37/36: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
BudjarnLambeth (talk | contribs)
mNo edit summary
+ name similar to 32/31. It's dumb to consider this a comma
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
|Ratio = 37/36
| Ratio = 37/36
|Name = 37-limit Wyschnegradsky ~quartertone (HEJI)
| Name = large tricesimoseptimal quartertone, 37-limit Wyschnegradsky ~quartertone (HEJI)
|Color name = 37o2, thiso 2nd
| Color name = 37o2, thiso 2nd
|Comma = yes
}}
}}
'''37/36''', or the '''31-limit Wyschnegradsky ~quartertone''', is a 2.3.37 subgroup comma. It is the amount by which 37/32 (the 37th harmonic) 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 37-limit (prefix???){{clarify}} interval.
'''37/36''', the '''large tricesimoseptimal''' ('''37-limit''') '''quartertone''', also known as the '''37-limit Wyschnegradsky ~quartertone''' in [[Helmholtz–Ellis notation]], is a [[37-limit]] (specifically 2.3.37-subgroup) [[quartertone]]. It is the amount by which the octave-reduced 37th harmonic [[37/32]] exceeds the Pythagorean (major) whole tone of [[9/8]]. It is wider than [[38/37]], the small tricesimoseptimal quartertone, by [[1369/1368]].  


[[Category:Commas named after individuals]][[Category:Commas named after their interval size]]
== 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.
 
== See also ==
* [[List of superparticular intervals]]

Latest revision as of 08:17, 3 March 2026

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

37/36, the large tricesimoseptimal (37-limit) quartertone, also known as the 37-limit Wyschnegradsky ~quartertone in Helmholtz–Ellis notation, is a 37-limit (specifically 2.3.37-subgroup) quartertone. It is the amount by which the octave-reduced 37th harmonic 37/32 exceeds the Pythagorean (major) whole tone of 9/8. It is wider than 38/37, the small tricesimoseptimal quartertone, by 1369/1368.

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.

See also