Kyle Gann:

Tuning for Custer: "If I Were an Indian..."

Custer: "If I Were an Indian..." is written in a rather forbidding-looking 20-pitch scale that actually results from the combination of two quite simple scales. The total scale is as follows:

Pitch:CC^+C#^+D D^EbEE^F F^+F#^+G
Ratio:1/12673/25604455/40969/8 297/2566/55/42673/20484/3 891/6401485/10243/2
Cents:074.8145.5203.9 257.2315.6386.3461.1498 572.8643.5702

G^AbAA^+ BbBb^BB^
99/648/55/3891/512 9/5297/16015/8495/256
755.2813.7844.4959.1 1017.61070.91088.31141.5

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:

+(plus)81/80raises a pitch by 21.5 cents
#(sharp)25/24raises a pitch by 71 cents
b(flat)24/25lowers a pitch by -71 cents
^(upward arrow)33/32raises 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.)

Actually, this scale breaks down into two simple just intonation scales, one based on C and the other on D^ (297/256). Here the two scales are broken apart:

Ratio:1/19/86/55/44/3 3/28/55/39/515/8

Pitch:D^E^F^+F#^+ G^A^+Bb^B^C^+C#^+
Ratio: 297/2562673/2048891/6401485/1024 99/64891/512297/160495/256 2673/25604455/4096
Ratio to D^:1/19/8 6/55/44/33/2 8/55/39/515/8

Comparison will show that the scales on C and D^ are identical, and that they provide two tonalities in both major and minor, with tonic pitches 257 cents apart. In essence, the piece contains two tonalities set off from each other by a near-quarter-tone relationship.

The idea of Custer: "If I Were an Indian..." is that Custer's texts reveal something akin to schizophrenia. Where he sustains a rational view of the contrast between White and Indian cultures, the music flows smoothly from one scale to the other. Where he takes up the White man's intolerant bias, the music adheres rigidly to the C scale. And where Custer expresses a deep, unconscious ambivalence, hypocritically blaming the Indian for sinister White actions, the two scales conflict with each other and undercut Custer's ostensive meaning. The scale, divided against itself, reflects Custer's deeply divided personality.

Kyle Gann, 1998
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