Meantone family: Difference between revisions

Line 328:

=Flattone=

[[~~Comma|~~Comma]]s: 81/80, 525/512

[[Comma]]s: 81/80, 525/512

The [[~~wedgie|~~wedgie]] for flattone is <<1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[~~7/4|~~7/4]] is a diminished seventh interval. Other intervals are [[~~7/6|~~7/6]], a diminished third, and [[~~7/5|~~7/5]], a doubly diminshed fifth. Good tunings for flattone are [[~~26edo|~~26edo]], [[~~45edo|~~45edo]] and [[~~64edo|~~64edo]].

The [[wedgie]] for flattone is <<1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval. Other intervals are [[7/6]], a diminished third, and [[7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].

[[7-limit|7-limit]] minimax

[[7-odd-limit|7-limit]] minimax

[|1 0 0 0>, |21/13 0 1/13 -1/13>,

|32/13 0 4/13 -4/13>, |32/13 0 -9/13 9/13>]

[[~~Eigenmonzo|~~Eigenmonzo]]s: 2, 7/5

[[Eigenmonzo]]s: 2, 7/5

[[9-limit|9-limit]] minimax

[[9-odd-limit|9-limit]] minimax

[|1 0 0 0>, |17/11 2/11 0 -1/11>,

|24/11 8/11 0 -4/11>, |34/11 -18/11 0 9/11>]

~~[[Eigenmonzo|Eigenmonzo]]s~~: 2, 9/7

Eigenmonzos: 2, 9/7

valid range: [692.308, 694.737] (26 to 19)

Line 360:

Map: [<1 0 -4 17|, <0 1 4 -9|]

[[~~wedgie|~~Wedgie]]: <<1 4 -9 4 -17 -32||

[[Wedgie]]: <<1 4 -9 4 -17 -32||

[[~~generator|~~Generator]]s: 2, 3

[[Generator]]s: 2, 3

EDOs: [[7edo|7]], [[19edo|19]], [[~~45edo~~|45]], [[~~64edo~~|64]]

EDOs: [[7edo|7]], [[19edo|19]], [[26edo|26]], [[45edo|45]]

[[~~Badness|~~Badness]]: 0.0386

[[Badness]]: 0.0386

==11-limit==

@@ Line 328: / Line 328: @@
 =Flattone=
-[[Comma|Comma]]s: 81/80, 525/512
+[[Comma]]s: 81/80, 525/512
-The [[wedgie|wedgie]] for flattone is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4|7/4]] is a diminished seventh interval. Other intervals are [[7/6|7/6]], a diminished third, and [[7/5|7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo|26edo]], [[45edo|45edo]] and [[64edo|64edo]].
+The [[wedgie]] for flattone is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval. Other intervals are [[7/6]], a diminished third, and [[7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].
-[[7-limit|7-limit]] minimax
+[[7-odd-limit|7-limit]] minimax
 [|1 0 0 0&gt;, |21/13 0 1/13 -1/13&gt;,
 |32/13 0 4/13 -4/13&gt;, |32/13 0 -9/13 9/13&gt;]
-[[Eigenmonzo|Eigenmonzo]]s: 2, 7/5
+[[Eigenmonzo]]s: 2, 7/5
-[[9-limit|9-limit]] minimax
+[[9-odd-limit|9-limit]] minimax
 [|1 0 0 0&gt;, |17/11 2/11 0 -1/11&gt;,
 |24/11 8/11 0 -4/11&gt;, |34/11 -18/11 0 9/11&gt;]
-[[Eigenmonzo|Eigenmonzo]]s: 2, 9/7
+Eigenmonzos: 2, 9/7
 valid range: [692.308, 694.737] (26 to 19)
@@ Line 360: / Line 360: @@
 Map: [&lt;1 0 -4 17|, &lt;0 1 4 -9|]
-[[wedgie|Wedgie]]: &lt;&lt;1 4 -9 4 -17 -32||
+[[Wedgie]]: &lt;&lt;1 4 -9 4 -17 -32||
-[[generator|Generator]]s: 2, 3
+[[Generator]]s: 2, 3
-EDOs: [[7edo|7]], [[19edo|19]], [[45edo|45]], [[64edo|64]]
+EDOs: [[7edo|7]], [[19edo|19]], [[26edo|26]], [[45edo|45]]
-[[Badness|Badness]]: 0.0386
+[[Badness]]: 0.0386
 ==11-limit==