82/81: Difference between revisions

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{{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 ~~(HEJI)~~''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 ~~(the 41st harmonic)~~ exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[~~Helmholtz-Ellis notation~~]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit ~~(prefix???~~) interval.

'''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]].

[[Category:Reversed meantone]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{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 (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.
+'''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]].
+[[Category:Reversed meantone]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]