1911edo
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Prime factorization
3 × 72 × 13
Step size
0.627943¢
Fifth
1118\1911 (702.041¢) (→86\147)
Semitones (A1:m2)
182:143 (114.3¢ : 89.8¢)
Consistency limit
11
Distinct consistency limit
11
| ← 1910edo | 1911edo | 1912edo → |
1911 equal divisions of the octave (1911edo), or 1911-tone equal temperament (1911tet), 1911 equal temperament (1911et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1911 equal parts of about 0.628 ¢ each.
Theory
1911edo is consistent in the 11-limit and tempers out the aluminium comma in the 5-limit. It provides the optimal patent val for the protactinium temperament in the 17-limit. However as may stem from consistency only in the 11-limit, the 13th harmonic has a large relative error. As such, 1911edo is best considered as a 2.3.5.7.11.17.19 subgroup tuning.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.086 | -0.128 | +0.091 | +0.016 | +0.289 | -0.089 | +0.132 | +0.297 | +0.250 | -0.295 |
| relative (%) | +0 | +14 | -20 | +14 | +3 | +46 | -14 | +21 | +47 | +40 | -47 | |
| Steps (reduced) |
1911 (0) |
3029 (1118) |
4437 (615) |
5365 (1543) |
6611 (878) |
7072 (1339) |
7811 (167) |
8118 (474) |
8645 (1001) |
9284 (1640) |
9467 (1823) | |
Subsets and supersets
1911edo has subset edos 1, 3, 7, 13, 21, 39, 49, 91, 147, 273, 637.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperaments |
|---|---|---|---|---|
| 13 | 793\1911 (58\1911) |
497.959 (36.421) |
4/3 (?) |
Aluminium |
| 91 | 793\1911 (16\1911) |
497.959 (10.047) |
4/3 (176/175) |
Protactinium |