82/81: Difference between revisions
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Clarify |
Recognize reversed meantone as a name |
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 82/81 | | Ratio = 82/81 | ||
| Name = 41-limit Johnston comma (HEJI) | | Name = reversed meantone comma, 41-limit Johnston comma (HEJI) | ||
| Color name = 41o1, fowo unison | | Color name = 41o1, fowo unison | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''82/81''', or the '''41-limit Johnston comma | '''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]]. | ||
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 == | |||
[[Tempering out]] this comma in the 2.3.41 subgroup leads to a rank-2 temperament known as [[reversed meantone]]. | |||
[[Category:Reversed meantone]] | |||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
Revision as of 17:39, 11 May 2026
| Interval information |
41-limit Johnston comma (HEJI)
reduced
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.
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.