117/88

Interval information

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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~3.86403 bits
[sound info]
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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.

See also

• 176/117 – its octave complement
• 44/39 – its fifth complement
• Gallery of just intervals