84edo: Difference between revisions

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== Theory ==

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~~.

84 = 7 × 12, and 84edo shares the [[3/2|perfect fifth]] with [[12edo]], [[tempering out]] the [[Pythagorean comma]] in its [[patent val]]. In the [[5-limit]] it tempers out the [[sensipent comma]]; in the [[7-limit]] [[225/224]], [[1728/1715]], [[2430/2401]], [[6144/6125]], [[support]]ing [[orwell]], [[compton]], and [[sensei]].

It has fairly good approximation to higher [[prime harmonic]]s such as [[13/1|13]], [[19/1|19]], [[23/1|23]], [[29/1|29]], and [[31/1|31]]. In fact, it is [[consistent]] to the no-11 no-17 [[25-odd-limit]]. In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 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 [[mos scale]]s of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.

It has fairly good approximation to higher [[prime harmonic]]s such as [[13/1|13]], [[19/1|19]], [[23/1|23]], [[29/1|29]], and [[31/1|31]]. In fact, it is [[consistent]] to the no-11 no-17 [[25-odd-limit]]. In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].

=== 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| 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.

84 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 28, it tempers out the [[oquatonic|oquatonic comma]], which maps 5/4 to 9\28.

== Intervals ==

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 == Theory ==
-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.
+= 7 × 12, and 84edo shares the [[3/2|perfect fifth]] with [[12edo]], [[tempering out]] the [[Pythagorean comma]] in its [[patent val]]. In the [[5-limit]] it tempers out the [[sensipent comma]]; in the [[7-limit]] [[225/224]], [[1728/1715]], [[2430/2401]], [[6144/6125]], [[support]]ing [[orwell]], [[compton]], and [[sensei]].
-It has fairly good approximation to higher [[prime harmonic]]s such as [[13/1|13]], [[19/1|19]], [[23/1|23]], [[29/1|29]], and [[31/1|31]]. In fact, it is [[consistent]] to the no-11 no-17 [[25-odd-limit]]. In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 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 [[mos scale]]s of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.
+It has fairly good approximation to higher [[prime harmonic]]s such as [[13/1|13]], [[19/1|19]], [[23/1|23]], [[29/1|29]], and [[31/1|31]]. In fact, it is [[consistent]] to the no-11 no-17 [[25-odd-limit]]. In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].
 === Prime harmonics ===
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 === Subsets and supersets ===
-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.
+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 28, it tempers out the [[oquatonic|oquatonic comma]], which maps 5/4 to 9\28.
 == Intervals ==