Back to all posts
  • PARTCHed - July 2019

    re-Genesis of a Music

      ~  A tale of obsession  ~
    by John Schneider

    Diamonds Are Forever

    I did it! I finally finished my Partch Adapted Guitar II and was riding high on Cloud Nine playing along with Partch’s 1950 recording of the Three Intrusions,  those haunting songs that went where no slide guitar had ever been before. You will remember that those amazing compositions were basically dramatic readings – vocalizations of a text from ancient China, and two from a wonderful Bay Area poet who wrote on themes from nature. BUT – they were for voice, Adapted Guitar II, and wondrously strange terraced marimba in the shape of a diamond. I had pretty much painted myself into a corner – without that other instrument, there really wasn’t much point in having this fabulous guitar just to be able to play with a record. Oh boy, here we go again. Time to make a Diamond Marimba!

    But why did Partch even make such a strange instrument? Was it just his wonderful imagination at work? It was nothing of the sort. Anyone who has ever cracked open a copy of Partch’s book Genesis of a Music is immediately aware that the composer was not only consummately literate, he was also profoundly numerate, that is, completely conversant in the language of numbers. Musical numbers of all sorts, too: frequencies of pitches, summation & difference tones measured in Hertz, sizes of intervals measured in cents (1¢ = 1/100th of an equal-tempered semitone), but most importantly, pitches described in musical fractions or “ratios,” so essential to understanding Partch’s language of intonational theory:

    The only, clear, logical, rational terms are numbers – the relationships of numbers. That is, frequency ratios or the ratios of parts of sounding bodies. Ancient people knew musical numbers. Modern man, including modern American music schools, persist in not knowing musical numbers. On the contrary, through my lifetime, I have seen how they jealously guard their precious misconception. And this, ironically, in a so-called scientific age. - Partch, H. “A Quarter-saw Section of Motivations and Intonations (1967),” Bitter Music. Chicago: University of Illinois Press, 1995; 197.

    In fact, much of his musical journey was determined by a youthful chance encounter with an English translation of Helmholtz’s classic On The Sensations of Tone (1870) that not only demonstrated that there were many more notes to the octave than were on the modern piano, but that their tuning was inaccurate and rather dissonant. Revealed were the scientific underpinnings of the most basic musical elements of melody & harmony, consonance and dissonance, and much more including the exact measurement of musical intervals using ratios. Soon, these discoveries inspired the young composer to burn all of his present efforts at composition and begin anew, with the knowledge of a new world of musical possibilities clearly before him.

    Another volume that captured Partch’s attention was Max Meyer’s The Musician’s Arithmetic (1929), and in particular his modern presentation of a graphic method of displaying harmonic relationships.  (The challenge of making the audible visible had been previously taken on by many, including Rameau, Salinas, and as far back as Al-Jurjani in the Golden Age of Islam.) Partch borrowed the concept of Meyer’s Tonality Diamond to illustrate the dual harmonic function of the notes in his Just Intonation scale: 

    3x3 Tonality Diamond in Pitches

    Beginning with simple triads in a 3-by-3 diamond configuration, it is easy to see that a G, Eb, and C MAJOR triads all share the note “G” – on the far left upward diagonal, the G is the root in the chord G-B-D; in the middle upward diagonal it functions as the 3rd in Eb-G-Bb; and lastly, the bottom upward diagonal uses the G as the 5th in the major triad C-E-G. But wait! If one starts on the same G on the far left and go in a downward/right diagonal, a MINOR triad is spelled. This time, the G is the 5th of the C-minor triad C-Eb-G, the 3rd in the E-minor triad E-G-B, and finally the root of a G-minor triad G-Bb-D. When that same diagram is written using ratios rather than pitch names, it looks like this:

    3x3 Tonality Diamond in Ratios

    If you’re wondering about those tiny superscript numbers to the upper right of each note name, they represent the amount that each equal tempered pitch has to be either raised or lowered to make it acoustically in tune with the note G. The G stays unchanged, hence the tiny “ ”. (You will also remember that 3/3 and 5/5 also reduce into the same ratio 1/1, so they are the identical pitch.)

    Partch’s musical language, however, was based on HEXADS, not triads, and they were tuned to the 4th, 5th, 6th, 7th, 9th, and 11th harmonic of any particular root. That generated a 6-by-6 diamond called an 11-limit expanded tonality diamond:

    6x6 Tonality Diamond in Ratios

    6x6 Tonality Diamond in Ratios

    Notice that the original 3-by-3 diamond is still in place at the far left, but now the Hexad G-B-D-F-A-C# climbs the leftmost upward diagonal, while the “G” that runs as an axis through the entire diamond has functions in all six upward hexads: as root for the G-hexad, 3rd for the Eb-hexad, 5th for the C-hexad, 7th for the A-hexad, 9th for the F-hexad, and 11th for the C#-hexad. It also has six more functions in the ‘minor’ downward hexads as well. Partch called the ‘major’ upward diagonals Otonalities, short for Over-tonality, while the ‘minor’ downward diagonals became Utonalities for Under-tonality.

    The diamond arrangement also goes a long way towards explaining Partch’s 43-tone scale, too, because it can be seen that there are more than one version for many notes. There are four “A”s, for example, each with a slightly different tuning [A-35, A-18, A+4, A+31]  depending on the note’s function, and this is true of all scale steps. Genesis of a Music also shows how these new pitches generate a greatly expanded twenty-eight distinct tonalities.

    Partch said of his Diamond Marimba, “This instrument is the theoretical Tonality Diamond brought to practical tonal life,” but since the wooden blocks or ‘keys’ are quite different in size, the actual instrument is not as elegantly symmetrical as the theoretical model:

    Block Plan of the Diamond Marimba

    The diagram also shows that the pitch G that runs through the middle is G5 = 784Hz, making the lowest note = Db4, and the highest = C#6. The ratio of 2/1 = ‘octave,’ so the dotted lines on the left simply show where these notes can be found. Here: try them yourself!

    Of course these diagrams are all in two dimensions, just as Partch’s original diamond laid all the keys flat. His genius was to then terrace the blocks such that a single, swift swipe of a mallet from top to bottom could arpeggiate a hexad, and—if needed—faster than any human ever could on a melodic marimba, a dramatic effect used in many of his pieces, first and most notably in his Intrusion, “The Waterfall.”

    Partch and the Diamond Marimba
    (photo: Fred Lyon)

    Clearly, this wonderful invention was the next instrument that I simply had to build, in order to pair it with my newly Adapted Guitar II. But this project was going to be very different from my previous two guitars, since they were both ‘adapted’ instruments, meaning that only the fingerboards of pre-existing commercially produced instruments had to be changed. On the Diamond marimba, everything would have to be made from scratch: this was definitely going to be a team effort.

    First and foremost, I would need details – lots of details. Genesis of a Music certainly had some, such as the height of the lowest and highest blocks, the distances from front-to-back and side-to-side, and even exact measurements of the base and the thickness of the four bronze posts that supported the diamond. But what about the bars or ‘blocks’ themselves? Every piece of wood is different, so I wouldn’t have been able to rely on Partch’s measurements even if he had published them, especially since he was using Pernambuco & Brazilian rosewood, very hard to find in the 21st century, and prohibitively expensive even if you could.

    Luckily, I had a bit of a head start. When I traveled to Newband’s performance in San Francisco in 1999 to meet the original Adapted Guitar II, I also took measurements and photos of the Diamond Marimba, just in case…

    Partch’s Diamond Marimba in 1999
    (photo: John Schneider)

    In its current form, Partch’s Diamond was a dizzying palimpsest of previous designs & rebuilds. The composer had originally hung the thirty-six bars from thin cord that suspended them at their nodes, a standard procedure that he doubtless learned from his visits to the J. C. Deagan factory in 1946. Now, however, the bars rested on small rectangles of foam. Most of the bars bore the scars of multiple drillings that had since been refilled, and some had even been drilled from top-to-bottom. The green frame had also been extended, while most of the bamboo resonators were split and held together with at least one hose clamp. So making an “authentic” copy of this instrument—which still sounded incredible, by the way—was a bit of a conundrum. 

    A little research and a few experiments made it clear that hanging marimba bars from cord was still a superior method, and that foam blocks did damp the vibration and cut down the ring time. At MicroFest 1998, I had had the pleasure of playing in the premier of a piece by Sasha Bogdanowitsch for flute, tuned harps, refretted guitar, voice, and just intonation marimba, so I knew exactly who to call. That marimba was made by Lou Harrison’s student and eventual assistant Bill Slye, and he agreed to cut and tune the keys for my Diamond. He came down from Santa Cruz to L.A. where we handpicked 18 board feet of Honduran Rosewood at an exotic hardwoods dealer.  

    For the frame, I turned to my neighbor Skip Abelson who was a custom furniture maker also specializing in metal fabrication. Perfect! We spent many weeks going over the design of the terraced mahogany platform that would hold both bars and resonators, and creating removable legs as well. Partch’s original was all of a piece, and when I met Newband’s Diamond player, I asked if there were any changes he would make. He immediately and emphatically suggested to make it more mobile, so we designed the resonators and legs to be removable.

    As for the resonators, I was fortunate enough to speak with Cris Forster who, as curator of the Harry Partch Foundation (1976–1980), had not only the restored and tuned virtually all the original instruments, but had also made his own Diamond. An exquisite craftsman and encyclopedic polymath—his Musical Mathematics (2010) is essential reading—Forster had chosen plexiglass resonators for his superb 13-limit, 54-key instrument [] and I followed suit. For that job, I contacted Richard Cooke from Freenotes who was an expert at resonating metal tubes and bars, sending him the specs for all 36 bars, and awaited the arrival of the perfectly tuned acrylic plexiglass tubes. While the platform was being built, we also fabricated two H-shaped removable legs made of square aluminum tubing that connected at 900 via welded bolts and wing-nuts.

    Not done yet! I acquired the U-shaped saddle bar suspension posts (36 x 4 = 144) that had to be drilled out and painted for my special design for hanging the bars, and selected the right kind of cord. I still needed felt spacers so the wooden bars wouldn’t clank against the posts, and 144 of them had to be hand cut, as was the special black felt to line the holes in the platform to hold the resonators. 

    New Diamond Marimba in process (December, 2000)
    (photo: John Schneider)

    But what was going to hold them in place? I didn’t want to glue them in, since they needed to be removable for safer, easier transport. So instead, we used various lengths of hex bolts that were specially sized for each resonator. The platform was then drilled and T-nuts hammered in so slight pressure from the bolt tips would gently hold tubes in position:

    New Diamond Marimba rear view (2001)
    (photo: John Schneider)

    Finally, on January 1, 2001, with all 36 keys attached and resonators in place, it’s mallet time! 

    New Diamond Marimba (2001)
    (photo: John Schneider)

    Rehearsals began soon after, and in a few months, my group Just Strings was able to perform Partch’s Three Intrusions (1949) at two MicroFest events - the first ever International Conference of Alternative Tunings (Claremont Colleges, April 2001) and the Partch Centennial Celebration (UCLA, May 2001):

    The Diamond has been an essential part of every performance ever since, including travelling to Holland for a 6-city tour in 2002 with the Amsterdam ensemble Scordatura. And yes, that is Partch’s original Kithara I (1938), but that’s a story for another time…

    Next up, Part 8: Organ transplant….