39edo: Difference between revisions
→Intervals: + intervals of 13 |
m →As a tuning of other temperaments: link here |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 14: | Line 14: | ||
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. | ||
| Line 223: | Line 223: | ||
| 2 | | 2 | ||
| 61.5 | | 61.5 | ||
| [[33/32]] | | [[33/32]], ''[[256/243]]'' | ||
| | | | ||
| ''[[21/20]]'', [[36/35]] | | ''[[21/20]]'', [[36/35]] | ||
| Line 272: | Line 272: | ||
| 9 | | 9 | ||
| 276.9 | | 276.9 | ||
| | | ''[[32/27]]'' | ||
| | | | ||
| | | | ||
| Line 307: | Line 307: | ||
| 14 | | 14 | ||
| 430.8 | | 430.8 | ||
| | | ''[[81/64]]'' | ||
| | | | ||
| ''[[35/27]]'' | | ''[[35/27]]'' | ||
| Line 384: | Line 384: | ||
| 25 | | 25 | ||
| 769.2 | | 769.2 | ||
| | | ''[[128/81]]'' | ||
| | | | ||
| ''[[54/35]]'' | | ''[[54/35]]'' | ||
| Line 419: | Line 419: | ||
| 30 | | 30 | ||
| 923.1 | | 923.1 | ||
| | | ''[[27/16]]'' | ||
| | | | ||
| | | | ||
| Line 468: | Line 468: | ||
| 37 | | 37 | ||
| 1138.5 | | 1138.5 | ||
| [[64/33]] | | [[64/33]], ''[[243/128]]'' | ||
| | | | ||
| [[35/18]], ''[[40/21]]'' | | [[35/18]], ''[[40/21]]'' | ||