901edo: Difference between revisions
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{{ | {{ED intro}} | ||
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. | ||
[[ | [[1802edo]], which doubles 901edo, corrects the mapping for 7. | ||
Latest revision as of 19:30, 20 February 2025
| ← 900edo | 901edo | 902edo → |
901 equal divisions of the octave (abbreviated 901edo or 901ed2), also called 901-tone equal temperament (901tet) or 901 equal temperament (901et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 901 equal parts of about 1.33 ¢ each. Each step represents a frequency ratio of 21/901, or the 901st root of 2.
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.
1802edo, which doubles 901edo, corrects the mapping for 7.