2197/2187
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| Ratio | 2197/2187 |
| Factorization | 3-7 × 133 |
| Monzo | [0 -7 0 0 0 3⟩ |
| Size in cents | 7.8979793¢ |
| Name | threedie |
| Color name | s3o32, satritho 2nd, Satritho comma |
| FJS name | [math]\text{dd2}^{13,13,13}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 22.1961 |
| Weil height (log2 max(n, d)) | 22.2026 |
| Wilson height (sopfr(nd)) | 60 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.7611 bits |
| Comma size | small |
| S-expression | S25 * S262 |
| open this interval in xen-calc | |
The threedie, 2197/2187, is a 3.13-subgroup analog of the 2.5-subgroup diesis. Measuring about 7.9 ¢, it is a small comma. Analogous to tempering out the diesis, which divides the octave into three sharp 5/4's, tempering out the threedie divides the tritave into three slightly flat 13/9's, since (13/9)3/3 = 2197/2187. Furthermore, tempering out the threedie divides 9/8 into three instances of 27/26. 596edo provides the optimal patent val for the corresponding rank-5 temperament.
It factors into simpler commas in the 2.3.5.13 subgroup as (325/324)(676/675), or can be expressed in the 2.3.7.13 subgroup as (169/168)/(729/728), i.e. S13/S27.