197ed12
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; and 154/153 in the 17-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.05 | -2.11 | +2.11 | +8.87 | -1.05 | -5.88 | +3.16 | -4.21 | +9.92 | -2.22 | +0.00 |
| Relative (%) | +4.8 | -9.6 | +9.6 | +40.6 | -4.8 | -26.9 | +14.5 | -19.3 | +45.4 | -10.2 | +0.0 | |
| Steps (reduced) |
55 (55) |
87 (87) |
110 (110) |
128 (128) |
142 (142) |
154 (154) |
165 (165) |
174 (174) |
183 (183) |
190 (190) |
197 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -7.55 | -4.82 | +6.76 | +4.21 | +8.44 | -3.16 | -9.41 | -10.87 | -7.98 | -1.17 | +9.22 |
| Relative (%) | -34.6 | -22.1 | +30.9 | +19.3 | +38.7 | -14.5 | -43.1 | -49.8 | -36.6 | -5.4 | +42.2 | |
| Steps (reduced) |
203 (6) |
209 (12) |
215 (18) |
220 (23) |
225 (28) |
229 (32) |
233 (36) |
237 (40) |
241 (44) |
245 (48) |
249 (52) | |