111ed6
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Prime factorization
3 × 37
Step size
27.9455¢
Octave
43\111ed6 (1201.66¢)
Twelfth
68\111ed6 (1900.3¢)
Consistency limit
5
Distinct consistency limit
5
| ← 110ed6 | 111ed6 | 112ed6 → |
111 equal divisions of the 6th harmonic (abbreviated 111ed6) is a nonoctave tuning system that divides the interval of 6/1 into 111 equal parts of about 27.9 ¢ each. Each step represents a frequency ratio of 61/111, or the 111th root of 6.
111ED6 is related to 43edo (meride tuning), but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 1.66 cents.
Lookalikes: 43edo, 68edt, 100ed5, 25edf
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.7 | -1.7 | +8.2 | +12.6 | +12.6 | +2.8 | +13.5 | -11.4 | -6.8 | +11.0 | +7.4 |
| Relative (%) | +5.9 | -5.9 | +29.5 | +45.0 | +45.0 | +10.1 | +48.2 | -40.9 | -24.5 | +39.5 | +26.4 | |
| Steps (reduced) |
43 (43) |
68 (68) |
100 (100) |
121 (10) |
149 (38) |
159 (48) |
176 (65) |
182 (71) |
194 (83) |
209 (98) |
213 (102) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.5 | -1.6 | -0.2 | +13.5 | +1.1 | +11.1 | +9.2 | -13.5 | -2.1 | +5.7 | +8.7 |
| Relative (%) | +30.3 | -5.7 | -0.7 | +48.2 | +3.9 | +39.5 | +33.0 | -48.2 | -7.4 | +20.5 | +31.1 | |
| Steps (reduced) |
224 (2) |
230 (8) |
233 (11) |
239 (17) |
246 (24) |
253 (31) |
255 (33) |
260 (38) |
264 (42) |
266 (44) |
271 (49) | |
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