2197/2187
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Ratio
2197/2187
Factorization
3-7 × 133
Monzo
[0 -7 0 0 0 3⟩
Size in cents
7.897979¢
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
| Interval information |
Satritho comma
(Shannon, [math]\sqrt{nd}[/math])
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.