197ed12
| ← 196ed12 | 197ed12 | 198ed12 → |
Division of the twelfth harmonic into 197 equal parts (197ED12) is very nearly identical to 55 EDO, but with the 12/1 rather than the 2/1 being just. The octave is about 1.05 cents stretched and the step size is about 21.84 cents.
Theory
This tuning tempers out 81/80 in the 5-limit; 121/120 in the 11-limit; 91/90 and 169/168 in the 13-limit; 154/153 in the 17-limit; 133/132 and 76/75 in the 19-limit; 117/115, 161/160, and 162/161 in the 23-limit; 116/115, 117/116, and 147/145 in the 29-limit; 93/92 and 156/155 in the 31-limit; 111/110 in the 37-limit; 86/85 and 129/128 in the 43-limit; 141/140 in the 47-limit; 123/122 in the 61-limit; 143/142 in the 71-limit; 146/145 and 147/146 in the 73-limit; 166/165 in the 83-limit; 98/97 in the 97-limit; 101/100 in the 101-limit; 103/102 in the 103-limit; 107/106 in the 107-limit; 114/113 in the 113-limit; and 127/125 in the 127-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.05 | -2.11 | +2.11 | +8.87 | -1.05 | -5.88 | +3.16 | -4.21 | +9.92 | -2.22 | +0.00 | -7.55 | -4.82 | +6.76 | +4.21 |
| Relative (%) | +4.8 | -9.6 | +9.6 | +40.6 | -4.8 | -26.9 | +14.5 | -19.3 | +45.4 | -10.2 | +0.0 | -34.6 | -22.1 | +30.9 | +19.3 | |
| Steps (reduced) |
55 (55) |
87 (87) |
110 (110) |
128 (128) |
142 (142) |
154 (154) |
165 (165) |
174 (174) |
183 (183) |
190 (190) |
197 (0) |
203 (6) |
209 (12) |
215 (18) |
220 (23) | |