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)<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 == | == 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 == | == 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 | 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]] | [[Category:Commas named for the intervals they stack]] | ||
Latest revision as of 13:56, 16 January 2025
| Interval information |
531441/528125, the dinos comma, is a 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. 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 an unnamed temperament.
Etymology
The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts". The same argument holds for hemimean comma (3136/3125 = (9/5)/(75/56)2) and 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).