117/88
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Ratio
117/88
Factorization
2-3 × 32 × 11-1 × 13
Monzo
[-3 2 0 0 -1 1⟩
Size in cents
493.1197¢
Name
major minthmic fourth
Color name
3o1u4, tholu 4th
FJS name
[math]\text{P4}^{13}_{11}[/math]
Special properties
reduced
Tenney height (log2 nd)
13.3298
Weil height (log2 max(n, d))
13.7407
Wilson height (sopfr(nd))
36
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~3.86403 bits
[sound info]
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
117/88 is the major minthmic fourth, a 13-limit ratio with a value of 493 cents. It is 352/351 against the just perfect fourth of 4/3. It arises in 13-limit just intonation by stacking 13/11 and 9/8, or by lowering 13/8 by 11/9.
Note that major minthmic modifies fourth and that major minthmic is the name of the temperament that tempers out 352/351. Major does not specify the size of the interval here.