Futility Row may well be the first piece written in the key of E-13-flat minor. That is, since my 1/1 is E-flat, the tonic here is the 65th harmonic (major third of the 13th harmonic), 27 cents sharper than E-flat. The piece is for three Disklaviers (computer-controlled pianos) tuned to what I call my 8x8 tuning (see below), comprising 33 pitches in all. I have a penchant for minor keys, and it's difficult to write a minor-key piece in a scale constructed from harmonic series'. I gained a new empathy for Haydn, who, in his minor-key symphonies, always seems to modulate into the major as quickly as possible. Schoenberg remarked that Chopin was lucky because, if he wanted to do something that sounded new, all he had to do was write something in F# major. Well I'm way ahead of Chopin, because not only am I the first to write something in E-13-flat minor as far as I know, I have lots of other exotic keys left to use.
This is a particularly Gannian piece in form and gestural style, with a rhythmic ostinato and several interruptive forays into the keys based on the harmonic series', with kind of a humorous "Western noir" feel to it. I got the idea while humming a song by Mikel Rouse, and so I dedicate it to him, whose music has so often been a means of bringing me back to earth.
As in my Orbital Resonance and Romance Postmoderne, the 33-pitch tuning of the three pianos is as follows. In addition to the pitch list on the left, the pitches are grouped into the eight harmonic series' in the right eight columns:
Pitch name Ratio Cents 1/1 3/2 5/4 7/4 9/8 11/8 13/8 15/8 Eb7+ 63/32 1173 9 7 Db^^ 121/64 1103 11 D 15/8 1088 15 5 3 1 Db13 117/64 1044 13 9 C#+ 225/128 977 15 Db7 7/4 969 7 1 C^ 55/32 938 11 5 C+ 27/16 906 9 3 C7+ 105/64 857 15 7 Cb13 13/8 840 13 1 B 25/16 773 5 Bb^ 99/64 755 11 9 Cb77+ 49/32 738 7 Bb13 195/128 729 15 13 Bb 3/2 702 3 1 Bbb713 91/64 773 13 7 A+ 45/32 590 15 9 5 3 Ab^ 11/8 551 11 1 Abb1313 169/128 481 13 Ab7+ 21/16 471 7 3 G^ 165/128 440 15 11 G+ 81/64 408 9 G 5/4 386 5 1 Gb13 39/32 342 13 3 Gb7^ 77/64 320 11 7 F#+ 75/64 275 15 5 F+ 9/8 204 9 3 1 Fb13^ 143/128 192 13 11 F7+ 35/32 155 7 5 E+ 135/128 92 15 9 Eb^ 33/32 53 11 3 Eb13 65/64 27 13 5 Eb 1/1 0 1 (If you don't have enough experience with just intonation to make sense of this chart, try reading the step-by-step Just Intonation Explained section.) In Johnston's notation, + raises a pitch by 81/80, # raises it by 25/24, b lowers it by 24/25, 7 lowers it by 35/36, ^ raises it by 33/32, 13 raises it by 65/64, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.
Kyle Gann
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