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When Joan Tower asked if I would write a piece for her 60th birthday concert, the "Tower" card of the Tarot deck - major arcana number XVI - immediately flashed into my mind. In most decks the card shows a stone tower being struck by lightning, as bricks fly off and two people, a man and a woman, fall out of windows near the top. Drawing the Tower card indicates that Everything You Know Is Wrong, that you're about to have a shake-up in your life that will expand your field of consciousness and show you that you've been operating on too narrow an understanding of things. Joan Tower often has that effect on people, students and colleagues both. In Arcana XVI I tried to slowly capture that effect; the piece at first seems so simple, couched in perfectly familiar chords, but soon more complex tunings enter and vastly expand the potential pitch field. I perversely used 24 pitches to the octave partly because Joan once told me she didn't like quarter-tone music, although this uneven scale is far from quarter-tone:
| Pitch: | C | Db7 | Db- | D | Eb7 | Eb | Eb^- | E | F7+ | F | F+ | Gb7 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ratio: | 1/1 | 21/20 | 16/15 | 9/8 | 7/6 | 6/5 | 11/9 | 5/4 | 21/16 | 4/3 | 27/20 | 7/5 |
| Cents: | 0 | 84 | 112 | 204 | 267 | 316 | 347 | 386 | 471 | 498 | 520 | 583 |
| Gb^- | G | G^- | Ab | Ab^- | A | Bbb7 | Bb7 | Bb | Bb^- | B | Cb^- |
| 22/15 | 3/2 | 55/36 | 8/5 | 44/27 | 5/3 | 42/25 | 7/4 | 9/5 | 11/6 | 15/8 | 88/45 |
| 663 | 702 | 734 | 814 | 845 | 884 | 898 | 969 | 1018 | 1049 | 1088 | 1161 |
(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, - lowers a pitch by 80/81, b lowers it by 24/25, 7 lowers it by 35/36, ^ raises it by 33/32, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.
Although the scale isn't quarter-tone, there are triads in-between other triads that sneak ominously between, say, E-flat major and E minor. Scored for three synthesizers, Arcana XVI is my first just-intonation work for live ensemble and without a prerecorded track. The work is dedicated, of course, to Joan.
Kyle Gann
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