15601edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 557205469 - Original comment: ** |
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{{ED intro}} It is the denominator of the next convergent for log<sub>2</sub>3 past [[665edo|665]], before [[31867edo|31867]], and has a fifth which is 0.000002 cents stretched. | |||
This system is at its best behavior in the 2.3.19.23 subgroup. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|15601}} | |||
=== Subsets and supersets === | |||
15601edo is the 1819th [[prime edo]]. | |||
31202edo, which doubles 15601edo, provides a good correction to harmonics 5, 7, 11, 13 and 17. [[78005edo]], which slices each step of 15601edo in five, is notable for an exceptional approximation quality of the 5-limit. | |||
{{Todo|inline=1|explain its xenharmonic value}} | |||
[[Category:3-limit record edos|#####]] <!-- 5-digit number --> | |||
Latest revision as of 16:28, 28 July 2025
| ← 15600edo | 15601edo | 15602edo → |
(convergent)
15601 equal divisions of the octave (abbreviated 15601edo or 15601ed2), also called 15601-tone equal temperament (15601tet) or 15601 equal temperament (15601et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 15601 equal parts of about 0.0769 ¢ each. Each step represents a frequency ratio of 21/15601, or the 15601st root of 2. It is the denominator of the next convergent for log23 past 665, before 31867, and has a fifth which is 0.000002 cents stretched.
This system is at its best behavior in the 2.3.19.23 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0000 | -0.0308 | +0.0351 | +0.0313 | +0.0338 | +0.0379 | +0.0064 | -0.0069 | -0.0278 | -0.0320 |
| Relative (%) | +0.0 | +0.0 | -40.0 | +45.6 | +40.7 | +44.0 | +49.2 | +8.3 | -9.0 | -36.2 | -41.7 | |
| Steps (reduced) |
15601 (0) |
24727 (9126) |
36224 (5022) |
43798 (12596) |
53971 (7168) |
57731 (10928) |
63769 (1365) |
66272 (3868) |
70572 (8168) |
75789 (13385) |
77290 (14886) | |
Subsets and supersets
15601edo is the 1819th prime edo.
31202edo, which doubles 15601edo, provides a good correction to harmonics 5, 7, 11, 13 and 17. 78005edo, which slices each step of 15601edo in five, is notable for an exceptional approximation quality of the 5-limit.
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Todo: explain its xenharmonic value |