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A Whole Different Serving of Tapioca: Exploring Just Intonation Dissonance

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A Whole Different Serving of Tapioca: Exploring Just Intonation Dissonance SPRING 2002 1 1 Volume 11, Number 1 THE JOURNAL OF THE JUST INTONATION NETWORK A PROJECT OF OTHER MUSIC, INC. A Whole Different Serving of Tapioca: Exploring Just Intonation Dissonance by Kyle Gann wrote a song, “Jargon,” completely in seconds, sevenths, Just Intonation dissonance, said Harry Partch in one of and ninths, and justified them with a satirical text (“Let tuning theory’s more ringing phrases, is “a whole dif- horrid Jargon split the air/And rive the Nerves asunder”). ferent serving of tapioca” from equally tempered dis- Somewhat analogously, I found a text and allowed pro- sonance. I had no idea what that meant when I first heard grammatic considerations to lead me into several differ- it. I’ve now used enough Just Intonation dissonance in ent kinds and degrees of just dissonance. my music to learn how right he was. My text was taken from My Life on the Plains, the My early Just Intonation works were rather fanatically autobiographical memoir of General George Armstrong consonant. Having expended years of time and energy Custer. 1 If ever a text cried out for dissonance, it was to achieve pure consonance, I was at a loss as to how to this, bristling with unacknowledged contradictions. One justify returning to dissonance, and as to what strategy or moment, Custer would admit that if he were an Indian, he theory to use as a guideline. After all, if you start working would ignore U.S. Government mandates and go live on in Just Intonation to get rid of beats in your sonic surface, the plains; a few pages later he would damn all Indians under what theoretical aegis do you bring beats back in? as brutes only governable by force. And so I was in danger of replicating the fate of one of Overall, the book seemed schizophrenic, so for our American forebears, William Billings (1746 –1800), “Custer: ‘If I Were an Indian…’ ” — the first movement who was criticized because his hymns made almost no of my music-theater piece Custer and Sitting Bull 2 — use of dissonance. And for exactly parallel reasons: Bill- I came up with a schizophrenic scale. Half of the scale ings had no theoretical sanction for breaking the rules was a normal major/minor Just Intonation scale on C that he had learned at such cost. In response, Billings (Table 1a). (text continued on page 4) Table 1a Pitch CDEb EFGAb ABb B 1 9 6 5 4 3 8 5 9 15 Ratio /1 /8 /5 /4 /3 /2 /5 /3 /5 /8 Cents 0 203.9 315.6 386.3 498.0 702.0 813.7 884.4 1017.6 1088.3 Table 1b Pitch CiY Cl+Di EiY FiY Fl+Gi AiY BR Bi Ratio 2673 4455 297 2673 891 1485 99 891 297 495 2560 4096 256 2048 640 1024 64 512 160 256 Cents 74.8 145.5 257.2 461.1 572.8 643.5 755.2 959.1 1070.9 1141.5 Volume“Just Intonation 11, Number is the 1 Best Intonation”1/1 ——Lou Harrison1 Example 1 4 3 3 3 / 4 ä j ÎÎä Voice À À À À. À À À À À À À.. À À À À À À À À À À À À À À 4 In- di - an can ne - ver be per- mit - ted ú. to view the ques - tion in this de - li - be - rate way. ú When the English & 4iYú Rú bú. Ï iYú ú Horn iY iY 4 j j & 4iYÏ Ï ÏÏä Ï Ï Ï ÎäÏ Ï Ï iY Ï Ï Ï Ï Ï Ï Ï Ï Marimba iYiÏ Ï Ï Ï Ï bÏ Ï Ï Ï iiY Ï Ï Ï Ï Ï Ï Ï Ï 4 À À À À À À À À À À À À À À À À À À À À À À À À Drum / 4 ú Rú w ú ú ? 4iY ú bw iY ú Bass 4 i i (Tapioca… continued from page 1) think of eleven as the number of mediation, providing as The other half was this same scale transposed it does so many midpoints between close 5- and 7-limit upward 257.2 cents to the 297 harmonic: that is, as a intervals, so 11 times 27 promised to mediate among quick calculation will show, to the eleventh harmonic of my other pitches. the Pythagorean major sixth. Stated in terms of C, the Among the paragraphs I chose from Custer’s book other scale’s numbers looked more impressive (given were evident many different degrees and levels of hypoc- in Table 1b in the specific Just Intonation pitch notation risy, a real connoisseur’s cornucopia of mendacity and devised by my teacher Ben Johnston). rationalization. At times, Custer was capable of very Keep in mind that although I have listed this second reasonably portraying the Indian people as victims of iY scale starting from C so it can be seen in conjunction white imperialist aggression. At these moments, I had i with the just scale on C, its actual tonic is D . Recalcu- the music move fluidly back and forth between the two 297 1 late the ratios with /256 as /1, and you’ll find the same scales, as in Example 1. When he began justifying the ratios as in the C major/minor scale in Table 1a. Washita massacre, however, I used intrusions in FiY to Thus, the entire movement operated within a bitonal, interrupt the Eb major statement of “Garry Owen,” the twenty-pitch just pitch collection, with one tonic on C 7th Cavalry’s theme song, as in Example 2. When Custer i i and the other on D , the 297th harmonic of C. I chose D reached the height of hypocrisy, accusing the Indians explicitly for its approximation of quarter-tone values. of depredations that were actually the direct result of Although I would never compose in equally tempered white actions, I undercut his sanctimonious speech in quarter tones, considering them merely a convenient Eb major with a bass line and a soprano countermelody addition to an equally tempered twelve-pitch scale that in the Di scale as in Example 3. And finally, after his was a historical mistake in the first place, I admit I’ve plea for mercy at his 1868 court martial (“Judge me not always found quarter tones rather raucously titillating to by what is known now, but in the light of what I knew the ear, and I wanted to build in as much incommensu- when these events transpired”), I climaxed with a final rability to Custer’s scale as possible. Also, I’ve come to chord in both keys at once (Example 4). Example 2 114 2 Å j 6 Voice / 8 À. 8 À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. À. My firm con- vic - tion based on a-ly na --of sis the cha -rac - ter traits of the In -andi - bÏ Ï . bÏ Ï Ï . bÏ Ï & 82 86 Ï bÏ bÏ Ï RÏ.iY Ï Ï Ï Ï bÏ bÏ Ï RÏ.i Ï Ï Ï Flute Ï bÏ i Ï bÏ iY Ï.i Ï Ï 2 6 English & 8 äÅr 8 Å r Å r Å r Å r Horn iY Ï bÏ. Ï iY Ï bÏ. Ï iY Ï RÏ. Ï iY Ï RÏ. Ï iY Ï ú. i ú. ú. iY ú. ? 2 · 6 bú. ú. bú. iY ú. Brass 8 8 i 4 1/1 Volume 11, Number 1 Example 3 154 3 3 3 4 Îä. r ä î j Å r Voice / 4 À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À Al- though ne- ver claimed as an ex - po - nent of the peace po- li - cy, Yet I en - ter- tained the most peace- a - ble sen - ti - ments iY Ï Ï Y Ï Ï RÏ Ï. iY ÏRÏ Ï Ï Ï Ï Ï RÏ Ï Ï Ï Ï Ï RÏ Ï Ï Ï Ï 4 îäJ J ä Y RÏ äÎ ä Y Ï Ï Ï Ï ÏYÏ Ï Flute & 4 J R Y 4 Ï Ï ÏbÏ Ï Ï Ï bÏ Ï Ï Ï Ï Ï Ï Ï Ï bÏ Trumpet & 4 Î bÏ Ï Ï Ï Ï ä J bú b in B Ï bÏ bbÏ ú ú bú Ï bbÏ ú ú bÏ Ï ? 4 bÏ Ï ú ú b ú Ï ú Ï Bassoon 4b Ï bÏ ? 4 Ï Double 4iY ú ú RÏ Bass iY Ï lYú ú iY ú Ï iY Ï iY i iY Ï I felt that these varied deployments of bitonal just century headaches because, occurring between D and A scales — successive, simultaneous, layered, fused — of- in a justly tuned scale based on C, it made the ii chord fered me a nuanced way to comment on Custer’s words, unavailable in a twelve-pitch just tuning. Besides, it as though the C scale were his conscious mind and the Di seemed appropriate that a Native American sun dance scale his unconscious poking its head out at inopportune would be pervaded by the spirit of the wolf. (for Custer) moments. Hypocrisy, however, is a rather I set up a series of drones (Table 2) that would move superficial emotional state, and this was still a superfi- gradually from the interval of a fourth to one of a fifth, 40 cial approach to Just Intonation dissonance.
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