4650edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|4650}} 4650edo is consistent in the 15-odd-limit, with optional additions of 19 and 31. It provides the optimal patent..." |
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{{EDO intro|4650}} | {{EDO intro|4650}} | ||
4650edo is [[consistent]] in the [[15-odd-limit]], with optional additions of [[19/16|19]] and [[31/16|31]]. It provides the optimal patent val for the 30th-octave temperament [[zinc]] in the 7-limit and the 13-limit. | 4650edo is [[consistent]] in the [[15-odd-limit]], with optional additions of [[19/16|19]] and [[31/16|31]]. Some of the simpler commas it [[tempering out|tempers out]] include [[250047/250000]] in the 7-limit; [[9801/9800]] and [[151263/151250]] in the 11-limit; [[10648/10647]] and [[123201/123200]] in the 13-limit. It provides the optimal patent val for the 30th-octave temperament [[zinc]] in the 7-limit and the 13-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|4650}} | {{Harmonics in equal|4650}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 4650 factors as {{Factorization|4650}}, 4650edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 15, 25, 30, 31, 50, 62, 75, 93, 150, 155, 186, 310, 465, 775, 930, 1550, 2325 }}. | |||
Since 4650 factors as {{Factorization|4650}}, 4650edo has subset edos {{EDOs| | |||
Revision as of 09:59, 12 January 2025
| ← 4649edo | 4650edo | 4651edo → |
4650edo is consistent in the 15-odd-limit, with optional additions of 19 and 31. Some of the simpler commas it tempers out include 250047/250000 in the 7-limit; 9801/9800 and 151263/151250 in the 11-limit; 10648/10647 and 123201/123200 in the 13-limit. It provides the optimal patent val for the 30th-octave temperament zinc in the 7-limit and the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.020 | +0.009 | -0.052 | -0.092 | -0.012 | +0.077 | +0.035 | +0.113 | +0.100 | -0.003 |
| Relative (%) | +0.0 | -7.6 | +3.4 | -20.0 | -35.7 | -4.5 | +29.8 | +13.7 | +43.7 | +38.8 | -1.3 | |
| Steps (reduced) |
4650 (0) |
7370 (2720) |
10797 (1497) |
13054 (3754) |
16086 (2136) |
17207 (3257) |
19007 (407) |
19753 (1153) |
21035 (2435) |
22590 (3990) |
23037 (4437) | |
Subsets and supersets
Since 4650 factors as 2 × 3 × 52 × 31, 4650edo has subset edos 2, 3, 5, 6, 10, 15, 25, 30, 31, 50, 62, 75, 93, 150, 155, 186, 310, 465, 775, 930, 1550, 2325.