Dinos comma: Difference between revisions

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'''531441/528125''', the '''dinos comma''', is a [[small comma|small]] [[13-limit]] [[comma]]. It can be expressed as ([[3159/3125]])/([[2197/2187]]), ([[9/5]])/(325/243)2, (9/5)/([[4/3]])2/([[325/324]])2 and ([[81/80]])/(325/324)2, among other expressions.

'''531441/528125''', the '''dinos comma''', is a [[small comma|small]] [[13-limit]] [[comma]]. It can be expressed as ([[3159/3125]])/([[2197/2187]]), ([[78732/78125]])/([[676/675]]), ([[9/5]])/(325/243)2, (9/5)/([[4/3]])2/([[325/324]])2 and ([[81/80]])/(325/324)2, among other expressions.

== Temperaments ==

Tempering out this comma means equating a stack of two 325/243 (marveltwinous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. [[flattone]] extension.

Tempering out this comma means equating a stack of two 325/243 (marveltwinous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. [[flattone]] extension. However, most of the case it is overshadowed by the 81/80. Tempering out this comma in its minimal prime [[subgroup]] of 3.5.13 leads to [[tetrameantone #b15 & b4p|an unnamed temperament]].

== Etymology ==

The name "dinos" is proposed by [[User:Dummy index|Dummy index]] in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for [[hemimean comma|hemimean comma (3136/3125 = (9/5)/(75/56)2)]] and [[hewuermera comma|hewuermera comma (589824/588245 = (9/5)/(343/256)2)]], but the comma is no-twos and requires only one additional prime ~~base~~ (3.5 for 9/5 and additional .13 for the comma).

The name "dinos" is proposed by [[User:Dummy index|Dummy index]] in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for [[hemimean comma|hemimean comma (3136/3125 = (9/5)/(75/56)2)]] and [[hewuermera comma|hewuermera comma (589824/588245 = (9/5)/(343/256)2)]], but the comma is no-twos and requires only one additional prime basis element (3.5 for 9/5 and additional .13 for the comma).

[[Category:Commas named for the intervals they stack]]

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-'''531441/528125''', the '''dinos comma''', is a [[small comma|small]] [[13-limit]] [[comma]]. It can be expressed as ([[3159/3125]])/([[2197/2187]]), ([[9/5]])/(325/243)<sup>2</sup>, (9/5)/([[4/3]])<sup>2</sup>/([[325/324]])<sup>2</sup> and ([[81/80]])/(325/324)<sup>2</sup>, among other expressions.
+'''531441/528125''', the '''dinos comma''', is a [[small comma|small]] [[13-limit]] [[comma]]. It can be expressed as ([[3159/3125]])/([[2197/2187]]), ([[78732/78125]])/([[676/675]]), ([[9/5]])/(325/243)<sup>2</sup>, (9/5)/([[4/3]])<sup>2</sup>/([[325/324]])<sup>2</sup> and ([[81/80]])/(325/324)<sup>2</sup>, among other expressions.
 == Temperaments ==
-Tempering out this comma means equating a stack of two 325/243 (marveltwinous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. [[flattone]] extension.
+Tempering out this comma means equating a stack of two 325/243 (marveltwinous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. [[flattone]] extension. However, most of the case it is overshadowed by the 81/80. Tempering out this comma in its minimal prime [[subgroup]] of 3.5.13 leads to [[tetrameantone #b15 & b4p|an unnamed temperament]].
 == Etymology ==
-The name "dinos" is proposed by [[User:Dummy index|Dummy index]] in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for [[hemimean comma|hemimean comma (3136/3125 = (9/5)/(75/56)<sup>2</sup>)]] and [[hewuermera comma|hewuermera comma (589824/588245 = (9/5)/(343/256)<sup>2</sup>)]], but the comma is no-twos and requires only one additional prime base (3.5 for 9/5 and additional .13 for the comma).
+The name "dinos" is proposed by [[User:Dummy index|Dummy index]] in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for [[hemimean comma|hemimean comma (3136/3125 = (9/5)/(75/56)<sup>2</sup>)]] and [[hewuermera comma|hewuermera comma (589824/588245 = (9/5)/(343/256)<sup>2</sup>)]], but the comma is no-twos and requires only one additional prime basis element (3.5 for 9/5 and additional .13 for the comma).
+[[Category:Commas named for the intervals they stack]]