37/36: Difference between revisions

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+significance in FJS
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'''37/36''', or the '''37-limit Wyschnegradsky ~quartertone''', is a 2.3.37 subgroup comma. It is the amount by which the octave-reduced 37th harmonic [[37/32]] exceeds the Pythagorean (major) whole tone of [[9/8]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoseptimal (37-limit) interval.
'''37/36''', or the '''37-limit Wyschnegradsky ~quartertone''', is a 2.3.37 subgroup comma. It is the amount by which the octave-reduced 37th harmonic [[37/32]] exceeds the Pythagorean (major) whole tone of [[9/8]]. It is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoseptimal (37-limit) interval.


[[Category:Commas named after composers]]
[[Category:Commas named after composers]]
[[Category:Commas named after their interval size]]
[[Category:Commas named after their interval size]]

Revision as of 17:17, 28 November 2024

Interval information
Ratio 37/36
Subgroup monzo 2.3.37 [-2 -2 1
Size in cents 47.43404¢
Name 37-limit Wyschnegradsky ~quartertone (HEJI)
Color name 37o2, thiso 2nd
FJS name [math]\displaystyle{ \text{P1}^{37} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 10.3794
Weil height (log2 max(n, d)) 10.4189
Wilson height (sopfr(nd)) 47
Comma size medium
Open this interval in xen-calc

37/36, or the 37-limit Wyschnegradsky ~quartertone, is a 2.3.37 subgroup comma. It is the amount by which the octave-reduced 37th harmonic 37/32 exceeds the Pythagorean (major) whole tone of 9/8. It is significant in the Functional Just System and Helmholtz-Ellis notation as the formal comma to translate a Pythagorean interval to a nearby tricesimoseptimal (37-limit) interval.