21ed5/2: Difference between revisions
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'''21ed5/2''' is the equal division of the [[5/2]] interval into 21 parts of approximately 75.539 [[cent]]s each. It roughly corresponds to [[16edo]]. | '''21ed5/2''' is the equal division of the [[5/2]] interval into 21 parts of approximately 75.539 [[cent]]s each. It roughly corresponds to [[16edo]]. | ||
== Theory == | == Theory == | ||
From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit. | From a no-threes point of view, 21ed5/2 tempers out [[50/49]] in the 7-limit (being a jubilic system similar to [[13ed5/2]]), [[625/616]] and [[176/175]] in the 11-limit, and 143/140, 715/686 and [[847/845]] in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic. | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|21|5|2}} | {{Harmonics in equal|21|5|2}} | ||
Revision as of 01:15, 12 July 2023
| ← 20ed5/2 | 21ed5/2 | 22ed5/2 → |
(semiconvergent)
(semiconvergent)
21ed5/2 is the equal division of the 5/2 interval into 21 parts of approximately 75.539 cents each. It roughly corresponds to 16edo.
Theory
From a no-threes point of view, 21ed5/2 tempers out 50/49 in the 7-limit (being a jubilic system similar to 13ed5/2), 625/616 and 176/175 in the 11-limit, and 143/140, 715/686 and 847/845 in the 13-limit. It is not particularly excellent as a no-threes system with the 5/4 and 7/4 being noticeably off, but can work for 5/2-equivalent jubilic.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.6 | -13.5 | +17.2 | +8.6 | -4.9 | +30.4 | +25.9 | -27.0 | +17.2 | +3.3 | +3.8 |
| Relative (%) | +11.4 | -17.9 | +22.8 | +11.4 | -6.4 | +40.3 | +34.2 | -35.7 | +22.8 | +4.4 | +5.0 | |
| Steps (reduced) |
16 (16) |
25 (4) |
32 (11) |
37 (16) |
41 (20) |
45 (3) |
48 (6) |
50 (8) |
53 (11) |
55 (13) |
57 (15) | |