1000edo
The 1000 edo divides the octave in 1000 equal parts of exactly 1.2 cents, or 1 millioctave each. It is notable mostly because it is the equal division corresponding to millioctaves.
| ← 999edo | 1000edo | 1001edo → |
1000edo is related to 200edo, but the patent vals differ on the mapping for 5 and 7. In the 5-limit, it tempers out luna comma, 274877906944/274658203125 and senior comma, [-17 62 -35⟩. In the 7-limit, it tempers out 4375/4374, 201768035/201326592, and 165288374272/164794921875, leading to the lunatic temperament and seniority temperament. It also tempers out 3025/3024, 9801/9800, and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, 4459/4455, and 10648/10647 in the 13-limit, leading to the deca temperament and donar temperament.
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Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [317 -200⟩ | ⟨1000 1585] | -0.0142 | 0.0142 | 1.18 |
| 2.3.5 | [38 -2 -15⟩, [55 -64 20⟩ | ⟨1000 1585 2322] | -0.0219 | 0.0159 | 1.33 |
| 2.3.5.7 | 4375/4374, 4202539929/4194304000, 578509309952/576650390625 | ⟨1000 1585 2322 2807] | +0.0215 | 0.0764 | 6.37 |
| 2.3.5.7.11 | 3025/3024, 4375/4374, 422576/421875, 5907360375/5905580032 | ⟨1000 1585 2322 2807 3459] | +0.0472 | 0.0854 | 7.12 |
| 2.3.5.7.11.13 | 1001/1000, 3025/3024, 4459/4455, 43904/43875, 708883245/708837376 | ⟨1000 1585 2322 2807 3459 3700] | +0.0631 | 0.0857 | 7.14 |