6691edo: Difference between revisions
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6691edo is a very strong [[11-limit]] system, with a lower 11-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any smaller 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}. | 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}. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|6691}} | {{Harmonics in equal|6691}} | ||
[[ | === Subsets and supersets === | ||
6691edo is the 863rd [[prime edo]]. | |||
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Revision as of 16:50, 20 August 2024
| ← 6690edo | 6691edo | 6692edo → |
6691edo is a very strong 11-limit system, with a lower 11-limit relative error than any smaller 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}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0029 | -0.0037 | -0.0021 | -0.0102 | +0.0642 | -0.0384 | +0.0210 | -0.0274 | +0.0447 | +0.0847 |
| Relative (%) | +0.0 | +1.6 | -2.1 | -1.2 | -5.7 | +35.8 | -21.4 | +11.7 | -15.3 | +24.9 | +47.2 | |
| Steps (reduced) |
6691 (0) |
10605 (3914) |
15536 (2154) |
18784 (5402) |
23147 (3074) |
24760 (4687) |
27349 (585) |
28423 (1659) |
30267 (3503) |
32505 (5741) |
33149 (6385) | |
Subsets and supersets
6691edo is the 863rd prime edo.
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