I invented and built the zoomoozophone (photo) during 1978 because it was 
necessary for me to continue composing at the time.  For the past decade most 
of my works had featured ringing metallic percussion with and without other 
instruments in complicated textures.  Over the course of several years I became 
frustrated by the limitation of 12 tones-per-octave equal temperament, both 
because the intervals are never in tune and because there simply weren't 
enough of them.  I had worked with Harry Partch during the late 60's/early 70's 
and 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 to metal 
surplus stores in downtown Manhattan and Brooklyn, experimentation with a 
wide variety of metals, shapes and sizes, and finally a prototype instrument on 
a plywood stand.  From the beginning, even the prototype was an instrument for 
composing and performance.  Over the next five years, I added resonators (with 
the help of Garry Kvistad), optional damper pedals, a better stand system and 
enlarged the range.  Since, 1980, the zoomoozophone has consisted of 129 
aluminum tubes suspended and tuned to 31 tones-per-octave just intonation. 
The zoomoozophone is modular and has been played by one to four 
zoomoozophonists.  It has always been my wish that other composers could 
have access to the zoomoozophone.  Muhal Richard Abrams, Elizabeth Brown, 
John Cage, David Krakauer, Joan La Barbara, Annea Lockwood, James 
Pugliese, Ezra Sims, Bob Telson and Lasse Thoresen, among others, have 
composed for it.

     The zoomoozophone owes much to Harry Partch, whom I had the good 
fortune to know from 1965 until his death in 1974.  While not based on any of 
Harry's instruments in particular, the zoomoozophone is derived from his ideas 
about Just Intonation and the Tonality Diamond.
 
 

     Just Intonation is the system of tuning pitches to the simplest (and most 
beautiful) possible intervals.  This simplicity may be both appreciated aurally, 
since the just-intoned intervals are strikingly clear and consonant; and 
understood conceptually since the intervals can be defined in terms of simple 
arithmetical relationships.

     Perhaps, for some readers, a bit of basic acoustics would be useful at this 
point.  All pitch relationships (intervals) may be described by a comparison of 
the relative speeds of vibration of the individual pitches.  Imagine any two voices 
or instruments.  One plays a pitch that vibrates 770 cycles per second and the 
other plays a pitch that vibrates 392 cycles per second.  The relationship 
between the two pitches is 770 to 392 which is reducible to 55 to 28---a fairly 
dissonant interval that sounds like a very large major seventh.  Now imagine the 
same two instruments playing 800 and 400 cycles per second respectively. 
800 to 400 or 800/400 is reducible to 2/1 which is called the octave, a very 
consonant interval.  All intervals, from the octave to the most dissonant, may be 
defined by such fractional relationships.  Generally, it may be said that the 
simplest fractional relationships sound the most consonant, and the most 
complex relationships sound the most dissonant.  In Just Intonation, the perfect 
fifth is 3/2, the perfect fourth is 4/3, the major third is 5/4, the minor third is 6/5, 
etc.

     Just Intonation is not the system used to tune instruments in current Western 
culture.  These small-number-ratio intervals do not exist on the piano or other 
Western fixed-pitch instruments, as well as in virtually all Western music of the 
last couple centuries.  In the current Western tuning system of 12-tone Equal 
Temperament, the octave is divided into twelve equal intervals which must be at 
least slightly out of tune in order to accomplish the desired equality.

     The reason that equality necessitates "out of tuneness" may be understood 
by further examination of the multiplicative, not additive, nature of pitch 
relationships.  As music theory is commonly taught, one adds and subtracts 
pitches to and from one another: i.e. a major third plus a minor third equals a 
perfect fifth.  This language of common music theory is cleverly designed to 
obscure (in the name of simplicity) the actual multiplicative relationships of 
intervals by having the musician add exponential values without necessarily 
understanding that one is even dealing with exponents.  In 12-tone Equal 
Temperament, the smallest interval (minor second) must be of a size that will 
produce an octave (2/1) when multiplied by itself 12 times.  The equal-tempered 
minor second is the twelfth root of 2 or 2^1/12, the major second equals 2^1/6, 
the minor third equals 2^1/4, the major third equals 2^1/3, etc.  The musician who 
thinks an equal-tempered major third plus a minor third equals a perfect fifth is 
actually expressing: 2^1/3 X 2^1/4 = 2^1/3+1/4 = 2^3/12+4/12 = 2^7/12.   And thus musicians, 
many of whose mathematical abilities stop at counting, can innocently practice 
logarithms.

     In Just Intonation, on the other hand, the math is much simpler.  One 
multiplies a major third by a minor third to obtain a perfect fifth: 5/4 X 6/5 = 3/2 
(perfect fifth).   One divides a perfect fourth by a major third to obtain a minor 
second: 4/3 ÷ 5/4 = 16/15.  Compared to 3/2 and 16/15, 2^7/12 and 2^1/12 sound 
unfocused.  For anyone who has the opportunity to make an aural comparison, 
the just-intoned intervals will be clearer and more consonant than the 
equal-tempered.  This doesn't mean that all just-intoned music will be 
consonant.  Unlike 12-tone Equal Temperament, Just Intonation is an open 
system to which any number of tones may be added.
 
 

     As far as I know, the Tonality Diamond is an original Partch concept.  A 
symmetrical arrangement of just-intoned pitches, the Tonality Diamond is the 
basis of most of Harry's instruments and music as well as the Zoomoozophone. 
To begin the Tonality Diamond, an arbitrary pitch must be chosen as the "central" 
pitch 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 
tube to a "G" 392-cycle tuning fork, available from a piano tuner's supply shop. 
This pitch (and all of its octave transpositions is called 1/1. The second step was 
to tune the next five pitch classes of the overtone series, creating a six-pitch chord:

     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
               tempered 
               minor seventh
     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 between 
               a tempered perfect and augmented eleventh (or perfect and augmented 
               fourth.

     Partch stopped at the 11th harmonic although that was an arbitrary choice. 
Stopping at the 11th harmonic is arbitrary, but provides an abundance of 
possibilities.   Partch invented a name for the above chord: otonality (short for 
overtonality) 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 
sensibly decided to call all members of the same pitch class by the same ratio and 
he chose to use the octave of ratios that exists between 1/1 and 2/1.  I.E. "D" is 
always 3/2 regardless of octave, and furthermore any calculation of ratios that 
results in a ratio outside of the above-defined  octave should be converted by 
multiplying or dividing by 2 as necessary.

     The next step, in theory and practice, is the tuning of the utonality (short for 
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:

     1/1
     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.  Any 
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 1/1. 

     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 U.
 

In the Tonality Diamond,  1/1 exists in every otonality  and utonality.  3/2 and 4/3  each exist in two of each.  All other pitches exist in one  of each.  The scale that can  be created by arranging the  pitches of the Tonality  Diamond sequentially is a  29-tone scale.   The scale is  not at all even, containing  surprising gaps and very  small intervals.   Adding

more pitches to the scale is a matter of personal choice.    Harry added 14 
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 
pitches.
 
 

     Hopefully now, some sense can be made out of the following description of the zoomoozophone: a 31-tones-per-octave, just-intonedmetalophone, played on 
usually with mallets, but also with bass bow, consisting of 129 suspended 
aluminum tubes.  The mallets used for the zoomoozophone are typical 
vibraphone/marimba mallets, 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 
arrangements.  The 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 
zoomoozophone.