32/31: Difference between revisions

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+significance in HEJI and correct the name
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{{Infobox Interval
{{Infobox Interval
| Name = 31st subharmonic, small tricesimoprimal quartertone
| Name = octave-reduced 31st subharmonic, small tricesimoprimal quartertone
| Color name = 31u2, thiwu 2nd
| Color name = 31u2, thiwu 2nd
| Sound = Ji-32-31-csound-foscil-220hz.mp3
| Sound = Ji-32-31-csound-foscil-220hz.mp3
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'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].
'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); 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.


== See also ==
== See also ==

Revision as of 17:13, 28 November 2024

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 norm (log2 nd) 9.9542
Weil norm (log2 max(n, d)) 10
Wilson norm (sopfr(nd)) 41

[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 significant in Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval.

See also