Regarding Ben

You can’t make a living giving keynote addresses, but through repetition you can become proficient enough at them to take them in stride. Here’s my keynote address honoring my teacher Ben Johnston, for the Microtonal Weekend at Wright State University, organized by composer and microtonal cellist Franklin Cox:

* * * * * * * * * * * * * * * * * * * * * * * * *

Ives once fantasized about “some century to come, when the school children will
whistle popular tunes in quarter-tones.” It has long seemed to me that when I
hear people whistling popular tunes, quarter-tones are indeed often involved,
but I think what Ives had in mind was that the popular tunes would be written
in intentional quarter-tones. I don’t think this is
likely to happen in my lifetime, but I do think that, thanks to several other
important composers, Ben Johnston chief among them, the time may soon come when
musicians feel free to hit the occasional seventh or even eleventh harmonic in
their music, vernacular and otherwise.

love listening to quarter-tone and sixth-tone music. It instantly puts you into
a world in which our habitual musical categories fall apart. You lose the
moorings that every musician gets trained into, and the rational part of your
brain, the part that can analyze and identify what we hear, gets
short-circuited, and has to surrender to pure sonic experience. However, in
general I find that, in a long quarter-tone piece, the delicious strangeness
becomes uniform, and settles into a monochrome grayness. It’s like being
dropped on an unfamiliar planet: the initial thrill of exoticness gives way to
relentless disorientation. The quarter-tone musical universe is too
strange, and difficult to get used to. In this world the
composer, faced with all those new available pitches – though of course there
are sensitive exceptions in the music of Wyschnegradsky, Eaton, and others –
the composer tends to exclude
familiar, and thus minimize contrast.

is the principle according to which Ben Johnston’s microtonal music – and not
only his music, but his entire approach to music – has always seemed stronger
to me, more inviting, and more enduring in its appeal. Its starting point is
the harmonies that have been used in music for hundreds of years. From that
point it grows outward into more exotic harmonics, which we learn by hearing,
as the fineness of our pitch discrimination increases, to incorporate into what
we are already familiar with. Theoretically speaking, Ben, like Harry Partch
before him, does not take a sudden left turn from 1920, as the quarter-tone
composers did, but goes back to the tuning arguments of the 16th century and starts over. For the Renaissance musician, a sharp multiplied a
musical frequency by the fraction 25/24 – and so does it in Ben’s music. In
Renaissance music, major triads represented a set of tones vibrating at ratios
of 4, 5, and 6 – and so they do for Ben. The C major scale represented the
center of the musical universe, and a take-off point for more exotic phenomena
– and so it does for Ben.

happened in the 16th century, limiting our musical resources for the
next 300 years, is that a decision was made to exclude the number 7, and all
larger prime numbers, from our theoretical vocabulary. Under English influence
in the 15th century during Henry V’s war of occupation, French
theorists were convinced to expand their tuning arsenal from 2 and 3, the
octave and perfect fifth, to 5, which gave them a consonant major third as
well. But when they came to the number 7, the seventh harmonic, despite the advocacy
of certain intelligentsia like Nicola Vicentino and the famous mathematician
Marin Mersenne, the theorists balked. The victorious Zarlino insisted on the
infamous senario, the numbers 1 through 6, as the basis of musical consonance.
He argued by analogy on the grounds that there are six directions (up, down,
right, left, forward, and backward), six zodiac signs (as long as you count
only the ones visible above the horizon), six visible planetary bodies (as long
as you don’t count the Sun), and so on. That there are seven days of the week,
let alone 13 full moons a year and a 19-year cycle of sun and moon phases, he
seems to have conveniently overlooked. The decision was cultural, political,
and even racist, besides being sixist
The hindus and arabs used prime tuning numbers larger than 5, and the good
Catholics of 16th-century Italy were not going to follow the path of
the heathens. And so for over 300 years, Europe and then America sweated by on
12 impoverished pitches only designed for the playing of simple triads.

was the decision that Harry Partch set out to undo in 1928 when he burned his
early music in a pot-bellied stove in New Orleans and started over with the 7th and 11th harmonics. It was Ben Johnston’s contribution to create a
notation in which to think musically with the 7th, 11th,
and even higher harmonics, and to pursue an expansion of acoustic-instrument
performance practice with those harmonics.

fact is probably already familiar to this audience, but I will recount it
ritualistically, that in Ben’s most famous work, his Fourth String Quartet
based on the common folk tune “Amazing Grace,” he gave us a vivid template in
how to expand music through the harmonic series. The piece, as you all know, is
a set of variations. The first statement of the theme uses only the primitive
pentatonic scale of the French 14th century, based on ratios of 2
and 3 – also presumed to be the scale of rustic folk fiddling. The first
variation adds in the pure thirds added by the fifth harmonic. The fourth
variation adds so-called “blues” notes of the seventh harmonic, and the fifth
brings in the seventh subharmonic, until at the end the music traverses a
symmetrical 23-tone scale firmly anchored in the key of G- (that’s G minus, not
G minor). At the very end, pitches are again subtracted precipitously, and the
music ends in a simple and familiar final cadence.

the same time, of course, Ben opens the piece with the beat divided only into
simple 8th-notes and triplets. When he adds in the fifth harmonic,
he also adds quintuplets to the rhythm, and as he folds in 7th harmonics he adds in septuplets, in systems so intricate that one variation is
based on a structural polyrhythm of 35 against 36, which also happens to be the
pitch ratio difference between a 7th harmonic and a regular
Renaissance-era minor seventh. In this mirroring of the same numbers in both
harmony and rhythm, Ben achieves in the work a beautiful manifestation of the
vision Henry Cowell sketched out imperfectly in his 1930 book New Musical
. In that book Cowell theorized
that the languages of pitch and rhythm could be developed isomorphically rather
than separately, as had been traditional. (Tomes have been written about Ben’s
microtonal usage, but his role as a rhythmic pioneer, I think, has never been
sufficiently acknowledged.)

Had Ben
never written another work, this piece, the Fourth Quartet, would have been a
sufficient blueprint for how music could expand its resources magnificently in
the 21st and 22nd centuries. It is an ontogeny on which a
phylogeny could be fashioned. All of my own music has taken place, rhythmically
and harmonically (even my non-microtonal music), within the expanded universe
opened up by that piece – not simply because I studied composition with Ben, but
because he solved, notationally, pragmatically, and creatively, the impasse
posed by the premature moratorium on prime numbers higher than 5 adopted in the
late Renaissance. (One could say something similar about Harry Partch, whose
own rhythmic explorations have also been too little noted, but Ben solved it
for those of us whose carpentry skills are less than impressive.)

first met Ben around 1976 when I was a student at Oberlin, but I didn’t get to
know him until 1983. At a wonderful concert of his music in Chicago, I went up
to him and asked if I could study with him. I had already finished my
doctorate, but I had never studied regularly with a very famous composer, so I
asked to drive downstate to Urbana every now and then for a lesson with him. It
turned out that he was also traveling to Chicago frequently to attend a Zen
temple, and so sometimes I would meet him there instead, and eventually I
started attending the Zen services with him before our lesson. What I didn’t
tell him was what I was saying to myself: that although I loved his music, I
wasn’t going to get involved in this microtonality business, because it was too
much work for too little payoff.

never proselytized for microtonality. But in my very first lesson, he made a
casual comment about how nice one of my harmonies would sound if you tuned it
properly, and he reeled off the fractions. I had been the star math student of
my high school, and merely realizing that I possessed what it would take to
enter Ben’s new harmonic world presented an attraction from which I was
helpless to draw back. He didn’t need to encourage or convince me. I suddenly
realized at that moment that a door had just shut behind me, and there was no
return. I wrote very little music in my four years with Ben, but I filled
entire notebooks with pages and pages of fractions. Not until 1991 did I
finally manage to write a piece that was completely microtonal in conception,
that couldn’t be meaningfully approximated on the piano. I figure Ben delayed
my composing career by five years. But he bestowed upon me the heady pleasure
of being able to compose harmonic progressions that had never been heard

can’t guess what might have happened if I had studied microtones with John
Eaton or Easley Blackwood instead, but I do know that Ben’s approach made
intuitive sense to me because it started with the familiar and moved out
gradually and organically into the exotic – sometimes in a calculated and
dramatic fashion. I remember when I first started driving to Urbana that he
would first bring in and enthusiastically play me the music he was working on.
He’d start playing – I particularly remember this happening with his piece for
trumpet and piano The Demon Lover’s Doubles
– and the music would seem rather normal. A couple of
minutes later, I’d start thinking, “Gee, Ben’s piano is badly out of tune,
you’d think he’d call a piano tuner.” And then by the end of the piece his
piano would have become miraculously in tune again. I was stumped. I didn’t
understand tuning enough at the time to realize what was happening; I know now
that his piano sounded more and more out of tune the further he strayed from
the central key it was tuned to.

want to replicate for you an experience Ben gave me once by playing you The
Demon Lover’s Doubles
. I used to have a
recording of this on cassette, but unfortunately it’s been misplaced over the
years, and so I’ve made a MIDI version whose quality I apologize for, but that
will at least give an accurate representation of the tuning.

[musical example]

This is a subversive piece. It
draws you into a false sense of security and then suddenly [at 2:28 out of 4:10] throws you into an
abyss in which you doubt your own senses – and it does so with just a simple
12-pitch scale tuned to one key. Looking back, I’m embarrassed that at 28 I was
too ignorant to fully get the joke. I’m also glad that I was forced to make a
MIDI version, because it wasn’t until I added the dynamics that I realized how
clever the conception is. The middle variation is loud and bangy, and then the
music turns mysteriously quiet just as the last four disorienting pitches get
added in. The whole scale is tuned to the key of D, but those last four pitches
– 15/14, 11/9, 15/11, and 14/9, if you’re keeping track – load in two more
unexpected dimensions of the harmonic series. You’ve been riding along
comfortably with 2, 3, and 5, just as your family had done for generations, and
suddenly you get a visit from 7 and 11. This simple-sounding world is not what
you thought. It contains a portal to the demonic world – a world that studying
with Ben soon made me eager to enter. And the music raises your sense threshold
with its grand loudness before suddenly sinking down to a pianissimo
level at which not only are you hearing something really
weird and unexpected, but you’re not quite sure what
you’re hearing because it’s suddenly so soft. It’s one of
the great sucker punches in music. And in 1985 I was a great sucker.

later found a more subtle example of Ben’s pitch magic in his Suite for
Microtonal Piano of 1977. In this piece the piano is tuned entirely to
overtones of C, specifically the 1st, 3rd, 5th,
7th, 9th, 11th, 13th, 15th,
17th, 19th, 21st, and 27th harmonics. According to one of the prevailing misconceptions about just
intonation, this should mean that only music in the key of C major should be
playable in this scale. However, Ben couches the second movement in the key of
D, and the fourth in the key of E with an interlude in G. Each of these
movements sounds perfectly at home in its tonic key, yet each offers a different
set of intervals to the tonic note, and thus a different repertoire of
peripheral harmonies. In effect, Ben has invented the possibility of treating
an unequal 12-pitch scale as a mode,
with different potentials on each tonic. The scale contains only five perfect
fifths, and it is on these fifths that Ben grounds his basic harmonies. Exotic
intervals available on D that aren’t available on C include the ratios 19/18,
11/9, 13/9, and 17/9. The range of chords on these pitches, which would sound
jazzy but rather tame on a conventionally tuned piano, offer a vastly expanded
range of consonance and dissonance of which Ben takes full advantage. The
climactic chord progression ranges from a chord whose ratios would have to be
analyzed as 27:32:44:52:72 down to one that is simple 2:3:4:6. This range
provides an entirely new dimension between extremes of consonance and
dissonance unknown in previous keyboard music. In 12-tone equal temperament,
dissonance depends mostly on seconds and sevenths; on Ben’s piano, one has not
only those but strangely tuned thirds and sixths, a completely different flavor
of dissonance – or as Harry Partch memorably put it: “an entirely different
serving of tapioca.

I’d now like to contextualize all
this with reference to Ben’s quiet, little noted, but persuasive contribution
as a music theorist. Though not as noisy or controversial about it as some
other composers later were (notably one of his more outspoken students), he was
probably, or seems so in retrospect, the first to publicly criticize serialism
on theoretical grounds, and not from a conservative position, but from a
radical one – not because it went too far, but because it didn’t go far enough.
Much later, Fred Lerdahl would write a paper about “cognitive constraints” in which
he demonstrated that our brains are not wired to process permutations as
musical phenomena; years later, George Rochberg would publicly stop writing
12-tone music and scandalize his colleagues by returning to Romanticism; soon,
the first minimalists would return to writing in a diatonic scale. But before
all of these, as early as 1959, Ben was writing about the limited
intelligibility offered by an interval scale in a 12-tone context. In 1962 he
drew on then-recent findings in experimental psychology to draw a distinction
between nominal, ordinal, interval, and ratio scales:

A nominal scale is a collection of equivalent and
interchangeable items. An ordinal scale is a collection which is rank-ordered
in terms of some attribute. An interval scale is a rank-ordered collection in
which the intervals of difference between items are equal. A ratio scale is a
rank-ordered collection in which the items are related by exact ratios…. Each
of these scales includes all of the measurement possibilities of its predecessors,
plus one more.[1]


The major and minor scales of European tonality are ratio
scales, because it is possible to judge the ratio of each frequency to the
tonic. Twelve-tone method gives us only an interval scale, because all we can
hang on to are a group of intervals whose size differences are uniform. It is
because the methodology of 12-tone music allowed only for interval scales and
not ratio scales that Ben was able to announce that, “in an important and basic
way serialism is… a less sophisticated
technique than tonal organization.”[2]
As long as the basis of music was triadic, he wrote, the out-of-tuneness of
12-tone equal temperament was of negligible importance, but in the long run the
system offered an inadequate conceptual model for expansion. “When many of
these usages become outmoded,” he wrote,

and a search for new principles of musical organization
begins, as has happened in the 20th century, the one-sided model
provided by equal temperament becomes a serious but largely unrecognized
limitation. When musical organization based upon a linear (interval) scale
replaces that based upon a ratio scale, there is a net loss in audible

Note, however, that unlike other
composers who identified a fatal flaw in the 12-tone language, Ben didn’t stop
writing in it. I once asked him why, since he was a just intonationist, he
continued to write 12-tone music, and he answered, “Well, I had learned all
that technique, and I didn’t want it to go to waste.” In his 12-tone music,
though, he applied his own critique as a reform. In his remarkable String
Quartet No. 6, the first hexachord of the row is a harmonic series on D, and
the second is an undertone series on D#. This means that all 12 notes of the
row are not equal in weight, because one note in each half of the row is the
fundamental from which the other five pitches are derived. The pitch matrix for
this row contains 63 different pitches within the octave. The piece rocks back
and forth between overtone series’ and undertone series’, in a thoroughly
tonalized 12-tone technique.

Ben’s point of view, reaching back
into the Renaissance and breaking with some of his immediate contemporaries,
brought him to take stands that were both radical and conservative. As he wrote
in 1976:

Feeling that the harmonic mode of pitch perception is far
too important a resource of human capability for it to be allowed to fall into
disuse, I have set about to reestablish ratio scale usage in pitch
organization. This has entailed a number of radical means (large numbers of
microtones, for instance, entailing new performance techniques, especially for
wind players), some strongly conservative practices such as the resumption of a
sharp awareness of degrees of consonance and dissonance as a major musical
parameter (which amounts to revoking Schoenberg’s much-touted “emancipation of
the dissonance”), and even some radical reactionary attitudes, for example, the
rejection of the idea that noise, “randomness,” and ultracomplex pitch are the
primary frontiers for avant-garde exploration.[4]


like to add to Ben’s critique the complementary formulation expressed by George
Rochberg, another excellent 12-tone composer who decided there was something
wrong with the idiom. According to Rochberg, every new era in music history
took the previous era’s practice as a basis and added to it. Not until the
atonal period ushered in in the 1930s, he wrote, did musicians begin to
prohibit use of the resources that had served previous composers. The 12-tone
style mandated an avoidance of octaves, an avoidance of triadic points of
tonality, an avoidance of evident regularity. And as Rochberg wrote, an
aesthetic based on negation and prohibitions cannot serve the human race for
long. As Ben put it,

It is clearly necessary to generalize the concept of
tonality if it is not to be abandoned altogether. The solution should have the
characteristic of including traditional methods within it, as special, limited


I don’t know how, or to what extent, this attitude seeped
into my mind through Ben, or how much it simply made irrefutable common sense.
But I do know that in 1983, around the time I started studying with Ben, I
overcame a deeply ingrained, college-implanted artificial squeamishness, and
started composing in triads. It has seemed increasingly obvious to me that we
can’t achieve our greatest potentials in music without using all the effective
musical devices that served composers in the past, as well as adding those
innovations which are unique to us. Serendipitously, Ben turned out to be the
perfect mentor, not only to allow that large thought to settle, but to stretch
it out in both directions, past and future, to make it seem infinitely
commodious and inexhaustible.

are many, many different approaches to microtonality. All of them are valid.
Each one suits a different set of creative needs. In the long run, some will
turn out to have been more fertile than others. For me, it is this capacity of
Ben’s approach to reach deeply into the past, and yet remain open-ended with regard
to the future that makes it the most rewarding. It satisfies my need for
history, flatters my limited mathematical talents, gives me adequate means for
organizing only five pitches to the octave or 500 as I need at the moment, and
offers me an infinity of potential organizations, absorbing even 12-tone music
itself into the ongoing evolution of tonality. I’ve always loved the words that
Ben wrote in his original liner notes to the “Amazing Grace” quartet. Because
that piece is so well known we forget that it is part of a pair with the Third
Quartet, which is serial in technique, and that in performance there is a
mandatory 60-to-120-minute silence between them, symbolizing the abyss between
one kind of musical practice and another, more fertile one. Ben writes,

It is an amazing grace to have come through an abyss. It is
an amazing grace to see once again that the simplest and purest of
relationships are the means to cope with the multitudinous and complex.[6]


seems to me that in this era of economic scarcity and questioning of the great
tradition of classical music, we have reached a temporary endpoint in the
extent of music’s outward development. The achievements of Stockhausen and
Brant with multiple orchestras are going to be difficult to surpass any time
soon, or even equal, and for most of us, even a conventional orchestra seems
out of reach – and when it is within reach, we can’t get enough rehearsal time
to try anything innovative. Exceeding the length of Feldman’s chamber pieces,
Glass’s operas, and John Luther Adams’s sound installations is a daunting and
possibly barren prospect. My prediction for the future, partly based on the
curiosity I’ve been sensing among young composers about microtonality, is that
for the next few decades the impulse for musical innovation will go inward to
its own materials rather than outward. Ben’s notation, his theoretical
framework, and the example of his music have already provided us with a map of
the vast inward musical universe whose exploration will take us decades if not
centuries. I read interviews with pop musicians and classical musicians who say
that everything’s already been done in music, all we can do is repeat. And I
remember the door onto a new universe that Ben opened for me, and I think,
“What in the world are they talking about?”

[1] “Scalar
Order as a Compositional Resource” (1962-3), in Gilmore, Bob, ed.,  Maximum Clarity, p. 10.

[2] “Musical
Intelligibility” (1963) in Maximum Clarity, p. 99.

[3] “Scalar
Order as a Compositional Resource” (1962-3) in Maximum Clarity, p. 14.

[4] “Rational
Structure in Music” (1976), in Maximum Clarity, p. 62.

[5] “Musical
Intelligibility” (1963) in Maximum Clarity, p. 99.

[6] Ben
Johnston, liner notes to Fine Arts Quartet, Gasparo CS 203.


Me and Ben with Momilani Ramstrum at Wright State University, March 14, 2010.


  1. says

    Yes, thanks a lot for this. I’m guessing some of my friends probably thought it was kind of weird that I suddenly started to become interested in microtones, but this saves me the trouble of having to write out an entire manifesto in order to try to justify myself.

    It’s a world with so much potential, and I think it’s all relevant to what’s happening in the world right now!