245/242: Difference between revisions

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~~The~~ '''frostma''' ~~([[ratio]]: 245/242~~, ~~[[monzo]]: {{monzo| -1 0 1 2 -2 }})~~ is a [[small comma|small]] [[11-limit]] [[comma]] ~~used in~~ the ~~construction~~ of ~~the~~ [[~~No-threes subgroup temperaments #Frostburn|frostburn~~]] ~~temperament~~.

'''245/242''', the '''frostma''', is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 21.3 [[cent]]s. It is the amount by which [[5/2]] exceeds a stack of two [[11/7]]'s.

It can be factored into ([[243/242]])([[245/243]]) and ([[896/891]])([[2835/2816]]).

It can be factored into ([[243/242]])⋅([[245/243]]) and ([[896/891]])⋅([[2835/2816]]).

== Temperaments ==

Tempering out this comma alone in the 11-limit results in the rank-4 '''frostmic ~~temperament~~''' (→ [[Catalog of rank-4 temperaments #Frostmic (245/242)]]), ~~where~~ a stack of two [[11/7]]'s is equated with a [[5/2]] major tenth, enabling [[frostmic chords]].

[[Tempering out]] this comma alone in the 11-limit results in the rank-4 '''frostmic''' temperament (→ [[Catalog of rank-4 temperaments #Frostmic (245/242)]]), or in the 2.5.7.11 subgroup, the rank-3 '''frost''' temperament. In either case, a stack of two 11/7's is equated with a 5/2 major tenth, enabling [[frostmic chords]]. It is also used in the construction of the [[No-threes subgroup temperaments #Frostburn|frostburn]] temperament.

== Etymology ==

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 | Comma = yes
 }}
-The '''frostma'''  ([[ratio]]: 245/242, [[monzo]]: {{monzo| -1 0 1 2 -2 }}) is a [[small comma|small]] [[11-limit]] [[comma]] used in the construction of the [[No-threes subgroup temperaments #Frostburn|frostburn]] temperament.
+'''245/242''', the '''frostma''', is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 21.3 [[cent]]s. It is the amount by which [[5/2]] exceeds a stack of two [[11/7]]'s.
-It can be factored into ([[243/242]])([[245/243]]) and ([[896/891]])([[2835/2816]]).
+It can be factored into ([[243/242]])⋅([[245/243]]) and ([[896/891]])⋅([[2835/2816]]).
 == Temperaments ==
-Tempering out this comma alone in the 11-limit results in the rank-4 '''frostmic temperament''' (→ [[Catalog of rank-4 temperaments #Frostmic (245/242)]]), where a stack of two [[11/7]]'s is equated with a [[5/2]] major tenth, enabling [[frostmic chords]].
+[[Tempering out]] this comma alone in the 11-limit results in the rank-4 '''frostmic''' temperament (→ [[Catalog of rank-4 temperaments #Frostmic (245/242)]]), or in the 2.5.7.11 subgroup, the rank-3 '''frost''' temperament. In either case, a stack of two 11/7's is equated with a 5/2 major tenth, enabling [[frostmic chords]]. It is also used in the construction of the [[No-threes subgroup temperaments #Frostburn|frostburn]] temperament.
 == Etymology ==