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
| ← 96ed12 | 97ed12 | 98ed12 → |
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 121/97, or the 97th root of 12.
Theory
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
| 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) | |
| 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) | |
Subsets and supersets
97ed12 is the 25th prime ed12, following 89ed12 and before 101ed12.