877edo
| ← 876edo | 877edo | 878edo → |
877 equal divisions of the octave (abbreviated 877edo or 877ed2), also called 877-tone equal temperament (877tet) or 877 equal temperament (877et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 877 equal parts of about 1.37 ¢ each. Each step represents a frequency ratio of 21/877, or the 877th root of 2.
Theory
877edo is consistent to the 15-odd-limit. It tempers out 3025/3024, 496125/495616, 420175/419904 and 40960000/40920957 in the 11-limit; 2080/2079, 3025/3024, 123201/123200, 91125/91091 and 65625/65536 in the 13-limit. Using the 2.3.7.11.23.43 subgroup, it tempers out 3312/3311. The equal temperament supports quartic, quarterframe and pulsar temperaments.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.017 | -0.453 | -0.069 | +0.107 | -0.391 | +0.404 | -0.592 | -0.224 | -0.615 | +0.232 |
| Relative (%) | +0.0 | -1.2 | -33.1 | -5.0 | +7.8 | -28.6 | +29.5 | -43.2 | -16.4 | -44.9 | +17.0 | |
| Steps (reduced) |
877 (0) |
1390 (513) |
2036 (282) |
2462 (708) |
3034 (403) |
3245 (614) |
3585 (77) |
3725 (217) |
3967 (459) |
4260 (752) |
4345 (837) | |
Subsets and supersets
877edo is the 151st prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1390 877⟩ | [⟨877 1390]] | 0.0052 | 0.0052 | 0.38 |
| 2.3.5 | [-20 -24 25⟩, [54 -37 2⟩ | [⟨877 1390 2036]] | 0.0685 | 0.0896 | 6.55 |
| 2.3.5.7 | 65625/65536, 420175/419904, [18 -18 13 -7⟩ | [⟨877 1390 2036 2462]] | 0.0575 | 0.0799 | 5.84 |
| 2.3.5.7.11 | 3025/3024, 496125/495616, 420175/419904, 40960000/40920957 | [⟨877 1390 2036 2462 3034]] | 0.0398 | 0.0797 | 5.82 |
| 2.3.5.7.11.13 | 2080/2079, 3025/3024, 123201/123200, 91125/91091, 65625/65536 | [⟨877 1390 2036 2462 3034 3245]] | 0.0508 | 0.0768 | 5.61 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 182\877 | 249.031 | [-26 18 -1⟩ | Monzismic |
| 1 | 231\877 | 316.078 | 6/5 | Counterhanson |
| 1 | 359\877 | 491.220 | 8388608/6328125 | Sesesix |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct