32/31

Interval information

Ratio	32/31
Subgroup monzo	2.31 [5 -1⟩
Size in cents	54.96443¢
Names	octave-reduced 31st subharmonic, small tricesimoprimal quartertone
Color name	31u2, thiwu 2nd
FJS name	[math]\displaystyle{ \text{m2}_{31} }[/math]
Special properties	superparticular, reduced, reduced subharmonic
Tenney height (log2 nd)	9.9542
Weil height (log2 max(n, d))	10
Wilson height (sopfr(nd))	41
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.43017 bits
[sound info]
Open this interval in xen-calc

32/31 is the small tricesimoprimal quartertone measuring about 55 ¢. It differs from 33/32, the undecimal quartertone, by 1024/1023 (approx. 1.69 ¢). It differs from 31/30, another tricesimoprimal quartertone, by 961/960 (approx. 1.80 ¢); they together make 16/15. This interval is approximated well (about 0.4 ¢ off) by 1\22 and extremely closely (about 0.0025 ¢ off) by 6\131. It can also serve as a generator for the escapade temperament (which both 22 and 131edo, among others, support).

This interval is significant in Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by Ali-Naqi Vaziri.

See also

• 31/16 – its octave complement
• 31/24 – its fifth complement
• Gallery of just intervals