Mint temperaments: Difference between revisions

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This ~~is a collection of low~~ [[~~complexity]], high [[error]], [[regular~~ temperament|~~temperaments~~]] which [[temper out]] the septimal ~~quarter-tone~~, [[36/35]]. 36 is ~~[[Wikipedia:~~ Square triangular number|both]] a [http://mathworld.wolfram.com/SquareNumber.html square] and a [[triangular number]], and this helps make 36/35 a septimal interval of considerable significance. These temperaments ~~equate~~ [[6/5]] with [[7/6]], [[5/4]] with [[9/7]], and [[7/4]] with [[9/5]], so minor and major thirds and sixths are intervals of 5 and 7 at the same time.

This page collects [[rank-2 temperament|rank-2]] '''mint temperaments''', which [[temper out]] the septimal quartertone, [[36/35]]. 36 is {{w|Square triangular number|both}} a [http://mathworld.wolfram.com/SquareNumber.html square] and a [[triangular number]], and this helps make 36/35 a septimal interval of considerable significance. These temperaments are of low [[complexity]] and high [[error]], equating [[6/5]] with [[7/6]], [[5/4]] with [[9/7]], and [[7/4]] with [[9/5]], so minor and major thirds and sixths are intervals of 5 and 7 at the same time.

For the family of [[rank-3 temperament]]s, see [[Mint family]].

Temperaments discussed elsewhere include

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* ''[[Rip]]'' (+2560/2401) → [[Ripple family #Rip|Ripple family]]

* ''[[Whitewood]]'' (+2187/2048) → [[Whitewood family #Septimal whitewood|Whitewood family]]

Discussed below are penta, progression, subklei, naian, slurpee, and shallowtone, in the order of increasing [[badness]].

== Penta ==

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 {{Technical data page}}
-This is a collection of low [[complexity]], high [[error]], [[regular temperament|temperaments]] which [[temper out]] the septimal quarter-tone, [[36/35]]. 36 is [[Wikipedia: Square triangular number|both]] a [http://mathworld.wolfram.com/SquareNumber.html square] and a [[triangular number]], and this helps make 36/35 a septimal interval of considerable significance. These temperaments equate [[6/5]] with [[7/6]], [[5/4]] with [[9/7]], and [[7/4]] with [[9/5]], so minor and major thirds and sixths are intervals of 5 and 7 at the same time.
+This page collects [[rank-2 temperament|rank-2]] '''mint temperaments''', which [[temper out]] the septimal quartertone, [[36/35]]. 36 is {{w|Square triangular number|both}} a [http://mathworld.wolfram.com/SquareNumber.html square] and a [[triangular number]], and this helps make 36/35 a septimal interval of considerable significance. These temperaments are of low [[complexity]] and high [[error]], equating [[6/5]] with [[7/6]], [[5/4]] with [[9/7]], and [[7/4]] with [[9/5]], so minor and major thirds and sixths are intervals of 5 and 7 at the same time.
+For the family of [[rank-3 temperament]]s, see [[Mint family]].
 Temperaments discussed elsewhere include
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 * ''[[Rip]]'' (+2560/2401) → [[Ripple family #Rip|Ripple family]]
 * ''[[Whitewood]]'' (+2187/2048) → [[Whitewood family #Septimal whitewood|Whitewood family]]
+Discussed below are penta, progression, subklei, naian, slurpee, and shallowtone, in the order of increasing [[badness]].
 == Penta ==

Mint temperaments: Difference between revisions

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