39edo: Difference between revisions
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39edo, with its 400{{c}} major third, [[tempering out|tempers out]] the [[128/125|diesis]] (128/125), and using the 39d val, the septimal comma, [[64/63]], as well as [[126/125]] are added to the comma list. In the 11-limit we find that the equal temperament tempers out [[99/98]] and [[121/120]]. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to [[12edo|12et]] in [[support]]ing [[augene]], and is in fact, an excellent choice for a 7-limit augene tuning. It also tempers out the [[amity comma]] (1600000/1594323), and supports the variant of amity known as [[accord]]. | 39edo, with its 400{{c}} major third, [[tempering out|tempers out]] the [[128/125|diesis]] (128/125), and using the 39d val, the septimal comma, [[64/63]], as well as [[126/125]] are added to the comma list. In the 11-limit we find that the equal temperament tempers out [[99/98]] and [[121/120]]. Tempering out both 128/125 and 64/63 makes 39et, in some few ways, allied to [[12edo|12et]] in [[support]]ing [[augene]], and is in fact, an excellent choice for a 7-limit augene tuning. It also tempers out the [[amity comma]] (1600000/1594323), and supports the variant of amity known as [[accord]]. | ||
Alternatively, the patent val tempers out [[49/48]] to yield [[semaphore]], and provides a reasonable tuning of [[triforce]] beyond [[15edo]], and optimizes both its semaphore and augmented components by tuning the fifth sharp. The 39c val supports [[negri]]. | Alternatively, the patent val tempers out [[49/48]] to yield [[semaphore]], and provides a reasonable tuning of [[triforce]] beyond [[15edo]], and optimizes both its semaphore and augmented components by tuning the fifth sharp. The 39c val supports [[negri]] and 5-limit [[Syntonic–chromatic_equivalence_continuum#Sixix_(5-limit)|sixix]]. | ||
If we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]] through the 39bc val, and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]] and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat. | If we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]] through the 39bc val, and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]] and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat. | ||
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods <br | ! Periods <br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
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| 5\39 | | 5\39 | ||
| 153.8 | | 153.8 | ||
| | | [[Nusecond]] (39df) | ||
| [[1L 6s]], [[7L 1s]], [[8L 7s]], [[8L 15s]], [[8L 23s]] | | [[1L 6s]], [[7L 1s]], [[8L 7s]], [[8L 15s]], [[8L 23s]] | ||
|- | |- | ||
| Line 1,123: | Line 1,123: | ||
| 10\39 | | 10\39 | ||
| 307.7 | | 307.7 | ||
| | | | ||
| [[3L 1s]], [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], [[4L 19s]], [[4L 23s]], [[4L 27s]], [[4L 31s]] | | [[3L 1s]], [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], [[4L 19s]], [[4L 23s]], [[4L 27s]], [[4L 31s]] | ||
|- | |- | ||
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|- | |- | ||
| 3 | | 3 | ||
| | | 3\39 | ||
| | | 92.3 | ||
| [[ | | [[Augene]] (39d) | ||
| [[3L 3s]], [[ | | [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]], [[12L 15s]] | ||
|- | |||
| 3 | |||
| 4\39 | |||
| 123.0 | |||
| [[Deflated]] (39bd) | |||
| [[3L 3s]], [[3L 6s]], [[9L 3s]], [[9L 12s]], [[9L 21s]] | |||
|- | |- | ||
| 3 | | 3 | ||
| | | 5\39 | ||
| | | 153.8 | ||
| [[Triforce]] (39) | | [[Triforce]] (39) | ||
| [[3L 3s]], [[6L 3s]], [[9L 6s]], [[15L 9s]] | | [[3L 3s]], [[6L 3s]], [[9L 6s]], [[15L 9s]] | ||
|- | |- | ||
| 3 | | 3 | ||
| | | 6\39 | ||
| | | 184.6 | ||
| [[ | | [[Terrain]] | ||
| [[3L 3s]], [[ | | [[3L 3s]], [[6L 3s]], [[6L 9s]], [[6L 15]], [[6L 21s]], [[6L 27s]] | ||
|- | |- | ||
| 13 | | 13 | ||
| | | 1\39 | ||
| | | 30.8 | ||
| [[Tridecatonic]] | | [[Tridecatonic]] | ||
| [[13L 13s]] | | [[13L 13s]] | ||
|} | |} | ||
<nowiki/>* [[ | <nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | ||
39et can be detempered to [[mirkat]] (39df & 72) and [[familia]] (39df & 113). | |||
== Octave stretch or compression == | == Octave stretch or compression == | ||
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It also offers ''many'' possible [[pentatonic]] scales, including the [[2L 3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using that scale or using something like the [[quasi-equal]] 8 8 8 8 7 or 8 8 7 8 8. | It also offers ''many'' possible [[pentatonic]] scales, including the [[2L 3s]] mos (which is 9 7 7 9 7). [[Slendro]] can be approximated using that scale or using something like the [[quasi-equal]] 8 8 8 8 7 or 8 8 7 8 8. | ||
An expressive [[pentatonic]] subset of [[oneirotonic]] - 9 6 9 9 6 - is available because 39edo contains [[13edo]]. | |||
Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated. | Many Asian{{clarify|which ones specifically}} and [[African music|African]] {{clarify|which ones specifically}} musical styles can thus be accommodated. | ||
== Scales == | == Scales == | ||
; [[Augene]] scales | |||
* | * Augene[6] [[MOS scale]]: 10 3 10 3 10 3 | ||
* [[ | * Augene[9] MOS: 3 7 3 3 7 3 3 7 3 | ||
* [[3L 6s]] (augene9) [[modmos]]: 7 3 3 3 7 3 3 7 3 | |||
* Augene[12] MOS: 3 3 4 3 3 3 4 3 3 3 4 3 | |||
* Augene[15] MOS: 3 3 1 3 3 3 3 1 3 3 3 3 1 3 3 | |||
; [[Quasisuper]] scales | |||
* Quasisuper[7] MOS: 7 7 2 7 7 7 2 | |||
* Quasisuper[7] [[5-limit|pental]] modmos: 7 6 3 7 6 7 33 | |||
* Extended quasisuper: 4 3 6 3 4 3 6 4 3 3 | * Extended quasisuper: 4 3 6 3 4 3 6 4 3 3 | ||
* Quasisuper[22] MOS | * Quasisuper[22] MOS (resembles [[Indian]] [[sruti]]): 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 | ||
* Slendro approximations: 9 7 7 9 7 or 8 8 8 8 7 or 8 8 7 8 8 | |||
; [[Amity]] scales | |||
* Amity[7] MOS: 6 6 5 6 5 6 5 | |||
* Amity[11] MOS: 5 1 5 5 1 5 1 5 5 1 5 | |||
* Amity[18] MOS: 1 4 1 4 1 1 4 1 1 4 1 4 1 1 4 1 4 1 | |||
* Amity[25] MOS: 1 3 1 1 1 3 1 1 3 1 1 1 3 1 1 1 3 1 1 3 1 1 1 3 1 | |||
* Amity[32] MOS: 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 | |||
; Others | |||
* Pelog approximation: 4 5 13 4 13 | |||
* Slendro/[[equipentatonic]] approximations: 9 7 7 9 7 ''or'' 8 8 8 8 7 ''or'' 8 8 7 8 8 | |||
* ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]'' | * ''The scales listed in: [[User:BudjarnLambeth/Quasipelog theory]]'' | ||
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[[Category:Listen]] | [[Category:Listen]] | ||