Fifth-chroma temperaments: Difference between revisions

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==== Primary ====

* 77 & 80: [[Novamajor]], a temperament with a generator of 5/4 * S12, named because the interval colour of ~405{{cent}} is named a "novamajor third" by [[User:Godtone]]

: * The "5-limit seed" of novamajor is by splitting 25/24 into five parts of ~sqrt(128/125) = (128/125)1/2.

* 77 & 84: [[Absurdity]], the 1\7-period (at least) 29-limit temperament; note that 70edo also supports it in a reduced/slightly modified form

: * The "5-limit seed" of absurdity is by tempering out (81/80)5 / (25/24) (the absurdity comma) so that 25/24 is split into five flattened (underexaggerated) ~81/80's, which is equivalent to interpreting 1\7 as (10/9)/(81/80) because 2 / ((10/9)/(81/80) = 800/729)7 is equal to the square of the absurdity comma.

* 80 & 84: unnamed? proposed name: "quarterchromatic" from quartering the octave and having a comma-sized generator, four of which functions melodically as a type of chroma (though not as 25/24)

==== Secondary ====

* 77 & 87: [[Restles]]

: * The "2.3.13 seed" of restles is [[lesser tendoneutralic]], which observes (16/13)/(39/32) = 512/507 so that this interval is what divides 25/24 into five in 2.3.5.13 restles.

* 84 & 87: [[Mutt]]

: * The "5-limit seed" of mutt is by splitting 25/24 into 5 parts of ~cbrt(128/125) = (128/125)1/3.

* 77 & 94: [[Tsaharuk]]

* 80 & 87: "alt artoneutral": a version of [[Hemifamity temperaments#Artoneutral|artoneutral]] that uses a different mapping for prime 7

: * This has the same "5-limit seed" as artoneutral, but is actually more optimal for the 5-limit.

* 80 & 94: unnamed? proposed name: "pseudohemipyth"

* 87 & 94: [[Artoneutral]]

: * The "5-limit seed" of artoneutral is by splitting 25/24 into 5 parts of ~sqrt(81/80) = (81/80)1/2.

=== New temperament definitions ===

@@ Line 56: / Line 56: @@
 ==== Primary ====
 * 77 & 80: [[Novamajor]], a temperament with a generator of 5/4 * S12, named because the interval colour of ~405{{cent}} is named a "novamajor third" by [[User:Godtone]]
+: * The "5-limit seed" of novamajor is by splitting 25/24 into five parts of ~sqrt(128/125) = (128/125)<sup>1/2</sup>.
 * 77 & 84: [[Absurdity]], the 1\7-period (at least) 29-limit temperament; note that 70edo also supports it in a reduced/slightly modified form
+: * The "5-limit seed" of absurdity is by tempering out (81/80)<sup>5</sup> / (25/24) (the absurdity comma) so that 25/24 is split into five flattened (underexaggerated) ~81/80's, which is equivalent to interpreting 1\7 as (10/9)/(81/80) because 2 / ((10/9)/(81/80) = 800/729)<sup>7</sup> is equal to the square of the absurdity comma.
 * 80 & 84: unnamed? proposed name: "quarterchromatic" from quartering the octave and having a comma-sized generator, four of which functions melodically as a type of chroma (though not as 25/24)
 ==== Secondary ====
 * 77 & 87: [[Restles]]
+: * The "2.3.13 seed" of restles is [[lesser tendoneutralic]], which observes (16/13)/(39/32) = 512/507 so that this interval is what divides 25/24 into five in 2.3.5.13 restles.
+* 84 & 87: [[Mutt]]
+: * The "5-limit seed" of mutt is by splitting 25/24 into 5 parts of ~cbrt(128/125) = (128/125)<sup>1/3</sup>.
 * 77 & 94: [[Tsaharuk]]
 * 80 & 87: "alt artoneutral": a version of [[Hemifamity temperaments#Artoneutral|artoneutral]] that uses a different mapping for prime 7
+: * This has the same "5-limit seed" as artoneutral, but is actually more optimal for the 5-limit.
 * 80 & 94: unnamed? proposed name: "pseudohemipyth"
 * 87 & 94: [[Artoneutral]]
+: * The "5-limit seed" of artoneutral is by splitting 25/24 into 5 parts of ~sqrt(81/80) = (81/80)<sup>1/2</sup>.
 === New temperament definitions ===