137edo: Difference between revisions
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{{EDO intro|137}} | |||
A diagram of 7-limit | == Theory == | ||
137edo provides the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament tempering out [[2430/2401]]. It tempers out 2109375/2097152 ([[semicomma]]) in the 5-limit; [[225/224]] and [[1728/1715]] in the 7-limit; [[243/242]] in the 11-limit; [[351/350]] in the 13-limit; [[375/374]] and [[442/441]] in the 17-limit; and [[324/323]] and [[495/494]] in the 19-limit. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|137}} | |||
=== Subsets and supersets === | |||
Since 137 is the 33rd [[prime number]], 137edo has no proper divisors aside from 1. | |||
== Diagrams == | |||
A diagram of 7-limit orwell based on the 31\137edo generator: | |||
[[File:137edo_MOS_031_demo_correction.png|alt=137edo_MOS_031_demo_correction.png|137edo_MOS_031_demo_correction.png]] | [[File:137edo_MOS_031_demo_correction.png|alt=137edo_MOS_031_demo_correction.png|137edo_MOS_031_demo_correction.png]] | ||
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[[:File:137edo_MOS_031.svg|137edo_MOS_031.svg]] | [[:File:137edo_MOS_031.svg|137edo_MOS_031.svg]] | ||
[[Category:Nuwell]] | [[Category:Nuwell]] | ||
[[Category:Orwell]] | [[Category:Orwell]] | ||
[[Category: | [[Category:Orson]] | ||
Revision as of 11:43, 2 September 2023
| ← 136edo | 137edo | 138edo → |
Theory
137edo provides the optimal patent val for 7-limit orwell temperament and for the planar temperament tempering out 2430/2401. It tempers out 2109375/2097152 (semicomma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242 in the 11-limit; 351/350 in the 13-limit; 375/374 and 442/441 in the 17-limit; and 324/323 and 495/494 in the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.23 | -0.91 | +3.44 | +0.51 | +0.35 | +0.15 | +0.30 | +2.38 | +4.00 | +2.41 |
| Relative (%) | +0.0 | -14.0 | -10.4 | +39.2 | +5.8 | +4.0 | +1.8 | +3.4 | +27.2 | +45.7 | +27.5 | |
| Steps (reduced) |
137 (0) |
217 (80) |
318 (44) |
385 (111) |
474 (63) |
507 (96) |
560 (12) |
582 (34) |
620 (72) |
666 (118) |
679 (131) | |
Subsets and supersets
Since 137 is the 33rd prime number, 137edo has no proper divisors aside from 1.
Diagrams
A diagram of 7-limit orwell based on the 31\137edo generator:
