Partch's 1974 Genesis of A Music is a kind of palimpsest. This book is a late manuscript overwritten in so many layers of thought, with so many different languages about music, that it is all but incomprehensible to the novice.
To understand the 1974 Genesis you have to recognize that this book is a agglomeration of different currents of Partch's thought and practice throughout his life. Some of the 1974 Genesis can be traced to lectures Partch made in Pasadena in 1933; some of the 1974 Genesis is a bitter diatribe caused by the most catastrophic event of Partch's life, when the Guggenheim Foundation found his 1935 report on just intonation incomprehensible and refused to renew his grant, throwing him out on the streets to wander homeless from one men's labor camp to another in the depths of the Great Depression for more than 7 years. Some of the 1974 Genesis is an attempt to buttress the just intonation theory presented in his earlier texts with results from the then new science of psychoacoustics (this section of the 1974 Genesis follows Helmholtz's lead). And some of the 1974 Genesis has swollowed up and absorbed Partch's interstitial 1942 monograph "Presenting the music of Harry Partch..."
Harry Partch's first manuscript on the theory and practice of just intonation appeared in 1933. Called Exposition of Monophony, this short 54-page text is far and away the best of all his writings on music. The Exposition sets forth Partch's ideas more clearly and more succinctly than his later essays or his subsequent two books, Genesis of A Music I (edition one, 1949) and Genesis of A Music (revised edition, 1974).
The 1933 Exposition starts with a discussion of string lengths, melodic intervals, and the ideas of the harmonic and subharmonic series.
Partch introduces the idea of a "limit" on page 5. A "limit" indicates the largest odd number used in a just intonation scale (multiplications by powers of 2 are allowed). Thus, a scale is called "a 5 limit tuning " if the largest prime number used in a ratio is 5.
If the largest prime number used in a ratio is 7, then the scale is called a "7 limit scale"...and so on.
The guts of the paper can be found on page 22, where Partch introduces the idea of what he calls "a tonality diamond." This is nothing more than a set of members of the harmonic series multiplied by their inverse values from the subharmonic series. From these values, Partch derives a just intonation scale.
Partch uses an 11-limit scale, which means that the largest odd number is 11. Taking all the odd numbers between 1 and 11, Partch sets up the following matrix:
1 3 5 7 9 11
1/3 3/3 5/3 7/3 9/3 11/3
1/5 3/5 5/5 7/5 9/5 11/5
1/7 3/7 5/7 7/7 9/7 11/7
1/9 3/9 5/9 7/9 9/9 11/9
1/11 3/11 5/11 7/11 9/11 11/11
All ratios greater than 2 are divided successively by 2 successively until they fall between 1 and 2; all ratios less than 2 are multiplied by 2 successively until the fall between 1 and 2. This is known as "octave reduction" and it's done because pitches an octave higher or lower sound like the same note, and we want to be sure that all the notes of our scale fall within the same octave.
Octave-reduced, Partch's "tonality diamond" is:
1 3 5 7 9 11
1/3 3/3 5/3 7/6 3/2 11/6
1/5 6/5 5/5 7/5 9/5 11/10
1/7 12/7 10/7 7/7 9/7 11/7
1/9 4/3 10/9 14/9 9/9 11/9
1/11 12/11 20/11 14/11 18/11 11/11
Because there are 6 elements on each side, matrix theory tells us there must be [(N2 - N)] - 1 elements, or 62 - 6 - 1 = 29 different pitches out of 36 ratios.
These are the basic pitches of Partch's just intonation scale.
Partch noticed early on that as you increase the number of pitches in this kind of scale, the notes tend to bunch up around the middle of the octave--most of the intervals in the scale occur between the 4/3 and the 3/2, and as the number of intervals grows progressively larger, the size of the smallest intervals shrinks dramatically. Conversely, as the size of the Partch-Novaro "diamond" increases, the size of the large empty spaces around the ends of the scale increases dramatically. (These "empty spaces" occur at either end of the scale, around the 2/1 and the 1/1. Partch mentions this problem in passing in the 1933 Exposition.)
To fill in these empty spaces at either end of his "tonality diamond" scale, Partch adds a number of secondary pitches obtained by transposing some of the main pitches to another key. Transposition in just intonation is accomplished by multiplying or dividing by a small integer ratio: to transpose up by a perfect fifth, multiply all pitches by 3/2. To transpose down by a perfect fifth, divide by 3/2.
Early on, between 1928 and 1932, Partch used 8 secondary ratios to fill in the ends of his orgiinal 29-pitch "tonality diamond" scale, but by the late 1950s he had added 14 secondary ratios to the basic 29 pitches for a total of 43 just pitches all told.
As mentioned, the main reason for this was melodic. Even with 29 "diamond" pitches, Partch's scale already has considerably more harmonic resources than the conventional 12-tone equal-tempered scale. However, as Partch's compositions grew more elaborate he also found it useful to employ the secondary pitches to facilitate complex modulations: the recording "A Quarter-Saw Cut of Intonations and Motivations" available on the Inova Release 2 set of CDs makes clear the advantages of these secondary pitches as Partch moved from one tonal area to another in his "tonal flux."
The rest of the 1933 Exposition of Monophony discusses some of the history of just intonation as a justification for using this kind of musical system. The Greeks used just intonation, as well other ancient cultures--this lends a certain aura of respectability to what (in 1933) must have seemed like a wild and outlandish musical system at the fringes of rational endeavor.
The 1933 Exposition is highly theoretical. Partch doesn't discuss his instruments in any detail...and with good reason. In 1933, he had only 1 microtonal instrument, the adapted viola. In partial recompense, Partch includes photographs in the 1933 manuscript of a mock-up of a just intonation keyboard as well as his "adapted viola," but this is all the reader gets in the way of assurance that Partch's system is a practical and not just a theoretical reality. For the most part, the 1933 Exposition emphasizes theory and mathematics.
By 1942, after spending 7 years as a homeless outcast on the road, Partch must have realized that a more practical approach was needed. If he was to attract new backers, Partch had to prove that his microtonal system of just intonation could generate actual vivid music and not just a bunch of typewritten numbers on the page.
His 1942 document "Introducing to the work of Harry Partch..." addresses this issue head-on. This document (reprorduced in its entirety in the booklet for the Inova Release 2 set of CDs) is a hands-on down-to-earth description of a set of new instruments Partch had built ebtween 1935 and 1942, and of the compositions he had written for them. There's precious little mathematical theory in the 1942 paper; almost the entire document is taken up with straightforward descriptions of how he made his music in a hands-on way.
The 1942 document differs radically from the 1933 Exposition probably because Partch recognized that his instruments and his music were going to be his biggest selling point to an American public obsessed with the cold practical bottom line.
After his request for an extension of his 1934 Guggenheim grant was turned down in 1935, Partch must have realized with a shock that papers discussing the abstract theory of just intonation wouldn't induce grant committees to cough up the bucks. To convince Americans to shell out cash for new music, Partch needed to show them something typically American--an end product.
This Partch had, by 1942. His large Kithara, his Ptolemy just intonation organ, and his adapted guitars had joined his adapted viola to produce a chamber ensemble capable of playing relatively elaborate just intonation music. (Elaborate, that is, relative to the primarily monodic music which the lack of any instruments other than the adapted viola had forced upon Partch in 1933. Alas, as he himself comments, the keyboard for the 1934 Ptolemy organ never worked properly and thus proved unsuitable for use in live concerts.)
Now, in 1942 with the American economy geared up for war, Partch had instruments for chamber music, and compositions to match--Barstow was composed in 1941 in a Men's Convict Labor Camp in 1941. (Partch was convicted a number of times of the crime of being poor. Reference to this can be heard in the repeated lines heard in Bitter Music: "Have you ever been arrested before?" Partch was constantly asked this question each time he was arrested for vagrancy and sentenced to a men's labor camp, or to jail.)
The better to prove that he wasn't just blowing smoke, Partch's 1942 paper concerns itself exclusively with instruments and compositions, with a frisson of biographical information garnished on top.
By 1949 Partch's new approach had succeeded. He won another grant.
By this time the Great Depression was history, as well as World War II and its attendant materials shortages--even pennies were smelted from steel between 1942 and 1945 (such was the shortage of copper), and other raw materials were rationed with equal frugality. Thus instrument-building ona large scale would have proven nearly impossible between 1942 and 1945.
But in 1949, armed with his new grant, Partch decided to chuck library research and trips to Europe. Instead, this time he used his grant money to build instruments and publish a book-a handbook that would show others how to create a microtonal just intonation orchestra.
To that end, he hied himself to the University of Wisconsin, where with student help and access to the woodworking and metalshop facilities he was able to carpenter more new just intonation instruments, as well as publish the first edition of Genesis of A Music.
The first edition of Genesis combines both the 1942 paper (in which Partch whittled his entire presentation down to instruments and music), and his original 1933 Exposition (in which Partch largely devotes himself to the acoustic and mathematical theory of just intonation along with some historical background).
As a result, the 1949 first edition of Genesis forms a peculiar hybrid. Half of the book concerns pictures and "how-to" descriptions of building microtonal instruments, while the other half of the book discusses acoustics, consonance and dissonance & the small-integer ratio mathematics behind just intonation musical scales.
The 1949 Genesis also introduces new musical terminology, and expands on Partch's brief discussion of musical resources of just intonation in the 1933 Exposition.
Starting in the 1949 Genesis, Partch introduces the ideas of what he calls "otonality" (pitches derived from the overtone series) and "utonality" (pitches derived from the undertone series). An 11/8, for example is an otonal pitch because it uses the harmonic series member 11 reduced by 3 octaves. But the ratio 16/11 is a utonal pitch, because it uses the inversion of the 11/8--that is, the 11th undertone transposed up 4 octaves.
Partch goes on to describe key centers which are either harmonic or subharmonic. If a key center is harmonic, he calls it an "otonality." (Short for "overtone tonality.")
If a key center is subharmonic, he calls it a "utonality." (Short for "undertone tonality.")
He discusses the ways in which harmonic progressions can move from otonality to utonality, or to other otonalities. This implies that some just pitches in Partch's system can be taken in more than one sense--viz., utonal as well as otonal. In fact, all the pitches in Partch's "Monophonic fabric" can be taken in more than one sense provided that the composer does not limit himself to 43 pitches...and this is the rationale behind Partch's mention in the 1967 tape "A Quarter-Saw Cut of Intonations and Motivations" that he did not limit himself to 43 pitches, nor to the 11 limit. Whenever Partch found himself musically compelled to take a pitch in two sense (an otonal chord member becoming utonal, or vice versa) he felt free to flexibly expand his scale to include more than 43 pitches and if necessary ratios higher than the 11 limit. (Partch himself testifies to these facts; John Cahlmers also testifies that he saw 13-limit pitches set up on several of Partch's instruments.)
By the 1960s Partch's orchestra of instruments had grown considerably. His compositions had also become large music-theater spectacles, combining voice with music and elaborately-sculpted instruments.
Thus, the 1974 second edition of Genesis of A Music includes a greatly expanded section on instrument-building. The 1974 text also includes a lengthy introductory polemic absent from the 1933 Exposition; this can only be understood as Partch's violent reaction to the contempt with which he was treated in 1935 and the emotional scarring he experienced after being forced to wander homeless for 7 years during the Great Depression. Pages 3 through 67 contain the polemic and are probably best skipped by beginners; they contribute nothing to an understanding of just intonation.
Pages 68 through 109 contain historical background and definitions of terms.
Pages 109 to 180 contain the guts of the book. This is where Partch sets out his just intonation system.
Pages 181 to 319 consist entirely of recipes for building Partch's instruments along with descriptions of how to tune and maintain them (plenty of pictures).
Pages 320 through 357 discuss the backgrounds of 6 of Partch's major theatrical compositions.
Pages 361 to 457 discuss various other musical tuning systems--24 tone equal temperament, 19 tone equal temperament, etc. Partch compares these with his own just intonation system and, not surprisingly, finds them wanting.
A beginner is probably best advised to stick to pages 68 through 180. A book on acoustics may also prove useful, as well as a hand calculator.
The 2nd edition of Genesis, from 1974, was intended to perform a number of incompatible functions. As such it qualifies as 4 books rolled into one.
Partch tries to give a historical background and an acoustic justification for just intonation; that's one book.
He also offers a set of detailed instrument-building instructions for the people who will come after him. Partch knows that sooner or later his instruments will fall apart, and duplicates will have to be carpentered--so he explains specifically (down to the type of silicone cement used) how to build and maintain Partch instruments, and how to tune them. That's the second book.
Partch also analyzes some of his major theater pieces in the manner of a composer explaining his work for the public. This is the third "book" rolled into the 1974 Genesis.
As well, Partch sets out to pre-emptively attack the musical establishment--having realized by this time that the musical establishment is never going to give him the time of day. This is the fourth "book."
All told, the 1974 Genesis should have been broken into 4 separate texts. But as usual Partch didn't have time, nor would he have had the money to publish them as separate tomes. Also, his energies were taken up in repairing and moving his instruments from place to place, as well as keeping the Harry Partch Foundation from coming apart (according to Partch's letters, some of the people who volunteered to help the Foundation eventually tried to take advantage of the grant money that flowed into it and as a result bad choices were often made for the location of Partch's studios and repair shops, etc). He also experienced tremendous problems with the students who performed his compositions--sometimes they would skip rehearsals, or send a roommate as a substitute at a performance. (For proof of this, see Jonathan Szanto's article on Partch, as well as Partch's letters from 1965-1974.) Too, Partch needed to spend time composing and grinding through the drudgery of making grant applications--otherwise his musical performances would have come to a stop.
Given all these demands on his time, it's surprising that Partch was able to edit the 1974 expanded edition of Genesis at all.
