Dinos comma
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| Ratio | 531441/528125 |
| Factorization | 312 × 5-5 × 13-2 |
| Monzo | [0 12 -5 0 0 -2⟩ |
| Size in cents | 10.836118¢ |
| 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), (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).