69edo: Difference between revisions
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== Theory == | == Theory == | ||
69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. Such a fifth is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes. | 69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. Such a fifth is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes. | ||
69edo offers two kinds of meantone dodecaphonic scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium|lithium]] scale, which has a 6:5 step ratio. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional chromatic. | |||
In the [[7-limit]] it is a [[mohajira]] system, tempering out 6144/6125, but not a septimal meantone system, as [[126/125]] maps to one step. It also [[support]]s the 12&69 temperament tempering out 3125/3087 along with [[81/80]]. In the 11-limit it tempers out [[99/98]], and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69. | In the [[7-limit]] it is a [[mohajira]] system, tempering out 6144/6125, but not a septimal meantone system, as [[126/125]] maps to one step. It also [[support]]s the 12&69 temperament tempering out 3125/3087 along with [[81/80]]. In the 11-limit it tempers out [[99/98]], and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69. | ||
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* Meantone[12], [[7L 5s]] (gen = 40\69) – 747474774747 | * Meantone[12], [[7L 5s]] (gen = 40\69) – 747474774747 | ||
* Baroque[12], 477474747747 (as proposed by Pianoteq plugin) | * Baroque[12], 477474747747 (as proposed by Pianoteq plugin) | ||
* Lithium[9], 11 6 6 11 6 6 11 6 6 - [[3L 6s]] | |||
* Lithium[12], 566656665666 | |||
== Music == | == Music == | ||