Aberschismic family: Difference between revisions

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=== Overview to extensions ===

==== 11- and 13-limit extensions ====

Strong extensions of aberschismic are [[#Pele|pele]], [[#Laka|laka]], [[#Akea|akea]], and [[#Lono|lono]]. The rest are weak extensions. Using the arrow to represent the syntonic~septimal comma, pele finds the [[11/8]] as a down diminished fifth (C–vG♭); laka, up augmented third (C–^E♯); akea, double-up fourth (C–^^F); lono, triple-down augmented fourth (C–v<sup>3</sup>F♯). All these extensions follow the trend of tuning the fifth a little sharp~~. Thus~~ a ~~successful~~ mapping of 13 ~~can be found by fixing the~~ [[13/11]] at the minor third (~~C–Eb~~), tempering out [[~~352/351~~]], [[847/845]], and [[2080/2079]].

Strong extensions of aberschismic are [[#Pele|pele]], [[#Laka|laka]], [[#Akea|akea]], and [[#Lono|lono]]. The rest are weak extensions. Using the arrow to represent the syntonic~septimal comma, pele finds the [[11/8]] as a down diminished fifth (C–vG♭); laka, up augmented third (C–^E♯); akea, double-up fourth (C–^^F); lono, triple-down augmented fourth (C–v<sup>3</sup>F♯). All these extensions follow the trend of tuning the fifth a little sharp, so a mapping for 13 arises from identifying [[13/11]] with the minor third (C–E♭), which is further facilitated by the fact that the minor third in aberschismic is the exact mean of [[6/5]] and [[7/6]], thus tempering out the [[semiparticular]] [[847/845]] ([[S-expression|S11/S13]]) and by extension [[352/351]] and [[2080/2079]].

Temperaments discussed elsewhere include:

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==== Subgroup extensions ====

A notable 2.3.5.7.19-subgroup extension, counterpyth, is considered in [[#Subgroup extensions]].

== Pele ==

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 === Overview to extensions ===
 ==== 11- and 13-limit extensions ====
-Strong extensions of aberschismic are [[#Pele|pele]], [[#Laka|laka]], [[#Akea|akea]], and [[#Lono|lono]]. The rest are weak extensions. Using the arrow to represent the syntonic~septimal comma, pele finds the [[11/8]] as a down diminished fifth (C–vG♭); laka, up augmented third (C–^E♯); akea, double-up fourth (C–^^F); lono, triple-down augmented fourth (C–v<sup>3</sup>F♯). All these extensions follow the trend of tuning the fifth a little sharp. Thus a successful mapping of 13 can be found by fixing the [[13/11]] at the minor third (C–Eb), tempering out [[352/351]], [[847/845]], and [[2080/2079]].
+Strong extensions of aberschismic are [[#Pele|pele]], [[#Laka|laka]], [[#Akea|akea]], and [[#Lono|lono]]. The rest are weak extensions. Using the arrow to represent the syntonic~septimal comma, pele finds the [[11/8]] as a down diminished fifth (C–vG♭); laka, up augmented third (C–^E♯); akea, double-up fourth (C–^^F); lono, triple-down augmented fourth (C–v<sup>3</sup>F♯). All these extensions follow the trend of tuning the fifth a little sharp, so a mapping for 13 arises from identifying [[13/11]] with the minor third (C–E♭), which is further facilitated by the fact that the minor third in aberschismic is the exact mean of [[6/5]] and [[7/6]], thus tempering out the [[semiparticular]] [[847/845]] ([[S-expression|S11/S13]]) and by extension [[352/351]] and [[2080/2079]].
 Temperaments discussed elsewhere include:
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 ==== Subgroup extensions ====
 A notable 2.3.5.7.19-subgroup extension, counterpyth, is considered in [[#Subgroup extensions]].
 == Pele ==