Kleismic family: Difference between revisions

Line 579:

* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~9/7 = {{monzo| 12/25 0 0 -1/25 }}

: {{monzo list| 1 0 0 0 | 6/25 0 0 12/25 | 6/5 0 0 2/5 | 0 0 0 1 }}

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

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

[[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges.

Line 627:

* [[7-odd-limit]]: ~6/5 = {{monzo| 1/3 0 1/7 -1/7 }}

: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]

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

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

* [[9-odd-limit]]: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}

: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]

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

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

Line 651:

* 11-odd-limit: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]

: ~~eigenmonzo (~~unchanged-interval) basis: 2.9/7

: unchanged-interval (eigenmonzo) basis: 2.9/7

@@ Line 579: / Line 579: @@
 * [[7-odd-limit|7-]] and [[9-odd-limit]]: ~9/7 = {{monzo| 12/25 0 0 -1/25 }}
 : {{monzo list| 1 0 0 0 | 6/25 0 0 12/25 | 6/5 0 0 2/5 | 0 0 0 1 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7
 [[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges.
@@ Line 627: / Line 627: @@
 * [[7-odd-limit]]: ~6/5 = {{monzo| 1/3 0 1/7 -1/7 }}
 : [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
 * [[9-odd-limit]]: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
 : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7
 {{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }}
@@ Line 651: / Line 651: @@
 * 11-odd-limit: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
-: eigenmonzo (unchanged-interval) basis: 2.9/7
+: unchanged-interval (eigenmonzo) basis: 2.9/7
 {{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }}