Archytas family: Difference between revisions

Line 2:

== Archytas ==

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

[[Comma list]]: [[64/63]]

Line 16:

: Angle (3/2, 5/4) = 90 degrees

[[POTE ~~generator~~]]s: ~3/2 = 709.3213, ~5/4 = 393.3747

[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.3213, ~5/4 = 393.3747

[[Minimax tuning]]:

* [[7-odd-limit]]

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

: [[Eigenmonzo]]s (unchanged intervals): 2~~, 6~~/5, 7/5

: [[Eigenmonzo basis]] (unchanged intervals): 2.5/3.7/3

* [[9-odd-limit]]

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

: [[Eigenmonzo]]s (unchanged intervals): 2~~, 6~~/5, 9/7

: [[Eigenmonzo basis]] (unchanged intervals): 2.5/3.9/7

{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 39d, 49, 88bcd, 110bcdd }}

Scales: [[archytas12]], [[archytas12synch]]

Line 37:

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 64/63, 100/99

Line 51:

: Angle (3/2, 6/5) = 75.0475 degrees

[[POTE ~~generator~~]]s: ~3/2 = 709.6869, ~5/4 = 391.4507

[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.6869, ~5/4 = 391.4507

[[Minimax tuning]]:

* [[11-odd-limit]]

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

: [[Eigenmonzo]]s (unchanged intervals): 2, 11/9, 9/7

: [[Eigenmonzo basis]] (unchanged intervals): 2.11/9.9/7

[[Badness]]: 0.469 × 10<sup>-3</sup>

Line 65:

== Vulcan ==

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 56/55, 64/63

Line 73:

Mapping generators: ~2, ~3, ~5

[[POTE ~~generator~~]]s: ~3/2 = 710.9720, ~5/4 = 401.2699

[[Optimal tuning]] ([[POTE]]): ~3/2 = 710.9720, ~5/4 = 401.2699

@@ Line 2: / Line 2: @@
 == Archytas ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: [[64/63]]
@@ Line 16: / Line 16: @@
 : Angle (3/2, 5/4) = 90 degrees
-[[POTE generator]]s: ~3/2 = 709.3213, ~5/4 = 393.3747
+[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.3213, ~5/4 = 393.3747
 [[Minimax tuning]]:
 * [[7-odd-limit]]
 : [{{monzo| 1 0 0 0 }}, {{monzo| 2 1/3 0 -1/3 }}, {{monzo| 2 -2/3 1 -1/3 }}, {{monzo| 2 -2/3 0 2/3 }}]
-: [[Eigenmonzo]]s (unchanged intervals): 2, 6/5, 7/5
+: [[Eigenmonzo basis]] (unchanged intervals): 2.5/3.7/3
 * [[9-odd-limit]]
 : [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 }}, {{monzo| 3/2 -1/2 1 -1/4 }}, {{monzo| 3 -1 0 1/2 }}]
-: [[Eigenmonzo]]s (unchanged intervals): 2, 6/5, 9/7
+: [[Eigenmonzo basis]] (unchanged intervals): 2.5/3.9/7
-{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 49 }}
+{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 39d, 49, 88bcd, 110bcdd }}
 Scales: [[archytas12]], [[archytas12synch]]
@@ Line 37: / Line 37: @@
 {{Main| Ares }}
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 64/63, 100/99
@@ Line 51: / Line 51: @@
 : Angle (3/2, 6/5) = 75.0475 degrees
-[[POTE generator]]s: ~3/2 = 709.6869, ~5/4 = 391.4507
+[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.6869, ~5/4 = 391.4507
 [[Minimax tuning]]:
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 0 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 -1 0 1/2 0 }}, {{monzo| 3 -1 0 -1/2 1 }}]
-: [[Eigenmonzo]]s (unchanged intervals): 2, 11/9, 9/7
+: [[Eigenmonzo basis]] (unchanged intervals): 2.11/9.9/7
-{{Val list|legend=1| 12, 15, 22, 27e, 34d, 49 }}
+{{Val list|legend=1| 12, 15, 22, 27e, 34d, 49, 181bbcddeeee }}
 [[Badness]]: 0.469 × 10<sup>-3</sup>
@@ Line 65: / Line 65: @@
 == Vulcan ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 56/55, 64/63
@@ Line 73: / Line 73: @@
 Mapping generators: ~2, ~3, ~5
-[[POTE generator]]s: ~3/2 = 710.9720, ~5/4 = 401.2699
+[[Optimal tuning]] ([[POTE]]): ~3/2 = 710.9720, ~5/4 = 401.2699
 {{Val list|legend=1| 5, 10, 12, 15, 27e }}