82/81: Difference between revisions
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'''82/81''', the '''reversed meantone comma''', or the '''41-limit Johnston comma''' in [[ | '''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 | 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 |
41-limit Johnston comma (HEJI)
reduced
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.