2.5.7 subgroup: Difference between revisions
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{{Main|Tour of regular temperaments#Clans defined by a 2.5.7 (yaza nowa) comma}} | {{Main|Tour of regular temperaments#Clans defined by a 2.5.7 (yaza nowa) comma}} | ||
Some important [[diesis|dieses]] in the 2.5.7 subgroup are: | |||
* [[128/125|2/(5/4)<sup>3</sup>]], the [[enharmonic diesis]] (or just "diesis"), leading to [[augmented]] if tempered out. | |||
* [[16807/16384|2/(8/7)<sup>5</sup>]], the [[cloudy comma]], leading to [[cloudy]] if tempered, which can be likened in structural role to the enharmonic diesis but for prime 7 instead of prime 5. Equating it with the enharmonic diesis to form a general-purpose diesis results in [[rainy]] temperament, as their difference is the [[rainy comma]]. | |||
* [[50/49|(10/7)/(7/5)]], the [[septimal tritonic diesis]], leading to [[jubilic]] if tempered out. | |||
* [[256/245|(8/7)<sup>2</sup>/(5/4)]], which can be likened in structural role to the septimal tritonic diesis, leading to [[bapbo clan|bapbo]] if tempered out, considered below: | |||
==== Didacus (3136/3125) ==== | ==== Didacus (3136/3125) ==== | ||
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<nowiki />* In 2.5.7-targeted DKW tuning | <nowiki />* In 2.5.7-targeted DKW tuning | ||
==== | ==== Exotemperaments ==== | ||
The [[bapbo clan|bapbo]] [[exotemperament]] tempers out [[256/245]] = S6⋅S8 = S4/S7, equating [[35/32]] with [[8/7]], and making [[5/4]] the square of 8/7, which hence serves as the generator. This comma is over 70 cents, and pathologically equates the outer edges of the clusters around 1\6 and 5\6 to each other without also equating the middle interval with them (if this is done, the tuning reduces to 6edo). Therefore, bapbo can safely be considered an exotemperament – perhaps an analogue to [[mavila]]. | The [[bapbo clan|bapbo]] [[exotemperament]] tempers out [[256/245]] = S6⋅S8 = S4/S7, equating [[35/32]] with [[8/7]], and making [[5/4]] the square of 8/7, which hence serves as the generator. This comma is over 70 cents, and pathologically equates the outer edges of the clusters around 1\6 and 5\6 to each other without also equating the middle interval with them (if this is done, the tuning reduces to 6edo). Therefore, bapbo can safely be considered an exotemperament – perhaps an analogue to [[mavila]]. | ||