69edo: Difference between revisions

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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{{c}}. 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 12-tone 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 and stems from a temperament tempering out 3125/3087 along with 81/80. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional diatonic.

69edo offers two kinds of meantone 12-tone 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 and stems from a temperament tempering out [[3125/3087]] along with [[81/80]]. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional diatonic.

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. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap|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. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap|31 & 69}} variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69.

The [[concoctic scale]] for 69edo is 22\69, and the corresponding rank two temperament is {{nowrap|22 & 69}}, defined by tempering out the [-41, 1, 17⟩ comma in the 5-limit.

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; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)

* [https://www.youtube.com/shorts/4XBELeySMPk ''Compass - Mili (microtonal cover in 69edo)''] (2025)

; [[Eliora]]

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 edo 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{{c}}. 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.
-edo offers two kinds of meantone 12-tone 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 and stems from a temperament tempering out 3125/3087 along with 81/80. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional diatonic.
+edo offers two kinds of meantone 12-tone 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 and stems from a temperament tempering out [[3125/3087]] along with [[81/80]]. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s|tcherepnin]] scale instead of traditional diatonic.
-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. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap|31 &amp; 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. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap|31 &amp; 69}} variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69.
 The [[concoctic scale]] for 69edo is 22\69, and the corresponding rank two temperament is {{nowrap|22 &amp; 69}}, defined by tempering out the [-41, 1, 17⟩ comma in the 5-limit.
@@ Line 591: / Line 591: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)
+* [https://www.youtube.com/shorts/4XBELeySMPk ''Compass - Mili (microtonal cover in 69edo)''] (2025)
 ; [[Eliora]]