82/81

Interval information

Ratio	82/81
Subgroup monzo	2.3.41 [1 -4 1⟩
Size in cents	21.2424¢
Name	41-limit Johnston comma (HEJI)
Color name	41o1, fowo unison
FJS name	[math]\displaystyle{ \text{P1}^{41} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	12.6974
Weil height (log2 max(n, d))	12.7151
Wilson height (sopfr(nd))	55
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.91191 bits
Comma size	small
Open this interval in xen-calc

82/81, or the 41-limit Johnston comma (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. It is the parent comma for the reversed meantone clan.

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 being used are virtually identical to Ben Johnston's plus and minus signs representing 81/80.