6691edo: Difference between revisions
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The '''6691 division''' divides the octave into 6691 equal parts of 0.17935 cents each. It is a very strong [[11-limit]] division, with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[40006edo|40006]]. | The '''6691 division''' divides the octave into 6691 equal parts of 0.17935 cents each. It is a very strong [[11-limit]] division, with a lower 11-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[40006edo|40006]]. It is also strong in the [[7-limit]], where only [[3125edo|3125]] is both smaller and with a lesser relative error. | ||
A basis for the 11-limit commas is {1771561/1771470, 3294225/3294172, 67110351/67108864, 78125000/78121827} and for the 7-limit commas, {78125000/78121827, 281484423828125/281474976710656, 8936733825332544112/8936247052719140625}. | |||
{{Harmonics in equal}} | {{Harmonics in equal}} | ||
{{stub}} | {{stub}} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
Revision as of 07:12, 14 January 2024
| ← 6690edo | 6691edo | 6692edo → |
The 6691 division divides the octave into 6691 equal parts of 0.17935 cents each. It is a very strong 11-limit division, with a lower 11-limit relative error than any division until 40006. It is also strong in the 7-limit, where only 3125 is both smaller and with a lesser relative error.
A basis for the 11-limit commas is {1771561/1771470, 3294225/3294172, 67110351/67108864, 78125000/78121827} and for the 7-limit commas, {78125000/78121827, 281484423828125/281474976710656, 8936733825332544112/8936247052719140625}.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -2.0 | +13.7 | +31.2 | +48.7 | -40.5 | -5.0 | +2.5 | -28.3 | -29.6 | -45.0 |
| Relative (%) | +0.0 | -2.0 | +13.7 | +31.2 | +48.7 | -40.5 | -5.0 | +2.5 | -28.3 | -29.6 | -45.0 | |
| Steps (reduced) |
12 (0) |
19 (7) |
28 (4) |
34 (10) |
42 (6) |
44 (8) |
49 (1) |
51 (3) |
54 (6) |
58 (10) |
59 (11) | |
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