131edo: Difference between revisions
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== Theory == | == Theory == | ||
131edo is the next [[ | 131edo is the next [[edo]] after [[81edo]] on the [[Golden meantone|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bophier]]. | ||
=== Odd harmonics === | |||
{{ | {{Harmonics in equal|131}} | ||
=== Subsets and supersets === | |||
131edo is the 32nd [[prime]] edo. | |||
== Scales == | |||
=== Mos scales === | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
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[[Category:Armodue]] | [[Category:Armodue]] | ||
[[Category:Bohpier]] | [[Category:Bohpier]] | ||
[[Category:Immunity]] | [[Category:Immunity]] | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category: | [[Category:Golden meantone]] | ||
Revision as of 16:56, 27 May 2024
| ← 130edo | 131edo | 132edo → |
Theory
131edo is the next edo after 81edo on the Golden Tone System (Das Goldene Tonsystem) of Thorvald Kornerup, using the 131b val. The patent val has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out 81/80 it tempers out the immunity comma, 1638400/1594323. In the 7-limit it tempers out 3125/3087 and 245/243, so that it supports bophier.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.39 | -1.58 | +2.17 | -2.38 | -1.70 | +2.22 | +1.81 | -4.19 | -4.38 | -3.61 | +3.79 |
| Relative (%) | +37.0 | -17.3 | +23.7 | -26.0 | -18.6 | +24.2 | +19.7 | -45.8 | -47.9 | -39.4 | +41.3 | |
| Steps (reduced) |
208 (77) |
304 (42) |
368 (106) |
415 (22) |
453 (60) |
485 (92) |
512 (119) |
535 (11) |
556 (32) |
575 (51) |
593 (69) | |
Subsets and supersets
131edo is the 32nd prime edo.
Scales
Mos scales
| 33 16 33 33 16 | Pentatonic (comparable with 8edo and 99edo) |
| 23 23 8 23 23 23 8 | Pythagorean tuning (comparable with 17edo) |
| 21 21 13 21 21 21 13 | Meantone tuning (comparable with 50edo) |
| 19 12 19 19 12 19 19 12 | Father Tuning (comparable with 55edo) |
| 18 18 18 18 18 18 18 5 | Porcupine Tuning (comparable with 29edo and 80edo) |
| 17 17 17 6 17 17 17 17 6 | Superdiatonic tuning (comparable with 23edo) |
| 16 16 16 16 16 16 16 16 3 | Bohpier tuning (comparable with 41edo) |
| 13 13 9 13 13 13 9 13 13 13 9 | Sensi-11 Tuning |
| 11 11 11 11 11 5 11 11 11 11 11 11 5 | De Vries 13-tone Tuning |
| 10 10 10 7 10 10 10 10 7 10 10 10 10 7 | Ketradektriatoh Tuning |
| 21 17 21 17 17 21 17 | mohaha7 |
| 4 17 17 17 4 17 17 4 17 17 | mohaha10 |