I invented and built the zoomoozophone (photo)
during 1978 because it was
for me to continue composing at the time. For the past decade most
my works had featured ringing metallic percussion with and without other
in complicated textures. Over the course of several years I became
by the limitation of 12 tones-per-octave equal temperament, both
the intervals are never in tune and because there simply weren't
of them. I had worked with Harry
Partch during the late 60's/early 70's
had known since then that this would probably happen to me sooner or later.
Not being a builder of any kind, I had to start at the beginning: trips
stores in downtown Manhattan and Brooklyn, experimentation with a
variety of metals, shapes and sizes, and finally a prototype instrument
plywood stand. From the beginning, even the prototype was an instrument
and performance. Over the next five years, I added resonators (with
help of Garry Kvistad), optional damper pedals, a better stand system and
the range. Since, 1980, the zoomoozophone has consisted of 129
tubes suspended and tuned to 31 tones-per-octave just intonation.
zoomoozophone is modular and has been played by one to four
It has always been my wish that other composers could
access to the zoomoozophone. Muhal Richard Abrams, Elizabeth Brown,
Cage, David Krakauer, Joan La Barbara, Annea Lockwood, James
Ezra Sims, Bob Telson and Lasse Thoresen, among others, have
The zoomoozophone owes much to Harry Partch, whom I had the good
to know from 1965 until his death in 1974. While not based on any
instruments in particular, the zoomoozophone is derived from his ideas
Just Intonation and the Tonality Diamond.
Just Intonation is the system of tuning pitches to the simplest (and most
possible intervals. This simplicity may be both appreciated aurally,
the just-intoned intervals are strikingly clear and consonant; and
conceptually since the intervals can be defined in terms of simple
Perhaps, for some readers, a bit of basic acoustics would be useful at
All pitch relationships (intervals) may be described by a comparison of
relative speeds of vibration of the individual pitches. Imagine any
instruments. One plays a pitch that vibrates 770 cycles per second
plays a pitch that vibrates 392 cycles per second. The relationship
the two pitches is 770 to 392 which is reducible to 55 to 28---a fairly
interval that sounds like a very large major seventh. Now imagine
two instruments playing 800 and 400 cycles per second respectively.
to 400 or 800/400 is reducible to 2/1 which is called the octave, a very
interval. All intervals, from the octave to the most dissonant, may
by such fractional relationships. Generally, it may be said that
fractional relationships sound the most consonant, and the most
relationships sound the most dissonant. In Just Intonation, the perfect
is 3/2, the perfect fourth is 4/3, the major third is 5/4, the minor third
Just Intonation is not the system used to tune instruments in current Western
These small-number-ratio intervals do not exist on the piano or other
fixed-pitch instruments, as well as in virtually all Western music of the
couple centuries. In the current Western tuning system of 12-tone
the octave is divided into twelve equal intervals which must be at
slightly out of tune in order to accomplish the desired equality.
The reason that equality necessitates "out of tuneness" may be understood
further examination of the multiplicative, not additive, nature of pitch
As music theory is commonly taught, one adds and subtracts
to and from one another: i.e. a major third plus a minor third equals a
fifth. This language of common music theory is cleverly designed
(in the name of simplicity) the actual multiplicative relationships of
by having the musician add exponential values without necessarily
that one is even dealing with exponents. In 12-tone Equal
the smallest interval (minor second) must be of a size that will
an octave (2/1) when multiplied by itself 12 times. The equal-tempered
second is the twelfth root of 2 or 21/12,
the major second equals 21/6,
minor third equals 21/4,
the major third equals 21/3,
etc. The musician who
an equal-tempered major third plus a minor third equals a perfect fifth
expressing: 21/3 X
21/4 = 21/3+1/4
= 23/12+4/12 = 27/12.
And thus musicians,
of whose mathematical abilities stop at counting, can innocently practice
In Just Intonation, on the other hand, the math is much simpler.
a major third by a minor third to obtain a perfect fifth: 5/4 X 6/5 = 3/2
fifth). One divides a perfect fourth by a major third to obtain
4/3 ÷ 5/4 = 16/15. Compared to 3/2 and 16/15, 27/12
and 21/12 sound
For anyone who has the opportunity to make an aural comparison,
just-intoned intervals will be clearer and more consonant than the
This doesn't mean that all just-intoned music will be
Unlike 12-tone Equal Temperament, Just Intonation is an open
to which any number of tones may be added.
As far as I know, the Tonality Diamond is an original Partch concept.
arrangement of just-intoned pitches, the Tonality Diamond is the
of most of Harry's instruments and music as well as the Zoomoozophone.
begin the Tonality Diamond, an arbitrary pitch must be chosen as the "central"
of the system. Harry Partch selected "G" (392 vibrations per second)
for his instruments as I did for the zoomoozophone.
Thus the first step, when I built the zoomoozophone was to tune an aluminum
to a "G" 392-cycle tuning fork, available from a piano tuner's supply shop.
pitch (and all of its octave transpositions is called 1/1. The second step
tune the next five pitch classes of the overtone series, creating a six-pitch
1/1 fundamental in overtone series, tonic in chord
3/2 3rd harmonic in overtone series, fifth in chord
(c. 1/50 of a semitone
higher than a tempered 5th)
5/4 5th harmonic in overtone series, major third
in chord (c. 1/6 of a semitone
flatter than a tempered third)
7/4 7th harmonic in overtone series, c 1/3 of a
semitone lower than a
9/8 9th harmonic in overtone series, c. 1/25 of
a semitone higher than a
tempered ninth (or second))
11/8 11th harmonic in overtone series, approximately the quartertone
a tempered perfect and augmented eleventh (or perfect and augmented
Partch stopped at the 11th harmonic although that was an arbitrary choice.
at the 11th harmonic is arbitrary, but provides an abundance of
Partch invented a name for the above chord: otonality (short for
and the above chord is called 1/1 otonality or 1/1 O.
Before explaining the next step, it should be pointed out that Partch rather
decided to call all members of the same pitch class by the same ratio and
chose to use the octave of ratios that exists between 1/1 and 2/1.
I.E. "D" is
3/2 regardless of octave, and furthermore any calculation of ratios that
in a ratio outside of the above-defined octave should be converted
or dividing by 2 as necessary.
The next step, in theory and practice, is the tuning of the utonality (short
undertonality - also a Partch
invention. This is done by inverting the otonality.
Instead of going up a 3/2,
one goes down a 3/2, which can be done by inverting
the ratio to 2/3 and then
multiplying by 2 to find the ratio 4/3 ("C"). Instead of
going up a 5/4, one goes
down a 5/4 major third which can be done by inverting
the ratio to 4/5 and then
multiplying by 2 to find the ratio 8/5 ("E ").
The process continues producing the following:
4/3 pure fifth below 1/1
8/5 pure third below 1/1
8/7 pure seventh (small minor seventh) below 1/1
16/9 pure ninth below 1/1
16/11 pure 11th below 1/1
The above chord is called 1/1 utonality or 1/1 U.
Each utonality pitch is the complement of its mirror-image otonality pitch.
pitch multiplied by its
inversion will equal 1/1 (or an octave transposition of 1/1).
3/2 X 4/3 = 12/6 = 2/1 or
It is conceptually simple, but challenging tuning, to fill in the Tonality
Diamond. From each
pitch in 1/1 U, a new otonality is created:
4/3 O, 8/5 O, 8/7 O, 16/9
O, 16/11 O. This step automatically also creates
utonalities connected to
each pitch in 1/1 O: 3/2 U, 5/4 U, 7/4 U, 9/8 U, 11/8
more pitches to the scale is
a matter of personal choice. Harry added 14
In the Tonality Diamond,
1/1 exists in every otonality
and utonality. 3/2
each exist in two of each.
All other pitches exist
of each. The scale
be created by arranging
pitches of the Tonality
Diamond sequentially is
The scale is
not at all even, containing
surprising gaps and very
pitches to the Tonality
Diamond 29-tone scale to create his famous 43-tone
scale. He did it by
continuing to symmetrically add more otonalities and
utonalities, for instance
creating a 3/2 O. When I built the zoomoozophone,
I was happy to add two pitches
(16/15 and 15/8) to fill the two largest gaps
in the 29-tone scale as
the instrument would have been too big if I kept adding
Hopefully now, some sense can be made out of the following description
of the zoomoozophone: a 31-tones-per-octave, just-intonedmetalophone, played
usually with mallets, but
also with bass bow, consisting of 129 suspended
aluminum tubes. The
mallets used for the zoomoozophone are typical
always yarn-wrapped. The range is from 4/3
(middle "C") to 16/11 (a
semitone and a half above the highest "C" on the piano.
The bottom two and a half
octaves are resonated by troughs underneath. The
higher range is sufficiently
bright without added resonance.
The zoomoozophone is physically divided into 5 sections each on its own
stand, except the top two
sections share a stand. Each section represents an
octave or a portion of an
octave. The 0 Octave (zero octave) consists of the
pitches from the lowest
pitch 4/3 (middle "C") to the 15/8 ("F#") above. The
1 Octave continues from
the next pitch 1/1 ("G") to the 15/8 ("F#") consists of
the next entire octave,
from 1/1 to 15/8. The 2 Octave consists of the next
octave, from 1/1 ("G" at
the top of treble staff) to the 15/8 ("F#") above. The
3 Octave consists of the
octave above that, again from 1/1 to 15/8. The
4 Octave, like the 0 Octave
is a partial octave, from 1/1 to the 16/11 above.
The positioning of the sections
is modular, allowing for a great variety of
0 Octave and 1 Octave have optional dampeners.
Perhaps the most significant mechanical accomplishment of the
zoomoozophone is a visually
clear, chromatic arrangement of the tubes and
a visually clear notation
system. Each octave looks like all of the other octaves,
both on the instrument itself
and on the written page. This has made it easier
than it might otherwise
have been for percussionists to adapt to the