245/242: Difference between revisions

Line 6:

'''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)]]), 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.

[[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 ==

@@ Line 6: / Line 6: @@
 '''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)]]), 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.
+[[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 ==