265edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|265}} | |||
It is [[contorted]] in the 5-limit, tempering out the same commas as [[53edo|53edo]], including 15625/15552 and 32805/32768. In the 7-limit it tempers out 16875/16807 and 420175/419904, so that it [[support]]s [[Kleismic_family#Sqrtphi|sqrtphi temperament]], for which it provides the [[Optimal_patent_val|optimal patent val]]. In the 11-limit it tempers out 540/539, 1375/1372 and 4375/4356, and gives the optimal patent val for 11-limit sqrtphi temperament. | |||
=== Prime harmonics === | |||
{{harmonics in equal|265}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 18:10, 3 June 2023
| ← 264edo | 265edo | 266edo → |
It is contorted in the 5-limit, tempering out the same commas as 53edo, including 15625/15552 and 32805/32768. In the 7-limit it tempers out 16875/16807 and 420175/419904, so that it supports sqrtphi temperament, for which it provides the optimal patent val. In the 11-limit it tempers out 540/539, 1375/1372 and 4375/4356, and gives the optimal patent val for 11-limit sqrtphi temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.07 | -1.41 | +0.23 | +1.13 | +1.74 | -0.80 | +1.35 | +1.16 | -1.65 | +0.62 |
| Relative (%) | +0.0 | -1.5 | -31.1 | +5.1 | +25.1 | +38.3 | -17.8 | +29.9 | +25.6 | -36.5 | +13.8 | |
| Steps (reduced) |
265 (0) |
420 (155) |
615 (85) |
744 (214) |
917 (122) |
981 (186) |
1083 (23) |
1126 (66) |
1199 (139) |
1287 (227) |
1313 (253) | |