82/81

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
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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.