User:Francium/925edo
| ← 924edo | 925edo | 926edo → |
925 equal divisions of the octave (abbreviated 925edo or 925ed2), also called 925-tone equal temperament (925tet) or 925 equal temperament (925et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 925 equal parts of about 1.3 ¢ each. Each step represents a frequency ratio of 21/925, or the 925th root of 2.
Theory
925edo is consistent to the 17-limit, tempering out 160083/160000, 472392/471625, 172032/171875 and 180224/180075 in the 11-limit; 1716/1715, 4096/4095, 34398/34375, 40656/40625 and 39366/39325 in the 13-limit; and 1701/1700, 1716/1715, 4096/4095, 12376/12375, 14400/14399 and 11016/11011 in the 17-limit. It is a very strong 2.3.11.13.17 tuning system, tempering out 34992/34969, 161109/161051, 243931419/243662848 and 1114112/1113879.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.117 | +0.281 | +0.255 | +0.033 | +0.121 | +0.126 | -0.432 | -0.382 | +0.477 | +0.478 |
| Relative (%) | +0.0 | -9.0 | +21.7 | +19.7 | +2.6 | +9.3 | +9.7 | -33.3 | -29.5 | +36.8 | +36.8 | |
| Steps (reduced) |
925 (0) |
1466 (541) |
2148 (298) |
2597 (747) |
3200 (425) |
3423 (648) |
3781 (81) |
3929 (229) |
4184 (484) |
4494 (794) |
4583 (883) | |
Subsets and supersets
Since 925 factors into 52 × 37, it has the subset edos 5, 25, 37, and 185.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1466 925⟩ | [⟨925 1466]] | +0.0370 | 0.0370 | 2.85 |
| 2.3.5 | [8 14 -13⟩, [-122 55 15⟩ | [⟨925 1466 2148]] | −0.0157 | 0.0803 | 6.19 |
| 2.3.5.7 | 2460375/2458624, 1640558367/1638400000, 2579890176/2573571875 | [⟨925 1466 2148 2597]] | −0.0345 | 0.0768 | 5.92 |
| 2.3.5.7.11 | 160083/160000, 472392/471625, 172032/171875, 180224/180075 | [⟨925 1466 2148 2597 3200]] | −0.0295 | 0.0694 | 5.35 |
| 2.3.5.7.11.13 | 1716/1715, 4096/4095, 34398/34375, 40656/40625, 39366/39325 | [⟨925 1466 2148 2597 3200 3423]] | −0.0301 | 0.0634 | 4.89 |
| 2.3.5.7.11.13.17 | 1701/1700, 1716/1715, 4096/4095, 12376/12375, 14400/14399, 11016/11011 | [⟨925 1466 2148 2597 3200 3423 3781]] | −0.0302 | 0.0587 | 4.52 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 243\925 | 315.243 | 6/5 | Parakleismic |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct