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86 Appendix A: Alternative Tunings
Sequential
49. Michael Harrison, Piano Tuning for “Revelation” (2001)
Original 1/1=F, here it is set to C.
60 = Cents 0. Ratio: 1/1 (JUST)
61 = Cents -27.264092 Ratio: 63/64 (JUST)
62 = Cents +203.910002 Ratio: 9/8 (JUST)
63 = Cents +176.64591 Ratio: 567/512
64 = Cents +407.820003 Ratio: 81/64 (JUST)
65 = Cents +470.780907 Ratio: 21/16 (JUST)
66 = Cents +611.730005 Ratio: 729/512
67 = Cents +701.955001 Ratio: 3/2 (JUST)
68 = Cents +674.690909 Ratio: 189/128
69 = Cents +905.865003 Ratio: 27/16 (JUST)
70 = Cents +968.825906 Ratio: 7/4 (JUST)
71 = Cents +1109.775004 Ratio: 243/128
72 = Cents +1200. Ratio: 2/1 (JUST)
50. Helmholtz’s two-keyboard Harmonium Tuning Untempered,
24 notes per octave
60 = Cents 0. Ratio: 1/1 (JUST)
61 = Cents +92.178716 Ratio: 135/128
62 = Cents +111.731285 Ratio: 16/15 (JUST)
63 = Cents +182.403712 Ratio: 10/9 (JUST)
64 = Cents +203.910002 Ratio: 9/8 (JUST)
65 = Cents +274.582429 Ratio: 75/64 (JUST)
66 = Cents +294.134997 Ratio: 32/27 (JUST)
67 = Cents +386.313714 Ratio: 5/4 (JUST)
68 = Cents +405.866283 Ratio: 512/405
69 = Cents +478.49243 Ratio: 675/512
70 = Cents +498.044999 Ratio: 4/3 (JUST)
71 = Cents +590.223716 Ratio: 45/32 (JUST)
72 = Cents +609.776284 Ratio: 64/45 (JUST)
73 = Cents +680.448711 Ratio: 40/27 (JUST)
74 = Cents +701.955001 Ratio: 3/2 (JUST)
75 = Cents +772.627428 Ratio: 25/16 (JUST)