Starling family: Difference between revisions

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The head of the '''starling family''' is starling, which tempers out [[126/125]], the starling comma or septimal semicomma. Starling has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by [[77edo]]. Other possible tunings are [[108edo]] and [[185edo]], and the nonpatent [[135edo]] val {{val| 135 214 314 379 }} (135c).

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* 7- and [[9-odd-limit]]: 3 and 7 just, 5 1/3-comma sharp

: {{monzo list| 1 0 0 0 | 0 1 0 0 | 1/3 2/3 0 1/3 | 0 0 0 1 }}

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.7

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7

{{Optimal ET sequence|legend=1| 7d, 8d, 12, 19, 27, 31, 46, 58, 77, 135c, 166c }}

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* 7- and [[9-odd-limit]]

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 1/3 2/3 0 1/3 0 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| -10/3 4/3 0 5/3 0 }}]

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.7

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7

{{Optimal ET sequence|legend=1| 12, 15, 19e, 27e, 31, 46, 58, 89, 135c, 193c, 224c }}

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* [[11-odd-limit]]

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 3/4 0 1/4 -3/8 }}, {{monzo| 1 1/2 0 1/2 -1/4 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| 2 -1/2 0 1/2 1/4 }}]

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7.11/9

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/9

{{Optimal ET sequence|legend=1| 7d, 8d, 12, 15, 19, 27e }} <nowiki>*</nowiki>

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[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Starling family| ]]

[[Category:Starling| ]]

[[Category:Rank 3]]

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+{{Technical data page}}
 The head of the '''starling family''' is starling, which tempers out [[126/125]], the starling comma or septimal semicomma. Starling has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by [[77edo]]. Other possible tunings are [[108edo]] and [[185edo]], and the nonpatent [[135edo]] val {{val| 135 214 314 379 }} (135c).
@@ Line 33: / Line 34: @@
 * 7- and [[9-odd-limit]]: 3 and 7 just, 5 1/3-comma sharp
 : {{monzo list| 1 0 0 0 | 0 1 0 0 | 1/3 2/3 0 1/3 | 0 0 0 1 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7
 {{Optimal ET sequence|legend=1| 7d, 8d, 12, 19, 27, 31, 46, 58, 77, 135c, 166c }}
@@ Line 86: / Line 87: @@
 * 7- and [[9-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 1/3 2/3 0 1/3 0 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| -10/3 4/3 0 5/3 0 }}]
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7
 {{Optimal ET sequence|legend=1| 12, 15, 19e, 27e, 31, 46, 58, 89, 135c, 193c, 224c }}
@@ Line 160: / Line 161: @@
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 3/4 0 1/4 -3/8 }}, {{monzo| 1 1/2 0 1/2 -1/4 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| 2 -1/2 0 1/2 1/4 }}]
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7.11/9
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/9
 {{Optimal ET sequence|legend=1| 7d, 8d, 12, 15, 19, 27e }} <nowiki>*</nowiki>
@@ Line 250: / Line 251: @@
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Starling family| ]] <!-- main article -->
 [[Category:Starling| ]] <!-- key article -->
 [[Category:Rank 3]]