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'''131-EDO''', or '''131-tET''', divides the octave into 131 equal steps of approx. 9.1603 Cents, each one. 131edo is the next [[EDO|EDO]], after [[81edo|81edo]], on the "Golden Tone System" ([[Das_Goldene_Tonsystem|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 [[Sensamagic_clan#Bohpier|bophier temperament]].
{{Infobox ET}}
{{ED intro}}


131edo is the 32nd [[prime_numbers|prime]] EDO.
== Theory ==
131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1|3]] is quite large. However, it 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 [[bohpier]].


<u>'''Some MOS Scales in 131-EDO:'''</u>
131edo is also notable for having a good approximation to [[natave|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and logarithmic divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[4/3]] (2\7[[EDN|edn]] = 54\131), [[5/4]] (2\9edn = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.


=== Odd harmonics ===
{{Harmonics in equal|131|columns=15}}
=== Subsets and supersets ===
131edo is the 32nd [[prime]] edo, following [[127edo]] and before [[137edo]].
== Scales ==
=== Mos scales ===
{| class="wikitable"
{| class="wikitable"
|-
|-
| | 33 16 33 33 16
| 33 16 33 33 16
| | [[3L_2s|Pentatonic]] (comparable with [[8edo|8edo]] and [[99edo|99edo]])
| [[3L_2s|Pentatonic]] (comparable with [[8edo]] and [[99edo]])
|-
|-
| | 23 23 8 23 23 23 8
| 23 23 8 23 23 23 8
| | [[5L_2s|Pythagorean tuning]] (comparable with [[17edo|17edo]])
| [[5L_2s|Pythagorean tuning]] (comparable with [[17edo]])
|-
|-
| | 21 21 13 21 21 21 13
| 21 21 13 21 21 21 13
| | [[5L_2s|Meantone tuning]] (comparable with [[50edo|50edo]])
| [[5L_2s|Meantone tuning]] (comparable with [[50edo]])
|-
|-
| | 19 12 19 19 12 19 19 12
| 19 12 19 19 12 19 19 12
| | [[5L_3s|Father Tuning]] (comparable with [[55edo|55edo]])
| [[5L_3s|Oneirotonic tuning]] (comparable with [[55edo]])
|-
|-
| | 18 18 18 18 18 18 18 5
| 18 18 18 18 18 18 18 5
| | [[7L_1s|Porcupine Tuning]] (comparable with [[29edo|29edo]] and [[80edo|80edo]])
| [[7L_1s|Porcupine tuning]] (comparable with [[29edo]] and [[80edo]])
|-
|-
| | 17 17 17 6 17 17 17 17 6
| 17 17 17 6 17 17 17 17 6
| | [[7L_2s|Superdiatonic tuning]] (comparable with [[23edo|23edo]])
| [[7L_2s|Superdiatonic tuning]] (comparable with [[23edo]])
|-
|-
| | 13 13 9 13 13 13 9 13 13 13 9
| 16 16 16 16 16 16 16 16 3
| | Improper [[Sensi-11_Tuning|Sensi-11 Tuning]]
| [[8L 1s|Bohpier tuning]] (comparable with [[41edo]])
|-
|-
| | 11 11 11 11 11 5 11 11 11 11 11 11 5
| 13 13 9 13 13 13 9 13 13 13 9
| | De Vries 13-tone Tuning
| [[8L 3s|Sensi-11 Tuning]]
|-
|-
| | 10 10 10 7 10 10 10 10 7 10 10 10 10 7
| 11 11 11 11 11 5 11 11 11 11 11 11 5
| | [[11L_3s|Ketradektriatoh Tuning]]
| De Vries 13-tone Tuning
|-
|-
| | 21 17 21 17 17 21 17
| 10 10 10 7 10 10 10 10 7 10 10 10 10 7
| | [[mohaha7|mohaha7]]
| [[11L_3s|Ketradektriatoh Tuning]]
|-
|-
| | 4 17 17 17 4 17 17 4 17 17
| 21 17 21 17 17 21 17
| | [[mohaha10|mohaha10]]
| [[mohaha7]]
|-
| 4 17 17 17 4 17 17 4 17 17
| [[mohaha10]]
|}
|}


[[Category:131-tone]]
[[Category:131edo]]
[[Category:Armodue]]
[[Category:Bohpier]]
[[Category:Bohpier]]
[[Category:Golden]]
[[Category:Golden meantone]]
[[Category:Immunity]]
[[Category:Immunity]]
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Prime EDO]]
[[Category:Golden meantone]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/131edo"