37/36

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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.48883 bits
Comma size	medium
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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.

Notation

This interval 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. In Helmholtz–Ellis notation, the symbol for the downward version of this interval is adapted from the demiflat in Ivan Wyschnegradsky's 72edo notation, whereas the upward version is a simple inverse of the downward version.