of an American Classical Tradition

Kyle Gann
Photo by Jordan Rathkopf

READ and watch a conversation with Kyle Gann.

Let us look at two classic anecdotes of American music. The Boston tanner William Billings (1746-1800), described as “a singular man, of moderate size, short of one leg, with one eye, without any address, and with an uncommon negligence of person,” was the most active American composer of choral music in the 18th century. His relationship with his Boston neighbors was marked by respect from certain circles and antagonism from others. In response to one of his concerts, local wags tied two cats together by the tails and hung them from the sign of his tannery, presumably to allow them to duplicate the perceived effect of his music. Unversed in European counterpoint, Billings relied more heavily on simple consonances than his Continental counterparts, and was at one point criticized for not using enough dissonance. In response, he wrote a brief but remarkable choral song entirely in dissonances of seconds and sevenths, to a text of his own:

Let horrid jargon split the air
And rive the nerves asunder;
Let hateful discord greet the ear
As terrible as thunder.

Even after more than 200 years, the piece shocks the ear with its joyous disregard for resolution. Zip ahead about a century and a half, and we find composer Henry Cowell dropping in on his friend Carl Ruggles. Cowell’s own words for the scene cannot be bettered:

One morning when I arrived at the abandoned school house in Arlington where he [Ruggles] now lives, he was sitting at the old piano, singing a single tone at the top of his raucous composer’s voice, and banging a single chord at intervals over and over. He refused to be interrupted in this pursuit, and after an hour or so, I insisted on knowing what the idea was. “I’m trying over this damned chord,” said he, “to see whether it still sounds superb after so many hearings.” “Oh,” I said tritely, “time will surely tell whether the chord has lasting value.” “The hell with time!” Carl replied. “I’ll give this chord the test of time right now. If I find I still like it after trying it over several thousand times, it’ll stand the test of time, all right!”

To this pounding of Ruggles’s dissonant chord, let us add two (pardon the double pun) strikingly resonant parallels: the six-year-old (in 1880) Charles Ives looking for a sound on his square piano to imitate the bang of the bass drum in his father’s band, and finding that only clusters played with his fist did the trick; and the twelve-year-old (in 1909) Henry Cowell playing clusters with his entire forearm in his The Tides of Mananaun, relishing the swirl of clashing overtones that resulted.

From such poundings on pianos and yowlings of cats American music began. Specifically, it sprang from a delight in sounds not found in “correct” European music. Such legends, with their delight in rebelliousness and transgression, are a far cry from the origin story of European music, by which Pythagoras heard four hammers hitting an anvil in the perfect concord C, F, G, C.

Americans, having first come to this continent in rejection of Europe’s social structures, turned to nature in their novels and paintings, and continue to do so in their music. For many, many composers, a return to nature means taking acoustics and particularly the harmonic series as source material. A significant number of the seminal American composers have staked their artistic claims on some constructed paradigm of “naturalness”: Cage’s randomness, Oliveros’s breathing, Reich’s natural processes, Partch’s natural scale, Branca’s rock vernacular stripped down to its basic strum. Most natural of all: banging on the piano keyboard, so beloved of Ives, Cowell, Varèse, Young, Garland.

If it is difficult to find the common thread among all these musics, it is because the American classical tradition gives rise to tremendous individuality, which is both its glory and its curse – curse, because audiences and critics have trouble seeing a tradition whose adherents are so remarkably different from each other. Partch’s music sounds nothing like Cage’s, nor Feldman’s like Nancarrow’s, nor Ashley’s like Branca’s. The gulf that separates Chopin from Wagner is dwarfed by America’s musical panorama. Yet what else would you expect from a culture that so deifies individualism? Why would a classical music tradition grow in America that did not reflect the people’s most basic values?

Most troubling of all—now that the American classical tradition is here, in all its multigenerational maturity and multidimensional splendor, and has already shown itself capable of having an impact on other musics of the world—why has its very existence been so difficult to accept?

Inner Pages:

Minimal Music, Maximal Impact

Without any doubt whatever, the most important musico-historical event of my lifetime has been the advent of minimalism. Like most composers of my generation, I have drawn musical ideas from many sources: non-Western cultures (Native American, in my case), microtonality, the American experimental tradition, Mozart, American vernacular musics, the Darmstadt avant-garde, and on and on and on. Most of those ideas, though, have been welcomed into my music in the context of minimalism’s revival of simplicity and audible structure; in fact, I could have never integrated some of those ideas had minimalism not provided an open enough framework. If you’re writing in a Babbitt-derived serialist style, for example, it’s difficult to work in elements of Japanese Gagaku no matter how-the-hell-impressed you are.

Minimalism hit me in my teens like a bolt of fate. About 1972 (I was 16), Steve Achternacht on radio station WRR-FM in Dallas played Terry Riley’s In C on the air. I was in the habit of recording anything 20th-century listed in the program guide – in fact, anything by a composer I hadn’t heard of. I was heavily into Ives and Varèse and Elliott Carter and Cage and Babbitt and Stockhausen, and my obsession was musical complexity. Whether structured or random, it didn’t matter. Then Terry Riley’s janglingly repetitive octave C’s started up (which we learned years later had been Steve Reich’s suggestion to hold the piece together), and I didn’t know how to react. This was crazy. All that pulsating repetition gave me a headache, every time I listened. But I kept listening anyway, and wore that tape down to a thin ribbon without any idea whether I liked it or not.
Next I went off to college (Oberlin Conservatory), where we young composers gloried in analyzing Webern, Berio, and Boulez. I was writing music of unremitting dissonance, crashing sevenths and ninths all over the place, simultaneous layers of activity, tone rows and chance processes all washing around in one big incomprehensible soup. Steve Reich’s ensemble actually came to Oberlin that year (spring of 1974) and I’m ashamed to admit I didn’t go: some older composers told me he was making boring music, just playing the same thing over and over again. And I believed them.

That summer, 1974, Reich’s Deutsche Grammophon three-record set came out: Drumming, Six Pianos, and Music for Mallet Instruments, Voices, and Organ. Almost the same week, in a curious old record store in Austin that’s no longer there, I ran across the old Chatham Square recording of Philip Glass’s Music in Changing Parts. I kicked myself for missing that Reich concert. It was like heaven itself had opened up to me and shown me not a vision of the future at all, but better than that, the beginning of the road to the future. I had come into the world at the end of an old, complex, overweighted style groaning with European modernist baggage, and history offered me a chance to step onto the ground floor of a bold new enterprise. I didn’t even try to resist.
In January of 1976 I formed a short-lived group called the Realtime Ensemble and gave the Dallas premieres of Music in Fifths, Piano Phase, and In C, along with my own minimalist works (my first was called Satie’s Dream, a 1975 “white-note” piece with no sharps or flats) and those of my friends. Ever since, I’ve been working out the implications I found in Glass’s Einstein on the Beach and La Monte Young’s The Well-Tuned Piano. A few years ago I interviewed Glass and told him I was still trying to rewrite the Bed Scene from Einstein. He replied, “So am I.”

What was it about the brazenly simple early minimalist style that seduced hundreds of complexity-loving proto- or postserialists like myself to strip down to a handful of pitches? Well, postserialism, as I saw it, was all about subtlety: the echo of a pitch cell, the gradual transformation of register, underlying rhythmic repetitions and retrogrades. But in serialism’s complicated musical contexts, you couldn’t hear any of that subtlety. We’d fill our scores with hundreds of great little devices, we thought, but they would disappear in performance, wasted, lost, overwhelmed. It was kind of painfully obvious that we were writing music not to be heard and loved, but only to be analyzed by future music students like ourselves.

Suddenly, in Drumming and Piano Phase and Music in Fifths, we could hear the type of effects we’d been seeking, blown up to an audible scale. In the phased repetitions of Reich’s Come Out, you heard speech become melody – a startlingly clear effect after lots of dubious ’60s experimentation with musical speech. In In C, we found melodic ideas echoing back and forth in random arrangements. In Glass’s Music In Fifths, we found bracingly irregular rhythms that, thanks to the minimalist melodic process, were not only playable but hearable. A lot of what serialists had aimed for in a vague, abstract way was now obtainable in a repetitive, audible, playable, feelable new set of processes.

And at the same time, music had become open once again to make one’s personal mark. The big, omnidissonant, ultracomplex style we had all been writing in was so impersonal, so unchanged from one work and one composer to another. Now, the slightest change of a tonality, a different scale, a different set of rhythmic values, made all the difference in the world. No one I knew thought Piano Phase was the be-all and end-all of music, but it was a starting point, something even I, young as I was, might take, develop, and improve upon.

So astounded was I that I expected all the world to take part in that revolution with me. And if the advent of minimalism was the great event of my life, the big disillusionment was the gradual realization that minimalism was never going to receive universal approval. Despite having produced the most publicly popular new works of the last third of the 20th century, minimalism remains controversial, damned in academic and intellectual circles. The fact that I like the music, am influenced by it as a composer, and teach it keeps me marginalized in academic circles. Even where minimalism has gained grudging acceptance by classical musicians, the idea that there are musical styles that have grown from minimalism is considered heresy. Forty-one years after La Monte Young’s Composition 1960 No. 7, 37 years after Terry Riley’s In C, 27 years after Reich’s Deutsche Grammophon set, 25 years after the premiere of Glass’s Einstein on the Beach, the classical music and academic establishments are still chopping away at the tree of minimalism. But that tree has deep roots, and it grows more quickly than anyone imagines. It won’t be chopped down.

After all, minimalism is not an isolated, aberrational phenomenon. It has important historical parallels from the past. It fits in, in interesting and unexpected ways, with the American Experimental Tradition that started with Henry Cowell and Charles Ives and continued through Varèse, Partch, Cage, Nancarrow, and others. Minimalism does not consist merely of the outputs of four famous composers – originally in the 1960s there were dozens of composers involved in a feverish, irascible exercise of group creativity. Nor has minimalism been a dead end: at least two important movements in American music have arisen from it, which I call Postminimalism and Totalism. Accept it or not, minimalism’s impact on American music has been powerful, and will continue to be so for many decades.

Inner Pages:

BETWEEN U S: A HyperHistory of American Microtonalists

There is nothing that musicians take more for granted than the fact that there are twelve pitches to an octave, and that these pitches divide the octave into twelve equal steps. Apparently few musicians question this arrangement, and only a tiny minority can explain whence it arose, why, and from what principles its authority derives. This 12-pitch assumption, however, is far from innocent. Twelve-tone equal temperament, as this common tuning is called, is a 20th-century phenomenon, a blandly homogenous tuning increasingly imposed on all the world’s musics in the name of scientific progress. In short, twelve-tone equal temperament is to tuning what the McDonald’s hamburger is to food.

How can this be so? What is so unnatural about twelve-tone equal temperament?

The basis of any natural system of tuning is that two pitches sound consonant (that is to say, sweet, or intelligible to the ear) when their sound waves vibrate at ratios of relatively small whole numbers. In an octave, for example, two pitches vibrate at a ratio of 2 to 1, one pitch vibrating twice as fast as the other. In a perfect fifth, such as C up to G, the ratio is 3 to 2. In a major third C to E, the ratio is 5 to 4.

The great problem that nature bequeaths to us in the mathematics of tuning – not an obstacle, but a wonderful challenge when viewed the right way – is that these simple intervals aren’t divisible by each other. To illustrate, we need a perceptual measure of interval size. The one invented by the great acoustician Alexander Ellis in the late 19th century is called a cent, and is equal, by definition to one 1200th of an octave, or 1/100th of a half-step.

An octave: (ratio 2:1) = 1200 cents
A perfect fifth: (ratio 3:2) = 701.955 cents
A major third: (ratio 5:4) = 386.3 cents

In the equal temperament we’re used to, three major thirds – C to E, E to G#, G# to C – equal one octave. But as you can see, three pure major thirds of 386.3 cents do not equal one octave, because 3 x 386.3 does not equal 1200. So equal temperament, our McDonald’s hamburger tuning, stretches every major third out to an arbitrarily out-of-tune 400 cents, somewhat the way McDonalds standardizes every patty to a flat quarter-pound of dubious relation to beef. These means that every major third on the piano is out of tune by 13.7 cents, creating busy little beat patterns between the overtones of every major third we hear. Unless you’ve had some exposure to Indian or Indonesian or some other non-Western musical tradition (or authentic barbershop quartet music, the last pure-tuned tradition in America), it’s quite likely that you’ve never heard a true major third in your life, nor a true major or minor triad.

Music schools teach that this Big Mac tuning has been around for centuries and represents an immutable endpoint of progress. It’s a lie. History, even in Europe, has provided many alternatives, Arabic and Asian cultures have provided rich tuning resources unknown to us, and many recent American composers have explored alternative tuning possibilities.

There are many reasons to write in other tunings, seemingly as many as there are composers who do it. La Monte Young seeks absolute purity of pitch so he can explore complex combinations of distant overtones never heard before. Harry Partch wanted to imitate in melody the subtle contours of the human voice, without compromise. Lou Harrison wants to recapture the sensuous presence that true intervals had before the 20th century. Ben Johnston wants his music perfectly in tune so it will have a healthful psychological effect on the listener. Myself, I enjoy the expanded composing resources of 30 or so pitches to the octave, and the option of creating amazing chromatic effects through minimal voice-leading. Some composers are seeking a magical harmonic alchemy written about in ancient treatises. Others just enjoy exotic out-of-tuneness. One of the exciting things about the microtonal field is that, despite its grounding in natural laws of acoustics, its diverse practitioners hardly agree on anything.

For those intrigued but unfamiliar with the wide range of microtonal strategies, this quick survey in four sections will explore several options for escaping equal temperament. We’ll look at forms of historical tunings, take a regrettably brief glimpse at other tunings of the world, and examine tunings devised by several American composers, both in the areas of just intonation and of equal temperaments based on divisions other than 12.
And for those who want more information, there are a lot of Web sites. Book publishers and academic musicians are absolutely convinced that alternate tuning is a strange, esoteric subject that no one except a few weirdos is interested in. If they’d look on the Web, they’d find thousands of tuning aficionados. You can learn everything you wanted to know about meantone at, and Terry Blackburn, Zeke Hoscan, and Stephen Malinowski have excellent pages on the mathematics of different European tunings. There’s a Pythagorean Web page. And one of the most forward-looking theoretical thinkers, with a lot of new tuning conceptions for new composition, is Joe Monzo. The tuning of our music evolves historically more rapidly than people realize, and it’s on the move again.

Just intonation isn’t for everyone. Its plethora of fractions can be daunting, and a lot of composers dissatisfied with 12-tone equal temperament simply can’t think creatively in a free field of fractions. Many of these composers have divided the octave, equally, into more than twelve pitches per octave. The great attraction of any kind of equal temperament is that it allows free transposition to any step of the scale. During the 19th century, transposition became so central to compositional thinking that many classically-oriented composers can’t imagine doing without it. Just intonation doesn’t make transposition impossible by any means, but a just-intonation scale limited in its number of pitches will make certain transpositions available, and others difficult.

It must be said, though, from my experience, that working with an unequal just-intonation scale is like carving in wood – the material has a grain to it that gives the artist something to work against. Working in equal temperament is like carving in plastic: every scale step is the same, and the scale doesn’t suggest very much about how to compose in it. Transposition in an unequal scale can lead to very interesting results, with old musical content expressed in new interval patterns. Many classically trained musicians, however, aren’t willing or ready to think in such terms.

That said, various equal temperaments were the usual deviation from 12-pitch tuning from the 1920s until at least the 1970s. Division into 24 pitches per octave used to be considered, in the first half of the 20th century, the most convenient alternative; this is known as quartertone tuning. Other composers have divided the whole-tone into 5, 6, 8, or 12 equal parts, for 30-tone, 36-tone, 48-tone, or 72-tone scales, each of which offers certain advantages. Other, seemingly more eccentric equal divisionsare actually quite natural, such as 19, 31, and 53 tones per octave.

From BETWEEN U S: A HyperHistory of American Microtonalists

Back in the ultramodern 1920s, quartertones seemed like the next logical step for deeper exploration of pitch language. The theory of acoustical tuning wasn’t taught in those days; thinkers as brilliant as Schoenberg and Cowell went around insisting that the 11th harmonic of C was F# (it’s 551 cents, halfway between F and F#, not 600 cents), and no one really believed that you could hear such tiny pitch differences. In addition, the nature of musical instruments, especially that behemoth the piano, was not going to change any time soon, but if you put two pianos together, you could tune one down 50 cents, and between them you’d have a quarter-tone scale, 24 equal steps to the octave. It was an interval not of acoustic necessity, but of convenience. Thinkers like Ferruccio Busoni theorized about splitting the half-step into three and four equal parts as well. In those days of talk about splitting the atom, it must have been in the air.

And so a number of composers wrote music in quartertones. Chief among these were (for quality) the American Charles Ives and (for quantity) the Czech Alois Hába. Ives’s main contribution was Three Pieces for Quarter-Tone Pianos, completed in 1926, one of his last works. His article “Some Quarter-Tone Impressions” (published by Norton with his Essays Before a Sonata) theorizes about what kind of harmonies quartertones would support. He postulates a triad in-between major and minor, say, C and G with a pitch between Eb and E; the chord sounds more stable, he claims, if you add a seventh halfway between Bb and B. The Quarter-Tone Pieces carry out these theories beautifully. The only recording I’ve ever found, however (and there are several), that really has the pianos exactly a quarter-tone apart is the old vinyl recording on Odyssey. All the others miss slightly.

Alois Hába (1893-1973) wrote a considerable amount of quartertone music. He also wrote string quartets that divided the whole step in to five equal parts (fifth-tone, or 30 equal steps to the octave) and six equal parts (or 36 steps to the octave). Haba’s opera The Mother is in quartertones, and is recorded on Supraphon. Another composer of divided half-steps is the Russian Ivan Wyschnegradsky (1893-1979), who had a vision in the street one day that he was supposed to write microtonal music. Musicians at McGill University, including the Mather-LePage Duo, put out two recordings of Wyschnegradsky’s multiple piano works, one for two pianos tuned a quarter-tone apart, another for three pianos tuned a sixth-tone apart. It’s visionary music, like Scriabin but creepily in-between-the-keys. The Arditti Quartet has supposedly made a recording of Wyschnegradsky’s string quartets that was released in Europe, but I’ve never found it.

Mexico’s Julian Carrillo also made a career out of what he portentously called “the Thirteenth Tone,” although what he actually did was to divide the half-step into four parts for 48 equal steps per octave. His Preludio a Cristobal Colon, published in Henry Cowell’s New Music Edition, is written for an ensemble in his special notation.

Ezra Sims of Boston has gone even further, writing in a special notation for 72 pitches per octave. Sweet, haunting, sometimes folk-music-based, Sims’s music sounds natural but is very careful about its intonation, not compromising on commas and raised and lower leading tones.

Each of these divisions has certain acoustical features in its favor; the more divisions, the more acoustical accuracy and the less convenience of notation and performance. Quartertone tuning captures several 11-based intervals, intervals based on the 11th harmonic:

11/8 = 551 cents
11/9 = 347 cents
11/6 = 1049 cents
12/11 = 151 cents

All are very close to quartertones. However, seven-based intervals are just as out of tune in quartertone music as they are in 12-tone equal temperament.
The 36-tone equal temperament, or dividing the half-step in three, is better for capturing intervals based on the 7th harmonic, or 7-based intervals.

7/4 = 969 cents
7/6 = 267 cents
8/7 = 231 cents
9/7 = 435 cents

Each of these is approximately 33 cents above or below an equal-tempered pitch. Sims’s 72-pitch tuning combines these possibilities, allowing pitches both 33 and 50 cents away from the 12 standard ones, and also allows much closer approximations of standard major and minor thirds. The use of 72-tone equal temperament allows perfect transposibility in eleven-limit tuning, but at the price of tremendous inefficiency. Partch, after all, gets perfect eleven-limit tuning with only 43 pitches, and I’ve never succeeding in needing more than 31.

Other intervals are possible with equal temperaments not derived from the whole- or half-step, but from circles of fifths.

From BETWEEN U S: A HyperHistory of American Microtonalists

Certain divisions of the octave are natural because they represent the points at which multiples of the perfect fifth coincide with multiples of the octave. For example, 12.

12 perfect fifths = 12 x 701.955 cents = 8423.46 cents

7 octaves = 7 x 1200 cents = 8400 cents

8400 and 8423 are pretty close, so if you fudge the fifths a little, you can divide the octave into 12 steps and get both fifths and octaves.

Like wise, 19:

19 perfect fifths = 19 x 701.955 cents = 13337 cents
11 octaves = 11 x 1200 cents = 13200

13337 and 13200 are, proportionately pretty close, so 19 ends up being one of the natural divisions of the octave if you want perfect fifths. So do 31, 34, and, more spectacularly, 53.

The Colorado-based guitarist Neil Haverstick plays, and has recorded with, a 19-tone guitar, on his impressive discs, The Gate and Acoustic Stick. The influence of tuning on Haverstick’s blues playing is fun to listen to; he sometimes has to extend the rhythm of blues phrases to fit in all his chromatic pitches. He also plays a 34-tone-to-the-octave guitar. Fretted instruments such as guitars and lutes have the oldest history of playing equal temperaments, since you have to have equal temperament if the frets are going to go straight across the fretboard. Just intonation on guitar (or any other unequal temperament) requires jagged frets that shift up and down for each string. Since at least the 16th century it’s been considered easier just to tune guitars in equal.

The 16th-century theorist Nicola Vicentino invented a 31-tone-to-the-octave harpsichord, the keys divided between two manuals and with some of the black keys split. He claimed that with his 31-tone scale one could play melodies from the Hebrew and Arabic worlds and the Slavic and Germanic countries without distorting them into the Italian scale. He understood that tuning is ultimately a multicultural issue, and that standardized, invariant tuning was a means of oppression used against foreign musicians from allegedly inferior cultures. Incidentally, in 31-tone equal temperament the perfect fifth is a slightly flat 696.77 cents, almost exactly the same size as the meantone fifth Vincentino was used to. [Ed. Note: The 31-tone system has inspired a great many new music composers both in the Netherlands and the United States — American tricesimoprimalists include Joel Mandelbaum, and Jon Catler who in the 1980s led a rock band called J. C. and the Microtones.]

A 53-tone equal temperament has sometimes been held up as a dream tuning. In 53-tone, each pair of adjacent pitches is separated by 22.64 cents. The major third in this scale is playable as 384.9 cents (instead of an optimum 386.3); the minor third is 316.98 cents (instead of 315.6); and the perfect fifth is 701.886 cents (instead of 701.955). All of the (five-limit) intervals of European music can be played within a half of a percent accuracy in 53-tone equal temperament. Inspired by such realizations, an Englishman named T. Perronet Thompson built a 53-pitch organ in the 1850s, its keyboard a Dr. Seussian fantasy of split keys, curved keys, different colored-keys, and knobs sticking up through other keys. Estimated arrival time moving from a C major chord to a G major chord is probably four minutes, as the organist cogitates on where the right keys are, but it was a wonderful idea.

A couple of other modern experiments with equal temperaments should be mentioned. One is Easley Blackwood‘s remarkable series of 12 Microtonal Etudes, each written in a different equal temperament from 13 to 24 pitches to the octave. Blackwood invented his own different notation for each division of the octave; the score is published, and the CD is available on Cedille. The electronic sounds are a little cheesy, and it’s a little disappointing that, instead of treating you to the most unusual intervals, he concentrates wherever possible on intervals found in 12-pitch tuning; for instance, 15-pitch equal contains the same major thirds as 12-pitch. But the tunings themselves are all the weirder for not being grounded in any natural acoustic basis, and they’ll stretch your ears.

Wendy Carlos has also worked with equal-tempered scales not based on the octave, so that you get different pitches from octave to octave. For example, if you have a scale of 35-cent increments, you’ll have a pitch at 1190 cents and 1225, but not at 1200. I haven’t had an opportunity to hear her results, but her Web page – which seems to say virtually nothing about her tunings — has some brief samples of her music. Recently, at the last Festival of Microtonal Music that Johnny Reinhard organizes, I heard Skip LaPlante’s Music for Homemade Instruments group-sing a happy little tune in 13-tone equal temperament. And they really did it. There may be no natural acoustical basis for a 13- division of the octave, but it can be sung, and it blows your mind to hear it.

From BETWEEN U S: A HyperHistory of American Microtonalists

If 12-tone equal temperament is the Big Mac of tunings, then just intonation is the health food. Just intonation means that the pitches have been defined in terms of whole-number ratios between frequencies. For example, if we’re in the key of C and I refer to a 6/5 E flat, that means an E flat that vibrates at a frequency 6/5 as fast as C; in other words, if C above middle C vibrates at 500 cycles per second (cps), 6/5 E flat will vibrate at 600 cps. The number of potential pitches in a just intonation system is equal to the number of possible fractions: namely, infinite. Naturally, composers cannot deal creatively with a disordered infinity of pitches. We need schemes to limit and justify and order the world of potential pitches. In fact, I believe that good music can only issue from an elegant tuning, and the more elegant the tuning, the more fertile it will be as a generator of musics.

In just intonation, we use fractions to define pitches. To know what pitch a fraction represents, we need to know what key we’re in. If we’re in the key of C, then we define C as 1/1, and D is 9/8. That means that D is defined as the pitch that vibrates 9/8 as fast as C. 9/8 is also the name of an interval – in this case, a whole step. Normally, in talking about justly tuned pitches, we express fractions in terms within a single octave, or between 1 and 2. If 9/8 is D, then 9/2 and 9/16 are also D, but we tend to only use 9/8 because it’s in the octave between 1 and 2. We’re used to calling pitches in different octaves all Cs, or all B flats, but it can be difficult for people to get used to the notion that 7/8 = 7/4 = 7/2 = 14/1. The pitches denoted by those fractions are all octaves of each other, because multiplication or division by 2 only changes octaves.

One of the ways we differentiate between different just intonation systems is by what prime numbers are employed factors in the tuning’s fractions. For instance, five-limit tuning is tuning in which all fractions can be expressed as powers or multiples of the numbers 2, 3, and 5 (not 1 because 1 is merely identity, and not 4 because 4 is merely an octave of 2). In seven-limit tuning, the list is expanded to 2, 3, 5, and 7. Eleven-limit tuning goes up to 2, 3, 5, 7, and 11, and so on. Finally we’ll address the possibility of 13-limit and higher tunings.

If the arithmetic here confuses you, you’ll find a fuller, more gradual explanation on my tuning page. If this sparks your interest, you’ll find all sorts of just-intonation resources at the Just Intonation Network Web page, which will lead you to an encyclopedic array of tuning sites. Or if this just scares you, you can go back to the tuning page.

From BETWEEN U S: A HyperHistory of American Microtonalists

You may have never been aware of it, but you’ve been listening to music in five-limit tuning all your life – or rather, an equal-tempered approximation of it. European music is based on the desire to get two intervals in tune: the perfect fifth (3/2) and the major third (5/4), as well as the minor third (6/5) between those two intervals. The basic problem of tuning is that any two prime-numbered intervals are incommensurate. That is, there is no number of major thirds that will equal any other number of perfect fifths. Major thirds are 386.3 cents wide, perfect fifths are 701.955 cents wide, and there just aren’t any reasonably small numbers those will both divide into evenly. [Another way to say it: Major thirds are based on 5, perfect fifths on 3, and no power of 5 (5, 25, 125, 625…) will ever equal a power of 3 (3, 9, 27, 81, 243…).] Therefore we have to make decisions about which pitches to have fifths on and which to have thirds on.

Let’s start by taking four pitches and tuning them to perfect fifths: F, C, G, and D, with C as our tonic, defined as 1/1.

F 4/3 = 498 cents
C 1/1 = 0 cents
G 3/2 = 702 cents
D 9/8 = 204 cents

If we continue tuning the circle of fifths to these perfect 3/2 fifths, we’ll end up with a 3-limit tuning known as Pythagorean, because it is limited to the intervals Pythagoras is alleged to have discovered. That gives us rather harsh major thirds of 81/64 (408 cents), though, and right now we’re looking for pure major thirds of 5/4 (386.3 cents). So let’s build a pure major third above and below each of our four established pitches. This gives us a pretty evenly-spaced 12-pitch scale:

C 1/1 = 0 cents
Db 16/15= 112 cents
D 9/8 = 204 cents
Eb 6/5= 316 cents
E 5/4 = 386 cents
F 4/3 = 498 cents
F# 45/32 = 590 cents
G 3/2 = 702 cents
Ab 8/5 = 814 cents
A 5/3 = 884 cents
Bb 9/5 = 1018 cents
B 15/8 = 1088 cents

This is a fine, perfectly in-tune scale with 12 pitches. Its only drawback is that it is only in tune for the key of C. For example, if you want to play a D chord, the interval between D 9/8 and A 5/3 isn’t 3/2, as a perfect fifth should be, but 40/27 (5/3 divided by 9/8 = 5/3 x 8/9 = 40/27). And at 680 cents instead of 702, that “wolf fifth” between D and A is going to howl. You can retune A to be in tune with D, but then your F chord is no longer in tune.

There is a fascinating recording of a piano work in five limit tuning: Terry Riley‘s The Harp of New Albion (Celestial Harmonies 14018). The work employs a piano tuned to the above scale on C#, except that the G is 64/45 instead of 45/32. And the movements of the piece run through several keys, including D and Bb, so that you get a powerful sense of what happens when you intentionally modulate within a limited five-limit system.

This is the basic problem with tuning Western music, with its need for fifths and thirds and its limitation of only 12 pitches. If we allowed ourselves more than 12 pitches per octave, the problem would have many easier solutions. In fact, there were experiments in 16th century Italy with constructing harpsichords with octaves of 19 and 31 pitches to the octave just to avoid this dilemma. The academics of their day, as academics always will, prevented such innovations from catching on. But all of our historical European tunings, from meantone to well temperament and even our present accursed equal temperament, are approximations of this five limit tuning. So you can explore those historical European solutions, or you can go on to the composers who, after being stalled for 330 years, finally plunged ahead into seven-limit tuning.

From BETWEEN U S: A HyperHistory of American Microtonalists

Back in the 16th century, lots of forward-looking musicians wanted to expand the range of European tuning to include intervals based not only on 3 (perfect fifths) and 5 (major and minor thirds), but also 7. After all, Indian and Arabic musicians had gaily been using 7-based intervals for centuries. But they were infidels, and one way the Christians wanted to distance them from the heathens was by insisting that no one could really perceive such tiny pitch differences. So the Italian academics won just after 1600 (over the continuing objections of the seminal mathematician Marin Mersenne), and closed off the wonderful number 7 to the Western world for more than 300 years, until Harry Partch rediscovered it and began using it in the 1920s.

Adding the number 7 and its octaves (14, 28) to our original stable of numbers (2, 3, 5) gives us a very interesting array of new intervals:

15/14 = 119.443 cents
8/7 = 231.174 cents
7/6 = 266.871 cents
9/7 = 435.084 cents
7/5 = 582.512 cents
10/7 = 617.488 cents
14/9 = 764.916 cents
12/7 = 933.129 cents
7/4 = 968.826 cents
28/15 = 1080.557 cents

Now keep in mind that the equal-tempered intervals we’re used to are all sizes divisible by 100. An equal tempered whole step is 200 cents, a perfect fourth is 500 cents, and so on. Seven-limit intervals often create intervals a third of a half-step away from their equal temperament semi-equivalents. The 8/7 “major second” is 31 cents “sharp.” The 7/6 “minor third” is 23 cents “flat.” This specific difference creates a certain flavor for seven-limit tuning, oddly off from the tuning we’re used to and sometimes bitterly flat, yet strangely consonant. In addition, the 7/5 tritone offers a much more consonant tritone than anything we’re used to in European tuning.

Add these 10 simple seven-based intervals to the basic five-limit intervals, and you get a scale that some would consider unwieldy. The most perplexing compositional problem of working in just intonation is, once you open up the field to seven, how do you choose which pitches to use?

One of the most brilliant solutions is the one La Monte Young adopted in his six-hour piano masterpiece The Well-Tuned Piano. He eliminated all factors of the number 5, so that he was only working with multiples of 2, 3, and 7. And he arrived at the eccentric yet very beautiful 12-pitch scale, suitable for piano tuning:

Eb 1/1 = 0 cents
E 567/512 = 177 cents
F 9/8 = 204 cents
F# 147/128 = 240 cents
G 21/16 = 471 cents
G# 1323/1024 = 444 cents
A 189/128 = 675 cents
Bb 3/2 = 702 cents
B 49/32 = 738 cents
C 7/4 = 969 cents
C# 441/256 = 942 cents
D 63/32 = 1173 cents

Note that the scale doesn’t uniformly ascend: G# is lower than G, and C# is lower than C. The scale is basically a five-pitch pentatonic scale around 0, 200, 450, 700, and 950 cents, with slightly different versions available for each pitch. Young kept the tuning secret for 27 years until I tuned my synthesizer to it and published it in an article (with his permission) in Perspectives of New Music, Winter 1993, Volume 31 Number 1. There’s a lot more to say about this scale, and I say some of it on my La Monte Young web page. Unfortunately, the Gramavision recording of The Well- Tuned Piano is out of print and nearly impossible to obtain. Please don’t ask me how to get a copy, because I can’t tell you. You can find out more about La Monte, though, at the Mela Foundation Web Page.

Michael Harrison, Young’s protege and piano tuner, also writes piano music in seven-limit just intonation. He has a CD available on New Albion records.

Another important masterpiece in seven-limit tuning is Ben Johnston‘s String Quartet No. 4, “Amazing Grace.” This lushly emotive 1973 work, a series of variations on the old hymn “Amazing Grace,” begins in a simple pentatonic scale and keeps adding new pitches with each variation until it runs through a glorious 22-pitch, seven-limit scale in the final variation. It’s Ben Johnston’s most popular work, and an instant favorite for everyone who hears it. The best recording is an old one by the Fine Arts Quartet on Gasparo records – unfortunately still only on vinyl. The Kronos Quartet has made a perfectly acceptable recording on Nonesuch, but their attention to tuning isn’t as meticulous.

From seven-limit tuning, the next logical step is eleven-limit tuning.

From BETWEEN U S: A HyperHistory of American Microtonalists

Eleven-limit tuning means that we define intervals and pitches by multiplying and dividing the numbers 2, 3, 5, 7, and 11, with no prime numbers larger than 11 used as factors. Adding 11 into the mix gives us a very interesting range of new intervals:

12/11 = 150.637 cents

11/10 = 165.004 cents
11/9 = 347.408 cents
14/11 = 417.508 cents
15/11 = 536.951 cents
11/8 = 551.318 cents
16/11 = 648.682 cents
22/15= 663.049 cents
11/7 = 782.492 cents
18/11 = 852.592 cents
20/11 = 1034.996 cents
11/6 = 1049.363 cents

Note that of these intervals, nine are within 15 cents of a quartertone (50 cents between two equal-tempered steps in 12-tone equal temperament), and six of those – 12/11, 11/9, 11/8, 16/11, 18/11, 11/6 – are within three cents. Eleven-limit tuning produces many of the pitches that we think of as quartertones. The peculiar quality of eleven-limit tuning is to smooth out the scale by giving us mediating pitches half-way in-between the pitches we’re used to.

The great champion of eleven-limit tuning, of course, is Harry Partch. His 43-tone scale, 43 non-equal steps to the octave, uses no prime factors larger than 11. I won’t give his scale here, because you can easily find it in his book Genesis of a Music and other places. There is loads of Harry Partch information on the Internet, the best sites being Corporeal Meadows and a British Harry Partch web page. In addition, all of Harry Partch’s major and minor works are being released on the innova and CRI labels.

The other person I can mention as having written a significant-sized output in eleven-limit tuning is myself, Kyle Gann. Eleven-limit tuning appeals to me for all those in-between notes, those quarter-tones that slide so easily between the pitches we’re used to. My own attraction to microtonality is the potential for extreme chromaticism and a minimalist approach to voice-leading in which lines can remain almost motionless while the harmony changes key wildly. You can hear this effect in my 1997 piece How Miraculous Things Happen, of which you can find an audio excerpt here. The piece uses 24 pitches to the octave (but very unevenly distributed, not quartertone), and capitalizes on the interval of 11/9 (347 cents) to slide smoothly between the minor (316 cents) and major (386) thirds. My largest just-intonation work so far is a 35-minute, one-man opera, Custer and Sitting Bull. The four movements of this work expand from 20 to 31 pitches, each movement based on a different tuning principle. You can also find audio samples of this piece at the same place, and program notes and tuning charts at my Custer and Sitting Bull web page.

Partch charmingly expressed his reasons for not proceeding past 11 to the 13-limit: “When a hungry man has a large table of aromatic and unusual viands spread before him he is unlikely to go tramping along the seashore and in the woods for still other exotic fare. And however skeptical he is of the many warnings regarding the unwholesomeness of his fare – like the ‘poison’ of the ‘love-apple’ tomato of a comparatively few generations ago – he has no desire to provoke further alarums.” Personally, I’ve never been able to get comfortable enough with my perception of the 13th harmonic as a consonance to pass that limit myself. But if you’re hungrier than Partch, and more attuned than myself, you’ll want to go on to the thirteen-limit and beyond.

From BETWEEN U S: A HyperHistory of American Microtonalists

There are an infinity of numbers, and an infinity of prime numbers. There are an infinity of fractions. There are, correspondingly, an infinity of pitches within any octave. Studies have suggested that, depending on circumstances of timbre, register, volume, and so on, the human ear and brain can distinguish about 250 pitches per octave. I myself have found, as a composer, that two pitches only 5 or 6 cents apart turn out to be impractically close, and I can’t meaningfully distinguish them within the context of a piece of music. Other composers, with other, more acoustically pure musical aims, may well find a vast gulf of difference between 200 and 205 cents. To be comfortable, I need at least 16 to 20 cents between the pitches in my scales, but Partch‘s scale contains pitches only 14.4 cents apart. There are, refreshingly, no rules here, and no limitations besides the composer’s own personal idiosyncrasies.

The number 13 opens up still further territories. The 13th harmonic is 840.53 cents above an octave of its fundamental, and some simple 13-based intervals include:

13/12 = 139 cents
13/11 = 289 cents
16/13 = 359 cents
13/10 = 454 cents
18/13 = 563 cents
13/9 = 637 cents
20/13 = 746 cents
13/8 = 841 cents
13/7 = 1072 cents

Note a preponderance of pitches about 40 cents away from our equal-tempered pitches.
The only composer I know of working consistently in 13-limit tuning is Mayumi Reinhard, and she swears that’s where the action is.

The 17th and 19th harmonics come too close to equal temperament to sound very exotic in most contexts; 17/16 is 105 cents, and 19/16 is 297.5 cents, both nearly divisible by 100. Ben Johnston‘s Suite for Microtonal Piano (1977), though, is a fine example of a piece in 19-limit tuning. The 12 pitches of the piano are tuned to the 16th, 17th, 18th, 19th, 20th, 21st, 22nd, 24th, 26th, 27th, 28th, and 30th harmonics of C. (This is still only 19-limit because all the other numbers factor down to prime numbers smaller than 19: 21 = 3 x 7, 22 = 2 x 11, and so on.) I don’t know of a better work for demonstrating the fascinating possibilities just intonation holds for modulation. The first and fifth movements are in the key of C, the second movement is in D, and the fourth is in E, meaning you get some pretty strange scales over D and E. The third movement is dodecaphonic. Johnston is possibly the only major composer who’s written dodecaphonic music in just tunings. The Suite for Microtonal Piano is recorded by Philip Bush on the Koch label, along with Johnston’s Sonata for Microtonal Piano (1964), a complexly prickly work in a highly extended five-limit tuning.

An equally fascinating work in 31-limit tuning is Johnston’s String Quartet No. 9, recorded by the Stanford Quartet (now renamed the Ives Quartet). Johnston has his intrepid string players play in a harmonic series scale from the 16th to the 32nd harmonic, including transpositions and inversions of the scale. The 31st harmonic is basically a quartertone between the 30th and 32nd, and when the strings cadence from dominant to tonic with that 31st harmonic, that cadence sounds nailed down for good. The work is mostly sweetly neoclassical, providing an unexpectedly normal context for odd harmonic events, and it’s very well performed. (The original 1964 tuning of La Monte Young‘s The Well-Tuned Piano was also in 31-limit tuning, not seven-limit as it eventually ended up.)

Johnston has more recently gone up to the 43rd harmonic (43-limit tuning) in recent works that aren’t recorded yet. The only person I know of to go higher than that in just intonation is La Monte Young in his sine-tone installations. For 20 years, Young has explored in his scintillating sound sculptures the harmonics between the higher octaves of the 7th and 9th harmonics. His current installation at the Mela Foundation is The Base 9:7:4 Symmetry in Prime Time When Centered Above and Below the Lowest Term Primes in the Range 288 to 224 with the Addition of 279 and 261…. The complete title is many times longer), which you can visit at 275 Church Street in New York City (call 212-925-5098 for times). It includes the 1072nd, 1096th, 2096th, and 2224th harmonics over its base drone, as well as other, lower tone complexes. All of these are octaves of prime-numbered harmonics: 1072 = 67 x 16, 1096 = 137 x 8, and so on. In more recent works Young has gone up above the 5000th harmonic. My sketchy introduction here can’t begin to do his sine-tone installations justice, but you can read more about them in my article “The Outer Edge of Consonance: The Development of La Monte Young’s Tuning Systems,” in Sound and Light: La Monte Young and Marian Zazeela (Lewisburg, PA: Bucknell University Press, 1996, pp. 152-190).

Until some madman surpasses Young, this takes us as far as we can go in discussion of new just-intonation dimensions.

From BETWEEN U S: A HyperHistory of American Microtonalists

Many musicians think that to attack today’s equal-tempered tuning is to attack the European classical music tradition itself. Not at all true, in fact, quite the opposite. Through most of European history – all except the last 100 years, in fact – tuning was an art, not a science, and the differences between different keys in the old keyboard tunings had an enormous, if subtle, influence in the way the great composers wrote their music. Ever wonder why F major is considered a calm, pastoral key, or why there are no Vivaldi concerti in F# major? Tuning is the answer. And the old tunings need not be dead, for they still have much to offer the modern composer. I keep my own pianos tuned to 18th-century well temperament, and compose for the wonderful variety of intervals it provides.

For simplicity’s sake I’m going to present only two phases of European tuning, meantone and well temperament.

From BETWEEN U S: A HyperHistory of American Microtonalists

Meantone is the name of one of the most elegant tunings in the history of European music, a beautiful tuning that provided near-perfect consonance in a variety of keys. The tuning was first explicitly defined in 1523 by an Italian theorist name Pietro Aaron, though it is suspected that some rough form of meantone had been in use through much of the 15th century. Meantone tuning dominated European music until the early 18th century, and continued being used in certain backwaters, especially England and especially among organ tuners, through the late 19th century. Having lasted some 250 to 400 years, depending on the area, meantone has been the most durable tuning in European history so far. [Ed. Note: It is also, most likely, the tuning that the European colonial settlers brought to America, and its compromises of good and bad triads undoubtedly informed the compositional choices of William Billings, Francis Hopkinson and other early American composers.]

Meantone is basically a 12-pitch keyboard tuning, a workable compromise that allows eight usable major triads and eight minor triads, the other four of each being real howlers. The premise of keyboard tuning in general is that you can have your major thirds in tune or your perfect fifths in tune, but both cannot be in tune, and some compromise is always necessary. Let’s look at why:

A well-tuned perfect fifth = 702 cents.
A well-tuned major third = 386.3 cents.
An octave = 1200 cents.

If we tune our perfect fifths in tune, we’ll have C to G, G to D, D to A, and A to E all 702 cents wide. 4 x 702 = 2808 cents. Therefore the two octaves and a major third from C to E (C G D A E) will be 2808 cents, and, subtracting two octaves or 2400 cents, the major third C to E will be 408 cents. 408 cents is an awfully wide and harsh major third, not really tunable by ear, bad for singing, and inharmonious.

Meantone’s solution is two squeeze down the perfect fifths until the major thirds are perfect. What we want is C to E at 386.3 cents. Therefore, two octaves and a major third will be 2786.3 cents, and each perfect fifth will be 1/4th of that amount, 696.575 cents. (The ratio between pitches of a meantone fifth is actually the fourth root of 5, since if you take the fourth root of 5 to the fourth power, you get 5, which is the ratio of two octaves and a pure major third.) (Don’t worry if you didn’t follow that. Not necessary.) The perfect fifth in meantone is just over 5 cents flat. But acoustically, the ear is less disturbed by out-of-tune fifths than by out-of-tune thirds, since with fifths the out-of-tune harmonics are higher up in register and further away and less obvious.

So meantone strives to give us as many perfect 5-to-4 major thirds as possible, which, when limited to 12 keys per octave on a keyboard, is 8. C, D, E, A, and G are tuned to slightly narrow fifths and slightly broad fourths, and then the rest of the pitches are tuned to pure major thirds: E-G#, F-A, A-C#, Eb-G, G-B, Bb-D, and D-F#. The result, notated in cents above C, is the following scale:

C 0
C# 76.0
D 193.2
Eb 310.3
E 386.3
F 503.4
F# 579.5
G 696.6
G# 772.6
A 889.7
Bb 1006.8
B 1082.9

And, if you’ve tuned your first five pitches right, C-E is a pure major third as well. The other four major thirds are 427 cents wide and sound terrible: G#-C, F#-Bb, C#-F, and B-Eb. In fact, as notated, those aren’t major thirds at all, but diminished fourths. In meantone, there is no such note as Db, but only C#. There is no D#, but only Eb. Unless, that is, you redo the tuning slightly to center it around some key other than C, as was sometimes done.

And so, in meantone, you simply can’t use triads with those unavailable major thirds. During the meantone period, you can’t really use keys with more than three sharps or flats in the key signature. Look through music of the 16th and 17th centuries, and you will find no pieces in Ab major, F# major, or Bb minor. Such keys need pitches that don’t exist in meantone tuning.

BUT – and this is the great advantage, the eight major and eight minor keys you can use sound so much sweeter than they do in our music. Those thirds sound so lovely, and thus all European music from the mid-15th to mid-18th centuries (and beyond) was based on the primacy of thirds. It became excusable to omit the fifth from a triad, but not the third, because the third was in tune and the fifth wasn’t. (I highly recommend Orlando Gibbons‘s Lord Salisbury Pavane and Galliard as a sterling example of exploration of meantone tuning. This late-16th-century work, a masterpiece of early keyboard music, meanders through every possible chord in meantone plus one dissonant B-major triad as a passing chord. Play through it in equal temperament and it sounds OK. Then play it in meantone, and its colors suddenly come alive, and you hear the work’s luscious beauty as Gibbons’s original audience did. Then play it in equal temperament again, and it collapses disappointingly back into black and white, just like Dorothy coming back to Kansas.)

Historically, there are different kinds of meantone, based on their division of the syntonic comma. The syntonic comma is the discrepancy between four perfect fifths and two octaves and a major third, about 21.5 cents. The classic Pietro Aaron meantone I’ve outlined above is called 1/4th-comma meantone, because 1/4 of the comma was subtracted from each perfect fifth. There are less extreme meantones such as 1/5th-comma, 1/6th-comma, even 5/18ths-comma. The less subtracted from each fifth, the more out-of-tune the thirds will be. 1/11th-comma meantone is actually identical to equal temperament. [The classic tuning book from which all this material is drawn is J. Murray Barbour’s Tuning and Temperament (New York: Da Capo Press, 1972).]
I wish I could recommend specific recordings in meantone tuning. I suspect that many exist, but early music groups, even when they are attentive to authentic tunings, are not often in the habit of specifying what keyboard tunings they use. Anyone can contact me at [email protected] with information about specific meantone recordings, I will add them to my historical tuning web page.

From BETWEEN U S: A HyperHistory of American Microtonalists

In 1893, the august Grove Dictionary of Music and Musicians stated that Johann Sebastian Bach wrote The Well-Tempered Clavier to demonstrate equal temperament. That was a misconception. And it has filtered down into hundred of music history texts, a lie so pervasively believed that it will take generations to correct.
Bach, after all, did not write The Equal-Tempered Clavier. But in his day, they did refer to a temperament in which all keys were usable as an “equal” temperament. But the truth was (and all this material comes from a wonderful book, Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament, East Lansing: Michigan State University Press, 1991, by piano technician Owen Jorgensen) that, back then, they had no way to truly divide the octave equally on a piano or harpsichord. They didn’t have oscillators or electronic tuners. And while, by Bach’s day, composers wanted to have all keys available, no one was interested in making them all the same. Each key had its own interval pattern and its own different color, so that one kind of music sounded better in E flat minor, while another came off much better in F major. There were reasons for choosing a specific key, and Bach wrote his preludes and fugues to illustrate those differences, not to suggest that they didn’t exist.

I do an experiment with my students: in a blindfold situation, I play the Bach preludes each in several different keys, and let them guess which key the prelude was written for. They usually get it right. The E flat minor Prelude, for example, sounds really flabby in E minor, and the C major prelude takes on a weird, too-bright quality in C#.

The tunings that dominated the 18th and most of the 19th centuries are now referred to as well temperaments. There were many different varieties. Tuning, for most of musical history, was an art, not a science, and each piano tuner has leeway to use his own taste. Some of these temperaments have reasonably familiar names: Werckmeister III, Kirnberger III, Vallotti-Young. (That’s Thomas Young, not La Monte – he wasn’t quite in the picture yet, or Beethoven’s sonatas might have sounded very different.) Some of these tunings you can find more information about on my Historical Tuning web page, but to save space I’ll only describe one here: Thomas Young’s well temperament of 1799.

The principle of well temperament is this: Imagine the circle of fifths. Now imagine that you squeeze the fifths nearest C slightly to make the thirds (C-E, G-B, F-A) a little flatter and more in tune. That means that you’ll have larger fifths and thirds on the opposite side of the circle of fifths, around F#. In most well temperament, and especially this one, the keys most closely related to C major/A minor have the flattest fifths and the most consonant thirds. Black-note keys like F# major and Eb minor have purely in-tune fifths, but their thirds are a little harsh and bitter. Therefore, when you want to write something like a Funeral March in an especially bitter, tragic key, you write it in B flat Minor – which is what Chopin did with his Funeral March Sonata. When you want a kind of majestic spookiness, as Beethoven did in the adagio of the Hammerklavier, you write it in F# minor, where the thirds aren’t bad and the fifths are especially stately and in tune.

A 0 cents
Bb 102 cents
B 196 cents
C 306 cents
C# 396 cents
D 502 cents
Eb 600 cents
E 698 cents
F 804 cents
F# 894 cents
G 1004 cents
G# 1098 cents

As you can see, no pitch here is more than 6 cents away from equal temperament, but the differences, if subtle, are still striking. The major third C-E is 392 cents, the major third F#-A# 408 cents, much harsher. All the black-key perfect fifths are perfectly 702 cents, while C-G is only 698 cents; the black-key fifths sound much purer. C# major and F# major are really active keys, bristling with overtones. C and F major are sweet, mild keys, and E flat minor is pungent. This is the tuning in which Beethoven heard his music (before he went deaf), and it clearly influenced his choices of keys, as it did for every other composer before the mid-19th century.

The first recording of Beethoven’s music in the original temperament appeared a couple of years ago: Beethoven in the Temperaments, with pianist Enid Katahn and piano tuner Edward Foote (Gasparo). The disc includes the Moonlight Sonata, the Waldstein, and the Pathetique in a late-18th-century well temperament that brings out subtle color differences among the keys.

Well temperament is hardly a dead issue even for composers today. The Californian composer Lou Harrison loves to use well temperament, and in fact wrote his entire Piano Concerto, recorded by New World Records, in Kirnberger III, which is fairly similar to Young’s tuning above. (Check out the Lou Harrison Web Page.) The mystic New York composer Elodie Lauten often writes music in well temperament, often combining it with equal temperament at the same time for a scintillating, slightly out-of-tune effect.

I have both my pianos tuned to Young’s 1799 temperament, my Steinway grand at home and the Disklavier in my Bard College office. I basically write for keyboard in well temperament, and I see no reason to go back to bland equal temperament. I know of no keyboard music that doesn’t sound better and more interesting in well temperament. The only music that equal temperament supports, as Lou has often put it, is 12-tone music; in 12-tone music, all the major thirds are theoretically equal, all the major 7ths, and so on, so I suppose one might want equal temperament to play 12-tone music authentically. But I see no other advantages. And how many of us play a repertoire dominated by 12-tone music?

Chronologically, this brings us back to 12-tone equal temperament – and if you can’t say anything good about a tuning, you shouldn’t say anything at all, I suppose, which is why I’ll direct you to the just intonation page or back to the tuning page.

From BETWEEN U S: A HyperHistory of American Microtonalists

A tremendous amount of work remains to be done in the realm of determining the tunings of non-Western musics. This is my academically acceptable way of professing ignorance. I have made some attempts on my own to match tunings of various non-European musics on my synthesizer, and to analyze pitch structures in terms of tuning. Not only is this sometimes difficult (especially when the music is fast or more than one pitch is sounded at a time), but the appropriate methodology varies from culture to culture. Many non-Western musics do not hold sustained pitches in place the way European music does, but slide and glissando and even yelp from one word to the next. An entire generation of musicologists could devote themselves to this problem without exhausting it. However – I’ll tell you what I know, and what I’ve found.

At Bard College we have a gamelan. Its official slendro scale is as follows:

Ab 16/15 = 112 cents
G 1/1 = 0 cents
Eb 8/5 = 814 cents
D 3/2 = 702 cents
C# 11/8 = 551 cents

These cent measurements arrived with the gamelan – the ratios I supplied myself. The gamelan instruments are in pairs, tuned about 30 cents apart to create the characteristic shimmering of gamelan music, but this tuning applies separately to each half of the pairs. I once wrote about gamelan music in terms of ratio tunings, and received an irate letter from some gamelan maven who informed me that gamelan musicians don’t tune in terms of ratios, and that I was imposing a foreign notion. And yet I’ve heard Lou Harrison talk about gamelans in terms of ratio tuning, and the cent-sequence 551, 702, 814, 0, 112 can only be interpreted as intending the ratios above. Not my field, but this particular bit of evidence leaves little room for interpretation.
Among Americans, Lou Harrison, Barbara Benary, Evan Ziporyn, and Jarad Powell, and many others, have written music for gamelan, and inspired by gamelan. With more than 200 Indonesian gamelans operating in the U.S., gamelan must really be considered a major current in American music.

Arabic music is well known for its use of 11-based intervals which sound, to our ears, like fairly exact quarter-tones. Treatises on Arabic music make reference within a scale on, say, G, to pitches halfway between Bb and B (11/9, or 347 cents) and halfway between F and F# (11/6, or 1049 cents). Modern transcriptions of Arabic songs and violin music sometimes use fairly standard quarter-tone notation for these pitches of the scale, and the quarter-tones are easily audible and very distinct on recordings.
That Indian ragas use a scale of 22 pitches is well known, but the exact tuning seems to be in doubt. The Hindu specialist Alain Danielou lists a tuning for the 22 pitches with some authority, but a student of mine (Jane Gilvin) researched Danielou and couldn’t locate any such tunings in the Sanskrit treatises he supposedly derived them from. Danielou, in his Music and the Power of Sound, interprets the Indian scale as pairs of notes, some five limit and others drawn from a cycle of 53 perfect fifths, and thus within three-limit tuning:

1/1 = 0 cents
256/243 = 90

16/15 = 112
10/9 = 182
9/8 = 204
32/27 = 294
6/5 = 316
5/4 = 386
81/64 = 408
4/3 = 498
27/20 = 520
45/32 = 590
64/45 = 610
3/2= 702
128/81 = 792
8/5 = 814
5/3 = 884
27/16 = 906
16/9 = 996
9/5 = 1018
15/8 = 1088
243/128 = 1110

Several of the paired notes are separated by the syntonic comma of 21.5 cents, or 81/80. It is unclear what authority Danielou asserts for these ratios, but he is a fascinating figure nonetheless.

Finally, many musicians believe that the “blue” notes that jazz singers and sax players play – bending the third, sixth, and seventh steps of the minor scale downward a touch – is a return to a seven-limit scale inherited from Africa. I have analyzed a few recordings by Billie Holiday with inconclusive results. There are certainly points at which she distinctly sings about a third of a half-step flat on those scale steps, with reference to the piano – and other places at which she sings in tune with the piano. My impression, drawn from the most modest evidence, is that sometimes she bends the third, sixth, and seventh scale steps downward for expressive purposes, and that she may find there “notches” representing the ratios 7/6 (267 cents), 14/9 (765 cents), and 7/4 (969 cents). Ben Johnston has written some jazz arrangements couched in such specific “mis-tunings.”

Through the spread of pop music, the Euramerican 12-pitch equal-tempered scale is in danger of wiping out indigenous tunings in much of the world, especially India and Southeast Asia, even in Arabic countries. At the same time, however, more and more American musicians are studying Eastern cultures, becoming experts in Indian or Indonesian performance, and absorbing new tunings. It is clear that if we want American music to join the rest of the world rather than squashing it, we need to get out of our 12-pitch equal-tempered RUT.

With that depressing thought you can go to the just intonation page, the historical European temperaments page, the equal temperaments page, or back to the tuning page.

From BETWEEN U S: A HyperHistory of American Microtonalists