Dinos comma

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
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531441/528125, the dinos comma, is a small 13-limit comma. It can be expressed as (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 (tridecimal marvelous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. flattone.

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 3136/3125 = (9/5)/(75/56)² (hemimean comma) and 589824/588245 = (9/5)/(343/256)^2 (hewuermera comma), but the comma is no-twos and requires only one additional prime base (3.5 for 9/5 and additional .13 for the comma).