245/242: Difference between revisions

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{{Infobox Interval

| Name = frostma

| Color name = luuzzy2, luluzozoyo 2nd

| Comma = yes

}}

~~The~~ '''frostma''' ~~([[ratio]]: 245/242~~, ~~[[monzo]]: {{monzo| -1 0 1 2 -2 }})~~ is a [[small comma|small]] [[11-limit]] [[comma]] ~~named after~~ [[~~User:Frostburn|Frostburn~~]] ~~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]]).

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

~~When tempered~~ out, ~~it equates~~ a stack of two [[11/7~~]]<nowiki/>~~s with a [[5/2]] ~~major tenth~~.

== 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.

== ~~History~~ ==

== Etymology ==

Before ~~the comma~~ got the name ''frostma'', it was known as the ''cassacot'', probably derived from [[cassandra]] and [[tetracot]]. However, ''cassandra'' was a misnomer for [[andromeda]]. The temperament's name was later corrected. Since then, ''cassacot'' has lost its root, thus justifying the new name.

This comma was named after [[User:Frostburn|Frostburn]] in 2022. Before it got the name ''frostma'', it was known as the ''cassacot'', probably derived from [[cassandra]] and [[tetracot]]. However, ''cassandra'' was a misnomer for [[andromeda]]. The temperament's name was later corrected. Since then, ''cassacot'' has lost its root, thus justifying the new name.

~~=== Quotes ===~~

~~''"~~245/242 should be the frostma because 243/242 is the rastma…~~"''~~ —[[Praveen Venkataramana]]

245/242 should be the frostma because 243/242 is the rastma…

</blockquote>

~~== See also ==~~

—[[Praveen Venkataramana]]

* [[Small comma]]

[[Category:Frostmic]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = frostma
+| Color name = luuzzy2, luluzozoyo 2nd
 | Comma = yes
 }}
-The '''frostma'''  ([[ratio]]: 245/242, [[monzo]]: {{monzo| -1 0 1 2 -2 }}) is a [[small comma|small]] [[11-limit]] [[comma]] named after [[User:Frostburn|Frostburn]] 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]]).
+It can be factored into ([[243/242]])⋅([[245/243]]) and ([[896/891]])⋅([[2835/2816]]).
-When tempered out, it equates a stack of two [[11/7]]<nowiki/>s with a [[5/2]] major tenth.
+== 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.
-== History ==
+== Etymology ==
-Before the comma got the name ''frostma'', it was known as the ''cassacot'', probably derived from [[cassandra]] and [[tetracot]]. However, ''cassandra'' was a misnomer for [[andromeda]]. The temperament's name was later corrected. Since then, ''cassacot'' has lost its root, thus justifying the new name.
+This comma was named after [[User:Frostburn|Frostburn]] in 2022. Before it got the name ''frostma'', it was known as the ''cassacot'', probably derived from [[cassandra]] and [[tetracot]]. However, ''cassandra'' was a misnomer for [[andromeda]]. The temperament's name was later corrected. Since then, ''cassacot'' has lost its root, thus justifying the new name.
-=== Quotes ===
+<blockquote>
-''"245/242 should be the frostma because 243/242 is the rastma…"'' —[[Praveen Venkataramana]]
+/242 should be the frostma because 243/242 is the rastma…
+</blockquote>
-== See also ==
+—[[Praveen Venkataramana]]
-* [[Small comma]]
 [[Category:Frostmic]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]