215edo: Difference between revisions
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{{EDO intro}} | {{EDO intro}} | ||
215et [[tempering out|tempers out]] [[4000/3969]] and [[65625/65536]], and the [[patent val]] provides the [[optimal patent val]] for the 53 & 162 temperament ([[ditonic|ditonic extension]]) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out [[2401/2400]], [[5120/5103]], and [[support]]s [[hemififths]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 215 factors into | Since 215 factors into 5 × 43, 215edo contains [[5edo]] and [[43edo]] as its subsets. | ||
[[Category:Ditonic]] | [[Category:Ditonic]] | ||
[[Category:Octagar]] | [[Category:Octagar]] | ||
Revision as of 15:32, 17 January 2025
| ← 214edo | 215edo | 216edo → |
215et tempers out 4000/3969 and 65625/65536, and the patent val provides the optimal patent val for the 53 & 162 temperament (ditonic extension) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports hemififths.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.30 | -1.20 | +2.34 | +2.60 | +1.24 | +2.26 | +0.10 | +1.09 | -1.70 | -1.94 | +2.42 |
| Relative (%) | +23.3 | -21.5 | +41.9 | +46.6 | +22.2 | +40.5 | +1.9 | +19.5 | -30.4 | -34.8 | +43.4 | |
| Steps (reduced) |
341 (126) |
499 (69) |
604 (174) |
682 (37) |
744 (99) |
796 (151) |
840 (195) |
879 (19) |
913 (53) |
944 (84) |
973 (113) | |
Subsets and supersets
Since 215 factors into 5 × 43, 215edo contains 5edo and 43edo as its subsets.