32/31
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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]\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]\sqrt{nd}[/math])
~4.43017 bits
[sound info]
open this interval in xen-calc
| Interval information |
small tricesimoprimal quartertone
reduced,
reduced subharmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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 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.