82/81: Difference between revisions

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Recognize reversed meantone as a name
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'''82/81''', the '''reversed meantone comma''', or the '''41-limit Johnston comma''' in [[HEJI]], is a 2.3.41-subgroup [[comma]]. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]].  
'''82/81''', the '''reversed meantone comma''', or the '''41-limit Johnston comma''' in [[Helmholtz–Ellis notation]], is a 2.3.41-subgroup [[comma]]. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]].  


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 quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.  
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 quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.  


== Temperaments ==
== Temperaments ==

Latest revision as of 17:43, 11 May 2026

Interval information
Ratio 82/81
Subgroup monzo 2.3.41 [1 -4 1
Size in cents 21.2424¢
Names reversed meantone comma,
41-limit Johnston comma (HEJI)
Color name 41o1, fowo unison
FJS name [math]\displaystyle{ \text{P1}^{41} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 12.6974
Weil norm (log2 max(n, d)) 12.7151
Wilson norm (sopfr(nd)) 55
Comma size small
Open this interval in xen-calc

82/81, the reversed meantone comma, or the 41-limit Johnston comma in Helmholtz–Ellis notation, is a 2.3.41-subgroup comma. It is the amount by which the octave-reduced 41st harmonic 41/32 exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma (81/80) by 6561/6560.

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 quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from Ben Johnston's plus and minus signs representing 81/80.

Temperaments

Tempering out this comma in the 2.3.41 subgroup leads to a rank-2 temperament known as reversed meantone.