82/81: Difference between revisions

(8 intermediate revisions by 4 users not shown)

Line 1:

{~~| class="wikitable"~~

{{Infobox Interval

|+Interval ~~information~~

| Ratio = 82/81

|Ratio

| Name = reversed meantone comma, 41-limit Johnston comma (HEJI)

|82/81

| Color name = 41o1, fowo unison

|-

| Comma = yes

~~|[[Smonzos and svals|Subgroup monzo]]~~

}}

~~|2.3.41 [1 -4 1⟩~~

'''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]].

|-

~~|Size in [[Cent|cents]]~~

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.

~~|21.242402¢~~

|-

== Temperaments ==

~~|Names~~

[[Tempering out]] this comma in the 2.3.41 subgroup leads to a rank-2 temperament known as [[reversed meantone]].

|41-limit Johnston comma (HEJI)

|}

[[Category:Reversed meantone]]

'''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.

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
-{| class="wikitable"
+{{Infobox Interval
-|+Interval information
+| Ratio = 82/81
-|Ratio
+| Name = reversed meantone comma, 41-limit Johnston comma (HEJI)
-|82/81
+| Color name = 41o1, fowo unison
-|-
+| Comma = yes
-|[[Smonzos and svals|Subgroup monzo]]
+}}
-|2.3.41 [1 -4 1⟩
+'''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]].
-|-
-|Size in [[Cent|cents]]
+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.
-|21.242402¢
-|-
+== Temperaments ==
-|Names
+[[Tempering out]] this comma in the 2.3.41 subgroup leads to a rank-2 temperament known as [[reversed meantone]].
-|41-limit Johnston comma (HEJI)
-|}
+[[Category:Reversed meantone]]
-'''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.
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]