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. | ||
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|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|31EDO]] but not in 69. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|69}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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== Scales == | == Scales == | ||
* Mavka[11] | * Mavka{{clarify}}[11], [[3L 8s]] – 66676667667 | ||
* | * Meantone[7], [[5L 2s]] (gen = 40\69) – 11 11 7 11 11 11 7 | ||
* | * Meantone[12], [[7L 5s]] (gen = 40\69) – 747474774747 | ||
== Music == | == Music == |