Tuning for Sitting Bull: "Do You Know Who I Am?"
Sitting Bull: "Do You Know Who I Am?" is couched in a rather idiosyncratic scale - or rather, a microtonally inflected mode - arrived at monophonically. I began with a song attributed to Sitting Bull by one of his comrades, and recorded as such in Frances Densmore's classic (though sometimes ethnologically misguided) Teton Sioux Music. I then took as many versions as I needed of each pitch to give the melody the same kind of suppleness that Native Americans use to sing their traditional melodies. The result was the following scale of 21 pitches:
| Pitch: | B | C# | C#+ | C#L | D7 | D7+ | D | E | EL | F7+ | F#7++ | F# | F#+ | G7 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ratio: | 1/1 | 10/9 | 9/8 | 8/7 | 7/6 | 189/160 | 6/5 | 4/3 | 48/35 | 7/5 | 189/128 | 40/27 | 3/2 | 14/9 |
| Cents: | 0 | 182.4 | 203.9 | 231.2 | 266.9 | 288.4 | 315.6 | 498 | 546.8 | 582.5 | 674.7 | 680.4 | 702 | 764.9 |
| G7+ | G | A7+ | A | A+ | A#+ | B7+ |
| 63/40 | 8/5 | 7/4 | 16/9 | 9/5 | 15/8 | 63/32 |
| 786.4 | 813.7 | 968.8 | 996.1 | 1017.6 | 1088.3 | 1172.7 |
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 |
| # | (sharp) | 25/24 | raises 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 |
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, 1998
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