97ed12

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97ed12

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Prime factorization	97 (prime)
Step size	44.3501 ¢
Octave	27\97ed12 (1197.45 ¢)
Twelfth	43\97ed12 (1907.05 ¢)
Consistency limit	10
Distinct consistency limit	8

97 equal divisions of the 12th harmonic (abbreviated 97ed12) is a nonoctave tuning system that divides the interval of 12/1 into 97 equal parts of about 44.4 ¢ each. Each step represents a frequency ratio of 12^1/97, or the 97th root of 12.

97ed12 is very nearly identical to 27edo, but with the 12/1 rather than the 2/1 being just. This compresses the octave by about 2.45 ¢.

Harmonics

Approximation of harmonics in 97ed12

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.5	+5.1	-5.1	+7.7	+2.5	+1.8	-7.6	+10.2	+5.2	+17.6	+0.0
	Relative (%)	-5.7	+11.5	-11.5	+17.5	+5.7	+4.0	-17.2	+23.0	+11.7	+39.7	+0.0
Steps (reduced)		27 (27)	43 (43)	54 (54)	63 (63)	70 (70)	76 (76)	81 (81)	86 (86)	90 (90)	94 (94)	97 (0)

Approximation of harmonics in 97ed12 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-5.5	-0.8	+12.8	-10.2	+17.9	+7.6	+2.7	+2.6	+6.9	+15.0	-17.6	-2.5
	Relative (%)	-12.5	-1.7	+28.9	-23.0	+40.4	+17.2	+6.2	+6.0	+15.5	+33.9	-39.6	-5.7
Steps (reduced)		100 (3)	103 (6)	106 (9)	108 (11)	111 (14)	113 (16)	115 (18)	117 (20)	119 (22)	121 (24)	122 (25)	124 (27)