176/117

Interval information

Ratio	176/117
Factorization	24 × 3-2 × 11 × 13-1
Monzo	[4 -2 0 0 1 -1⟩
Size in cents	706.8803¢
Name	major minthmic fifth
Color name	3u1o5, thulo 5th
FJS name	[math]\text{P5}^{11}_{13}[/math]
Special properties	reduced
Tenney height (log2 nd)	14.3298
Weil height (log2 max(n, d))	14.9189
Wilson height (sopfr(nd))	38
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~3.51559 bits
[sound info]
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176/117, the major minthmic fifth, is a 13-limit interval of 706.8 ¢. It is 352/351 sharp of the just perfect fifth of 3/2. It arises in 13-limit just intonation by lowering 22/13 by 9/8 or by stacking 16/13 and 11/9.

Note that major minthmic modifies fifth 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

• 117/88 – its octave complement
• 182/121 – the minor minthmic fifth
• Gallery of just intervals