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	L3uug51, lathuthuquingu 1sn
FJS name	[math]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~2.21911 bits
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), (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).