84edo: Difference between revisions

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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.

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

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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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.

== ~~Interval table~~ ==

== Intervals ==

For this table, the notation of Orwell[9] from the [[4L 5s]] page is taken. Notes are denoted as LsLsLsLss = JKLMNOPQRJ, and raising and lowering by a chroma (L − s), 3 steps in this instance, is denoted by & "amp" and a "at" (the symbol "@" unlike in the 4L 5s page cannot be used because of technical details).

{| class="wikitable"

@@ Line 5: / Line 5: @@
 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.
-In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].
+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 ===
@@ Line 14: / Line 14: @@
 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.
-== Interval table ==
+== Intervals ==
 For this table, the notation of Orwell[9] from the [[4L 5s]] page is taken. Notes are denoted as LsLsLsLss = JKLMNOPQRJ, and raising and lowering by a chroma (L − s), 3 steps in this instance, is denoted by & "amp" and a "at" (the symbol "@" unlike in the 4L 5s page cannot be used because of technical details).
 {| class="wikitable"