84edo: Difference between revisions

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== Theory ==

In the [[13-~~limit~~]] ~~it is~~ the [[~~optimal~~ patent val]] ~~for~~ the ~~rank five temperament tempering out~~ [[~~144/143~~]].

84edo is where the orwell temperament takes its name from, since the generator of [[7/6]] is equal to 19 steps of the edo, referencing the [[Wikipedia: Nineteen Eighty-Four|book 1984]]. Orwell in 84edo comes in two varieties – the 84e val {{val| 84 133 195 236 '''290''' }}, supporting the original orwell, and its [[patent val]] {{val| 84 133 195 236 '''291''' }} supporting [[newspeak]]. 84edo orwell offers mosses of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.

~~84edo is where~~ the [[~~orwell~~]] ~~temperament takes its name from, since the generator of 7/6~~ is equal to 19 steps of the edo, referencing the [[Wikipedia:Nineteen Eighty-Four|book 1984]]. From a regular temperament perspective, orwell in 84edo comes in two varieties – the 84e val {{val| 84 133 195 236 '''290''' }}, supporting the ~~original orwell, and its~~ [[patent val]] ~~{{val| 84 133 195 236 '''291''' }} representing [[newspeak]]. 84edo orwell offers mosses of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.~~

In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].

~~Being a small multiple of 12, 84et tempers out the [[Pythagorean comma]], thus supporting~~ the ~~period~~-12 temperament ~~[[compton]]. Being a small multiple of 28, it tempers~~ out ~~the~~ [[~~Oquatonic|oquatonic comma~~]]~~, which maps 5/4 to 9\28~~.

=== Prime harmonics ===

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=== Subsets and supersets ===

84edo is a [[largely composite]] number. Since 84 factors as {{factorization|84}}, 84edo has subset edos {{EDOs|1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42}}.

84edo is a [[largely composite]] number. Since 84 factors as {{factorization|84}}, 84edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 }}. Being a small multiple of 12, 84et tempers out the [[Pythagorean comma]], thus supporting the 1/12-octave temperament [[compton]]. Being a small multiple of 28, it tempers out the [[oquatonic|oquatonic comma]], which maps 5/4 to 9\28.

== Table of intervals ==

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 == Theory ==
-In the [[13-limit]] it is the [[optimal patent val]] for the rank five temperament tempering out [[144/143]].
+edo is where the orwell temperament takes its name from, since the generator of [[7/6]] is equal to 19 steps of the edo, referencing the [[Wikipedia: Nineteen Eighty-Four|book 1984]]. Orwell in 84edo comes in two varieties – the 84e val {{val| 84 133 195 236 '''290''' }}, supporting the original orwell, and its [[patent val]] {{val| 84 133 195 236 '''291''' }} supporting [[newspeak]]. 84edo orwell offers mosses of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.
-edo is where the [[orwell]] temperament takes its name from, since the generator of 7/6 is equal to 19 steps of the edo, referencing the [[Wikipedia:Nineteen Eighty-Four|book 1984]]. From a regular temperament perspective, orwell in 84edo comes in two varieties – the 84e val {{val| 84 133 195 236 '''290''' }}, supporting the original orwell, and its [[patent val]] {{val| 84 133 195 236 '''291''' }} representing [[newspeak]]. 84edo orwell offers mosses of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.
+In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].
-Being a small multiple of 12, 84et tempers out the [[Pythagorean comma]], thus supporting the period-12 temperament [[compton]]. Being a small multiple of 28, it tempers out the [[Oquatonic|oquatonic comma]], which maps 5/4 to 9\28.
 === Prime harmonics ===
@@ Line 14: / Line 12: @@
 === Subsets and supersets ===
-edo is a [[largely composite]] number. Since 84 factors as {{factorization|84}}, 84edo has subset edos {{EDOs|1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42}}.
+edo is a [[largely composite]] number. Since 84 factors as {{factorization|84}}, 84edo has subset edos {{EDOs| 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 }}. Being a small multiple of 12, 84et tempers out the [[Pythagorean comma]], thus supporting the 1/12-octave temperament [[compton]]. Being a small multiple of 28, it tempers out the [[oquatonic|oquatonic comma]], which maps 5/4 to 9\28.
 == Table of intervals ==