82/81
Jump to navigation
Jump to search
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]\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]\sqrt{nd}[/math])
~3.91191 bits
Comma size
small
open this interval in xen-calc
| Interval information |
reduced
(Shannon, [math]\sqrt{nd}[/math])
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.