84edo: Difference between revisions

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{{Infobox ET

|Prime factorization = 2<sup>2</sup> × 3 × 7

| Prime factorization = 2<sup>2</sup> × 3 × 7

|Step size = 14.2857¢

| Step size = 14.2857¢

|Fifth = 49\84 ([[12edo|7\12]])

| Fifth = 49\84 (700.0¢) (→ [[12edo|7\12]])

|Semitones = 7:7 (~~100¢~~:~~100¢~~)

| Semitones = 7:7 (100.0¢ : 100.0¢)

|Consistency = 7}}

| Consistency = 9

}}

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

~~=== Orwell ===~~

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.

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 MOS of size 9, 13, 22, and 31~~, of which ~~the 31 note scale is the maximum evenness scale~~.

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.

=== ~~Other~~ ===

=== Prime harmonics ===

84edo is a significantly composite number, with divisors of 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Being a small multiple of 12, it tempers out the [[Pythagorean comma]], thus supporting period-12 temperament [[compton]]. Being a small multiple of 28, it tempers out the [[Oquatonic|oquatonic comma]], which maps 5/4 to 9\28.{{Primes in edo|84}}

=== Miscellaneous properties ===

84edo is a significantly composite number, with divisors of 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

== Table of intervals ==

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 {{Infobox ET
-|Prime factorization = 2<sup>2</sup> × 3 × 7
+| Prime factorization = 2<sup>2</sup> × 3 × 7
-|Step size = 14.2857¢
+| Step size = 14.2857¢
-|Fifth = 49\84 ([[12edo|7\12]])
+| Fifth = 49\84 (700.0¢) (→ [[12edo|7\12]])
-|Semitones = 7:7 (100¢:100¢)
+| Semitones = 7:7 (100.0¢ : 100.0¢)
-|Consistency = 7}}
+| Consistency = 9
+}}
 {{EDO intro|84}}
@@ Line 10: / Line 11: @@
 In the [[13-limit]] it is the [[optimal patent val]] for the rank five temperament tempering out [[144/143]].
-=== Orwell ===
+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.
-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 MOS of size 9, 13, 22, and 31, of which the 31 note scale is the maximum evenness scale.
+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.
-=== Other ===
+=== Prime harmonics ===
-edo is a significantly composite number, with divisors of 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Being a small multiple of 12, it tempers out the [[Pythagorean comma]], thus supporting period-12 temperament [[compton]]. Being a small multiple of 28, it tempers out the [[Oquatonic|oquatonic comma]], which maps 5/4 to 9\28.{{Primes in edo|84}}
+{{Harmonics in equal|84}}
+=== Miscellaneous properties ===
+edo is a significantly composite number, with divisors of 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
 == Table of intervals ==