901edo: Difference between revisions
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{{EDO intro|901}} | {{EDO intro|901}} | ||
901edo is [[consistent]] to the 15-odd-limit | 901edo is [[consistent]] to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| -16 35 -17 }} (minortone comma) and {{monzo| -68 18 17 }} (vavoom comma) in the 5-limit; [[4375/4374]], [[2100875/2097152]], and {{monzo| 7 -4 -16 13 }} 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]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|901|columns=11}} | {{Harmonics in equal|901|columns=11}} | ||
=== | === Subsets and supersets === | ||
901 | 901 factors into {{factorization|901}}. In light of containing [[17edo]] and [[53edo]] as subsets, it supports the [[chlorine]] temperament, which has period 17, and [[iodine]] temperament, which has period 53. | ||
Revision as of 11:31, 2 November 2023
| ← 900edo | 901edo | 902edo → |
901edo is consistent to the 15-odd-limit. The equal temperament tempers out [-16 35 -17⟩ (minortone comma) and [-68 18 17⟩ (vavoom comma) in the 5-limit; 4375/4374, 2100875/2097152, and [7 -4 -16 13⟩ 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.
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) | |
Subsets and supersets
901 factors into 17 × 53. In light of containing 17edo and 53edo as subsets, it supports the chlorine temperament, which has period 17, and iodine temperament, which has period 53.