163edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|163}} | {{EDO intro|163}} | ||
==Theory== | == Theory == | ||
163edo tempers out 15625/15552 (kleisma) and 22876792454961/21990232555520 in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 413343/409600 in the 7-limit; 2187/2156, 2420/2401, 2835/2816 and 4375/4356 in the 11-limit; 351/350, 640/637, 975/968, 1188/1183, and 1573/1568 in the 13-limit. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|163}} | |||
=== | === Miscellany === | ||
163edo is the 38th [[prime edo]]. | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 09:16, 15 December 2022
| ← 162edo | 163edo | 164edo → |
Theory
163edo tempers out 15625/15552 (kleisma) and 22876792454961/21990232555520 in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 413343/409600 in the 7-limit; 2187/2156, 2420/2401, 2835/2816 and 4375/4356 in the 11-limit; 351/350, 640/637, 975/968, 1188/1183, and 1573/1568 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.57 | -3.49 | +2.95 | +2.22 | +0.83 | -1.26 | +1.30 | -1.89 | -3.03 | +0.38 | -2.51 |
| Relative (%) | -34.9 | -47.4 | +40.1 | +30.2 | +11.3 | -17.2 | +17.7 | -25.6 | -41.2 | +5.2 | -34.1 | |
| Steps (reduced) |
258 (95) |
378 (52) |
458 (132) |
517 (28) |
564 (75) |
603 (114) |
637 (148) |
666 (14) |
692 (40) |
716 (64) |
737 (85) | |
Miscellany
163edo is the 38th prime edo.