901edo: Difference between revisions
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'''901edo''' is the [[EDO|equal division of the octave]] into 901 parts of 1.33185 [[cent]]s each. It is [[consistent]] to the 15-odd-limit, tempering out {{monzo| -16 35 -17 }} (minortonic comma) and {{monzo| -68 18 17 }} (vavoom comma) in the 5-limit; [[4375/4374]], [[2100875/2097152]], and 12401793332096/12359619140625 in the 7-limit; [[41503/41472]], 160083/160000, 234375/234256, and 806736/805255 in the 11-limit; [[4225/4224]], 4459/4455, [[6656/6655]], 34398/34375, and 50421/50336 in the 13-limit, supporting [[mitonic]], [[vavoom]], [[chlorine]], and [[ | '''901edo''' is the [[EDO|equal division of the octave]] into 901 parts of 1.33185 [[cent]]s each. | ||
== Theory == | |||
It is [[consistent]] to the 15-odd-limit, tempering out {{monzo| -16 35 -17 }} (minortonic comma) and {{monzo| -68 18 17 }} (vavoom comma) in the 5-limit; [[4375/4374]], [[2100875/2097152]], and 12401793332096/12359619140625 in the 7-limit; [[41503/41472]], 160083/160000, 234375/234256, and 806736/805255 in the 11-limit; [[4225/4224]], 4459/4455, [[6656/6655]], 34398/34375, and 50421/50336 in the 13-limit, supporting [[mitonic]], [[vavoom]], and [[egads]]. | |||
901 is 17 × 53. In light of contaning 17edo and 53edo as subsets, it supports the [[chlorine]] temperament, which has period 17, and [[iodine]] temperament, which has period 53. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|901|columns=11}} | {{Harmonics in equal|901|columns=11}} | ||
[[Category:Equal divisions of the octave|###]]<!-- 3-digit number --> | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | |||
Revision as of 14:11, 5 October 2022
| ← 900edo | 901edo | 902edo → |
901edo is the equal division of the octave into 901 parts of 1.33185 cents each.
Theory
It is consistent to the 15-odd-limit, tempering out [-16 35 -17⟩ (minortonic comma) and [-68 18 17⟩ (vavoom comma) in the 5-limit; 4375/4374, 2100875/2097152, and 12401793332096/12359619140625 in the 7-limit; 41503/41472, 160083/160000, 234375/234256, and 806736/805255 in the 11-limit; 4225/4224, 4459/4455, 6656/6655, 34398/34375, and 50421/50336 in the 13-limit, supporting mitonic, vavoom, and egads.
901 is 17 × 53. In light of contaning 17edo and 53edo as subsets, it supports the chlorine temperament, which has period 17, and iodine temperament, which has period 53.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.068 | -0.076 | -0.568 | +0.069 | -0.128 | +0.261 | -0.510 | +0.361 | -0.054 | +0.358 |
| Relative (%) | +0.0 | -5.1 | -5.7 | -42.7 | +5.2 | -9.6 | +19.6 | -38.3 | +27.1 | -4.1 | +26.9 | |
| Steps (reduced) |
901 (0) |
1428 (527) |
2092 (290) |
2529 (727) |
3117 (414) |
3334 (631) |
3683 (79) |
3827 (223) |
4076 (472) |
4377 (773) |
4464 (860) | |