Tuning for Custer's Ghost to Sitting Bull
Custer's Ghost to Sitting Bull is based on a drone on G, though it occasionally dips down to F#. The music slides continually up and down the following 31-tone scale, moving in small nuances intended to sound like the glissandos of the wind:
| Pitch: | G | G^ | Ab7+ | Ab | Ab^ | A | A+ | AL | Bb7 | Bb | Bb^- | B | BL | C7 | C | C+ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ratio: | 1/1 | 33/32 | 21/20 | 16/15 | 11/10 | 10/9 | 9/8 | 8/7 | 7/6 | 6/5 | 11/9 | 5/4 | 9/7 | 21/16 | 4/3 | 27/20 |
| Cents: | 0 | 53 | 84 | 112 | 165 | 182 | 204 | 231 | 267 | 316 | 347 | 386 | 435 | 471 | 498 | 520 |
| C^ | Db7 | Dv | D | Eb7 | Eb | Ev+ | E | EL | F7+ | F | F+ | F^ | F#+ | Gv |
| 11/8 | 7/5 | 16/11 | 3/2 | 14/9 | 8/5 | 18/11 | 5/3 | 12/7 | 7/4 | 16/9 | 9/5 | 11/6 | 15/8 | 64/33 |
| 551 | 583 | 649 | 702 | 765 | 814 | 853 | 884 | 933 | 969 | 996 | 1018 | 1049 | 1088 | 1147 |
I have notated this scale (as closely as html will allow) in Ben Johnston's excellent microtonal notation, in which accidentals make the following alterations:
| Sign: | Ratio: | Effect | |
|---|---|---|---|
| + | (plus) | 81/80 | raises a pitch by 21.5 cents |
| - | (minus) | 80/81 | lowers a pitch by -21.5 cents |
| # | (sharp) | 25/24 | raises a pitch by 71 cents |
| b | (flat) | 24/25 | lowers a pitch by -71 cents |
| 7 | (seven) | 35/36 | lowers a pitch by -49 cents to get a seventh harmonic |
| L | (upside-down 7) | 36/35 | raises a pitch by 49 cents |
| ^ | (upward arrow) | 33/32 | raises a pitch by 53 cents to get an eleventh harmonic |
| v | (downward arrow) | 32/33 | lowers a pitch by -53 cents |
In addition, F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.
(If you don't have enough experience with just intonation to make sense of these charts, try reading the step-by-step Just Intonation Explained section.)
Kyle Gann
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