636edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
Since {{nowrap|636 {{=}} 12 × 53}}, 636edo shares the excellent [[3/1|harmonic 3]] with [[53edo]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|636}} | {{Harmonics in equal|636}} | ||
=== Subsets and supersets === | |||
Since 636 factors into {{factorization|636}}, 636edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 53, 106, 159, 212, and 318 }}. | |||
== Intervals == | == Intervals == | ||
{{ | {{Main|Table of 636edo intervals}} | ||
Latest revision as of 17:47, 20 February 2025
| ← 635edo | 636edo | 637edo → |
636 equal divisions of the octave (abbreviated 636edo or 636ed2), also called 636-tone equal temperament (636tet) or 636 equal temperament (636et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 636 equal parts of about 1.89 ¢ each. Each step represents a frequency ratio of 21/636, or the 636th root of 2.
Theory
Since 636 = 12 × 53, 636edo shares the excellent harmonic 3 with 53edo.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.068 | +0.479 | -0.901 | -0.136 | -0.375 | -0.905 | +0.411 | +0.705 | +0.600 | +0.917 | +0.028 |
| Relative (%) | -3.6 | +25.4 | -47.8 | -7.2 | -19.9 | -48.0 | +21.8 | +37.4 | +31.8 | +48.6 | +1.5 | |
| Steps (reduced) |
1008 (372) |
1477 (205) |
1785 (513) |
2016 (108) |
2200 (292) |
2353 (445) |
2485 (577) |
2600 (56) |
2702 (158) |
2794 (250) |
2877 (333) | |
Subsets and supersets
Since 636 factors into 22 × 3 × 53, 636edo has subset edos 2, 3, 4, 6, 12, 53, 106, 159, 212, and 318.