227edo: Difference between revisions
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m Added "harmonics in equal" table |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|227}} | |||
The equal temperament tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], 2200/2187, 3388/3375, and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], and [[847/845]]. | |||
227edo is accurate for the 13th harmonic, as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|227}} | |||
=== Subsets and supersets === | |||
227edo is the 49th [[prime edo]]. | |||
[[Category:Countercata]] | [[Category:Countercata]] | ||
Revision as of 09:20, 4 September 2023
| ← 226edo | 227edo | 228edo → |
The equal temperament tempers out 15625/15552 (kleisma) and [61 -37 -1⟩ in the 5-limit; 5120/5103, 65625/65536, and 117649/116640 in the 7-limit, so that it supports countercata. In the 11-limit, it tempers out 385/384, 2200/2187, 3388/3375, and 12005/11979, so that it provides the optimal patent val for 11-limit countercata. In the 13-limit, it tempers out 325/324, 352/351, 625/624, and 847/845.
227edo is accurate for the 13th harmonic, as the denominator of a convergent to log213, after 10 and before 5231.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.13 | -0.41 | -1.43 | -1.54 | +0.00 | +0.77 | -1.48 | +0.80 | +1.26 | +2.10 |
| Relative (%) | +0.0 | +21.4 | -7.8 | -27.0 | -29.1 | +0.0 | +14.6 | -28.0 | +15.1 | +23.8 | +39.7 | |
| Steps (reduced) |
227 (0) |
360 (133) |
527 (73) |
637 (183) |
785 (104) |
840 (159) |
928 (20) |
964 (56) |
1027 (119) |
1103 (195) |
1125 (217) | |
Subsets and supersets
227edo is the 49th prime edo.