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 | 493.11972¢ |
| 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{n\cdot d}[/math]) |
~4.34474 bits |
[sound info] | |
| open this interval in xen-calc | |
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.