Dinos comma: Difference between revisions

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== Temperaments ==
== Temperaments ==
Tempering out this comma means equating a stack of two 325/243 (tridecimal marvelous 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.


== 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 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 base (3.5 for 9/5 and additional .13 for the comma).

Revision as of 12:07, 23 September 2024

Interval information
Ratio 531441/528125
Factorization 312 × 5-5 × 13-2
Monzo [0 12 -5 0 0 -2
Size in cents 10.83612¢
Name dinos comma
Color name L3uug^51, lathuthuquingu 1sn
FJS name [math]\displaystyle{ \text{P1}_{5,5,5,5,5,13,13} }[/math]
Special properties reduced
Tenney height (log2 nd) 38.0301
Weil height (log2 max(n, d)) 38.0391
Wilson height (sopfr(nd)) 87
Comma size small
Open this interval in xen-calc

531441/528125, the dinos comma, is a 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.

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.

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 base (3.5 for 9/5 and additional .13 for the comma).