84edo: Difference between revisions
enrichment with information, emphasizing relation to orwell, i'll add relative error later because it isn't simply absolute calibrated to edo size, it's by complexity |
→Regular temperament properties: stylistic, explaining relation to orwell, adding rank 2 temps and stuff |
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|Semitones = 7:7 (100¢:100¢) | |Semitones = 7:7 (100¢:100¢) | ||
|Consistency = 7}} | |Consistency = 7}} | ||
{{EDO intro|84}} | |||
== Theory == | == 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 === | ||
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]]. | |||
{{Primes in edo|84}} | 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. | ||
=== Other === | |||
84edo is a significantly composite number, with divisors 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Being a small multiple of 12, it tempres out the [[Pythagorean comma]], thus supporting period-12 temperament [[compton]]. Being a small multiple of 28, it tempers out the [[oquatonic comma]], which maps 5/4 to 9\28.{{Primes in edo|84}} | |||
== Table of intervals == | == Table of intervals == | ||
| Line 155: | Line 159: | ||
|1.151 | |1.151 | ||
| | | | ||
|} | |||
=== Rank-2 temperaments by generator === | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per octave | |||
!Generator | |||
!Cents | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
| rowspan="2" |1 | |||
| rowspan="2" |[[Wikipedia:Nineteen Eighty-Four|19\84]] | |||
| rowspan="2" |271.428 | |||
| rowspan="2" | 7/6 | |||
|[[Orwell]] (84e val) | |||
|- | |||
|[[Newspeak]] (84p val) | |||
|- | |||
|1 | |||
|27\84 | |||
|385.714 | |||
|5/4 | |||
|[[Mutt]] | |||
|- | |||
|12 | |||
|27\84 | |||
(6\84) | |||
|385.714 | |||
(85.714) | |||
|5/4 | |||
(20480/19683) | |||
|[[Compton]] | |||
|- | |||
|28 | |||
|49\84 | |||
(1\84) | |||
|500.000 | |||
(14.286) | |||
|4/3 | |||
(105/104) | |||
|[[Oquatonic]] | |||
|} | |} | ||
== Scales == | == Scales == | ||