Compton family: Difference between revisions

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The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth ~~will be that~~ of 12edo, ~~two~~ [[~~cent~~]]~~s flat~~, ~~the tuning of the larger primes is not so constrained, and the point of~~ these temperaments is to ~~improve on it~~.

The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth is fixed to 7 steps of 12edo, about 2{{cent}} flat of [[just]], these temperaments aim to add tunings for higher primes which are more in tune than in 12edo.

== Compton ==

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* CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})

Badness (Sintel): 1.14

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==== Duodecic ====

Subgroup: 2.3.5.7.11.13

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Badness (Sintel): 1.27

=== Paly ===

{{Todo|inline=1|complete section|unify precision|comment= Sort the comma basis. Normalize the mapping. Unify the cent values in optimal tunings to 4 decimal places. Add the optimal ET sequence. <br>Add the data for the 11-, 13-, and 17-limit versions. }}

==== 19-limit ====

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120

Optimal tunings:

* WE: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}

: error map: {{val| -0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875 }}

* CWE: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}

: error map: {{val| -0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487 }}

Badness (Sintel): 2.383

== Duodecim ==

Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.

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[[Badness]] (Sintel): 1.24

~~[[Category:Temperament families]]~~

[[Category:Compton family| ]]

[[Category:Compton| ]]

[[Category:~~Rank~~ 2]]

[[Category:Temperament families]]

[[Category:Catalogs of rank-2 temperaments]]

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 {{Technical data page}}
-The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth will be that of 12edo, two [[cent]]s flat, the tuning of the larger primes is not so constrained, and the point of these temperaments is to improve on it.
+The '''compton family''', otherwise known as the '''aristoxenean family''', of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[Pythagorean comma]] ([[ratio]]: 531441/524288, {{monzo|legend=1| -19 12 }}, and hence the fifths form a closed 12-note [[circle of fifths]], identical to [[12edo]]. While the tuning of the fifth is fixed to 7 steps of 12edo, about 2{{cent}} flat of [[just]], these temperaments aim to add tunings for higher primes which are more in tune than in 12edo.
 == Compton ==
@@ Line 191: / Line 191: @@
 * CWE: ~16/15 = 100.0000{{c}}, ~7/4 = 965.8666{{c}} (~64/63 = 34.1334{{c}})
-{{Optimal ET sequence|legend=0| 12, 24, 36, 72ce }}
+{{Optimal ET sequence|legend=0| 12, 24, 36 }}
 Badness (Sintel): 1.14
@@ Line 241: / Line 241: @@
 ==== Duodecic ====
+{{Distinguish|Duodecim}}
 Subgroup: 2.3.5.7.11.13
@@ Line 284: / Line 286: @@
 Badness (Sintel): 1.27
+=== Paly ===
+{{Todo|inline=1|complete section|unify precision|comment= Sort the comma basis. Normalize the mapping. Unify the cent values in optimal tunings to 4 decimal places. Add the optimal ET sequence. <br>Add the data for the 11-, 13-, and 17-limit versions. }}
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120
+{{Mapping| 24 38 56 48 83 108 98 102 | 0 0 0 1 0 -1 0 0 }}
+Optimal tunings:
+* WE: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}
+: error map: {{val| -0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875 }}
+* CWE: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}
+: error map: {{val| -0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487 }}
+Badness (Sintel): 2.383
 == Duodecim ==
+{{Distinguish|Duodecic}}
 Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.
@@ Line 414: / Line 436: @@
 [[Badness]] (Sintel): 1.24
-[[Category:Temperament families]]
 [[Category:Compton family| ]] <!-- main article -->
 [[Category:Compton| ]] <!-- key article -->
-[[Category:Rank 2]]
+[[Category:Temperament families]]
+[[Category:Catalogs of rank-2 temperaments]]