727edo
| ← 726edo | 727edo | 728edo → |
727 equal divisions of the octave (abbreviated 727edo or 727ed2), also called 727-tone equal temperament (727tet) or 727 equal temperament (727et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 727 equal parts of about 1.65 ¢ each. Each step represents a frequency ratio of 21/727, or the 727th root of 2.
Theory
727edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 24057/24010, 160083/160000, 137781/137500 and 496125/495616 in the 11-limit; 729/728, 1716/1715, 78975/78848, 34398/34375 and 160083/160000 in the 13-limit. It supports exodia.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.442 | -0.069 | +0.087 | +0.767 | -0.011 | -0.363 | -0.511 | +0.684 | -0.402 | -0.354 | +0.611 |
| Relative (%) | -26.8 | -4.2 | +5.3 | +46.5 | -0.7 | -22.0 | -30.9 | +41.5 | -24.3 | -21.5 | +37.0 | |
| Steps (reduced) |
1152 (425) |
1688 (234) |
2041 (587) |
2305 (124) |
2515 (334) |
2690 (509) |
2840 (659) |
2972 (64) |
3088 (180) |
3193 (285) |
3289 (381) | |
Subsets and supersets
727edo is the 129th prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1152 727⟩ | [⟨727 1152]] | 0.1394 | 0.1394 | 8.45 |
| 2.3.5 | [8 14 -13⟩, [-96 43 12⟩ | [⟨727 1152 1688]] | 0.1028 | 0.1250 | 7.57 |
| 2.3.5.7 | 703125/702464, 5250987/5242880, 43046721/42875000 | [⟨727 1152 1688 2041]] | 0.0693 | 0.1229 | 7.45 |
| 2.3.5.7.11 | 24057/24010, 160083/160000, 137781/137500, 496125/495616 | [⟨727 1152 1688 2041 2515]] | 0.0561 | 0.1130 | 6.84 |
| 2.3.5.7.11.13 | 729/728, 1716/1715, 78975/78848, 34398/34375, 160083/160000 | [⟨727 1152 1688 2041 2515 2690]] | 0.0631 | 0.1043 | 6.32 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 191\727 | 315.268 | 6/5 | Parakleismic |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct