Father family: Difference between revisions

Line 1:

The '''father family''' of ~~temperaments~~ tempers out [[16/15]], the just diatonic semitone. This equates [[4/3]] with [[5/4]], so these are "fourth-thirds", or father, temperaments.

The '''father family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] [[16/15]], the just diatonic semitone. This equates [[4/3]] with [[5/4]], so these are "fourth-thirds", or father, temperaments. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that is 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].

In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that's 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].

== Father ==

[[Subgroup]]: 2.3.5

Line 15:

Line 16:

[[Minimax tuning]]:

* [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }}

: [[Eigenmonzo basis|~~Eigenmonzo~~ (unchanged-interval) basis]]: 2.5/3

: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3

Line 29:

Line 30:

== Septimal father ==

Line 43:

Line 45:

[[Minimax tuning]]:

* [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }}

: [[Eigenmonzo basis|~~Eigenmonzo~~ (unchanged-interval) basis]]: 2.7/5

: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5

* [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9

: [[Eigenmonzo basis|~~Eigenmonzo~~ (unchanged-interval) basis]]: 2.9/7

: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7

Line 149:

Line 151:

Badness: 0.025592

~~== Quint ==~~

~~[[Subgroup]]: 2.3.5.7~~

~~[[Comma list]]: 16/15, 27/25~~

~~{{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}~~

~~: mapping generators: ~9/8, ~7~~

~~{{Multival|legend=1| 0 0 5 0 8 12 }}~~

~~[[Optimal tuning]] ([[POTE]]): ~9/8 = 1\5, ~7/4 = 1017.903~~

~~{{Optimal ET sequence|legend=1| 5, 15ccd }}~~

~~[[Badness]]: 0.048312~~

[[Category:Temperament families]]

[[Category:Father family| ]]

[[Category:Father| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-The '''father family''' of temperaments tempers out [[16/15]], the just diatonic semitone. This equates [[4/3]] with [[5/4]], so these are "fourth-thirds", or father, temperaments.
+The '''father family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] [[16/15]], the just diatonic semitone. This equates [[4/3]] with [[5/4]], so these are "fourth-thirds", or father, temperaments. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that is 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].
-In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that's 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].
 == Father ==
+{{Main| Father }}
 [[Subgroup]]: 2.3.5
@@ Line 15: / Line 16: @@
 [[Minimax tuning]]:
 * [[5-odd-limit]]: ~3/2 = {{monzo| 1 1/2 -1/2 }}
-: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5/3
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3
 {{Optimal ET sequence|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }}
@@ Line 29: / Line 30: @@
 == Septimal father ==
+{{Main| Father }}
 {{See also| Trienstonic clan #Father }}
@@ Line 43: / Line 45: @@
 [[Minimax tuning]]:
 * [[7-odd-limit]]: ~3/2 = {{monzo| 1/2 0 -1/4 1/4 }}
-: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7/5
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
 * [[9-odd-limit]]: ~3/2 = {{monzo| 1 -2 0 1 }} = 14/9
-: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/7
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
 {{Optimal ET sequence|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
@@ Line 149: / Line 151: @@
 Badness: 0.025592
-== Quint ==
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16/15, 27/25
-{{Mapping|legend=1| 5 8 12 0 | 0 0 0 1 }}
-: mapping generators: ~9/8, ~7
-{{Multival|legend=1| 0 0 5 0 8 12 }}
-[[Optimal tuning]] ([[POTE]]): ~9/8 = 1\5, ~7/4 = 1017.903
-{{Optimal ET sequence|legend=1| 5, 15ccd }}
-[[Badness]]: 0.048312
 [[Category:Temperament families]]
 [[Category:Father family| ]] <!-- main article -->
+[[Category:Father| ]] <!-- key article -->
 [[Category:Rank 2]]