Septiennealimmal clan: Difference between revisions

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[[Optimal tuning]]s:

* [[CTE]]: ~2592/2401 = 133.~~33... = 1\9~~, ~3/2 = 702.0044

* [[CTE]]: ~2592/2401 = 133.3333, ~3/2 = 702.0044

: [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }}

* [[POTE]]: ~2592/2401 = 133.~~33... = 1\9~~, ~3/2 = 701.9649

* [[POTE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9649

: error map: {{val| 0.0000 +0.0099 -0.1944 }}

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=== Septiennealic ===

Septiennealic finds a somewhat high-damage but very simple/intuitive mapping of prime 13 ~~via explaining ~7~~/~~6 = 2\9 as a consequence of~~ ~14/13~~~13/12 =~~ 1\9.

Septiennealic finds a somewhat high-damage but very simple and intuitive mapping of prime 13 by fixing 13/12~14/13 at 1\9.

A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]] ~~(though if~~ we include a somewhat more complex mapping for 11 via 63 ~~& 99~~, it is the optimal patent val and largest in the sequence).

A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]]. If we include a somewhat more complex mapping for 11 via {{nowrap| 36e & 63 }}, it will become the optimal patent val and largest in the sequence.

[[Subgroup]]: 2.3.7.13

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[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.~~33... = 1\9~~, ~3/2 = 702.638

[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.333, ~3/2 = 702.638

[[Badness]] (Dirichlet): 0.540

[[Badness]]:

* Smith: 0.0134

* Dirichlet: 0.540

=== Ennea ===

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Optimal tunings:

* CTE: ~121/112 = 133.~~333~~, 343/198 = 951.0143 (~99/98 = 17.6810)

* CTE: ~121/112 = 133.3333, 343/198 = 951.0143 (~99/98 = 17.6810)

* POTE: ~121/112 = 133.~~333~~, 343/198 = 950.9591 (~99/98 = 17.6258)

* POTE: ~121/112 = 133.3333, 343/198 = 950.9591 (~99/98 = 17.6258)

{{Optimal ET sequence|legend=0| 54, 63, 72, 135, 342, 477, 1089, 1566 }}

@@ Line 21: / Line 21: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2592/2401 = 133.33... = 1\9, ~3/2 = 702.0044
+* [[CTE]]: ~2592/2401 = 133.3333, ~3/2 = 702.0044
 : [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }}
-* [[POTE]]: ~2592/2401 = 133.33... = 1\9, ~3/2 = 701.9649
+* [[POTE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9649
 : error map: {{val| 0.0000 +0.0099 -0.1944 }}
@@ Line 29: / Line 29: @@
 === Septiennealic ===
-Septiennealic finds a somewhat high-damage but very simple/intuitive mapping of prime 13 via explaining ~7/6 = 2\9 as a consequence of ~14/13~13/12 = 1\9.
+Septiennealic finds a somewhat high-damage but very simple and intuitive mapping of prime 13 by fixing 13/12~14/13 at 1\9.
-A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]] (though if we include a somewhat more complex mapping for 11 via 63 & 99, it is the optimal patent val and largest in the sequence).
+A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]]. If we include a somewhat more complex mapping for 11 via {{nowrap| 36e & 63 }}, it will become the optimal patent val and largest in the sequence.
 [[Subgroup]]: 2.3.7.13
@@ Line 39: / Line 39: @@
 {{Mapping|legend=2| 9 0 11 19 | 0 1 1 1 }}
-[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.33... = 1\9, ~3/2 = 702.638
+[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.333, ~3/2 = 702.638
 {{Optimal ET sequence|legend=1| 27, 36, 99, 135f, 171f }}
-[[Badness]] (Dirichlet): 0.540
+[[Badness]]:
+* Smith: 0.0134
+* Dirichlet: 0.540
 === Ennea ===
@@ Line 55: / Line 57: @@
 Optimal tunings:
-* CTE: ~121/112 = 133.333, 343/198 = 951.0143 (~99/98 = 17.6810)
+* CTE: ~121/112 = 133.3333, 343/198 = 951.0143 (~99/98 = 17.6810)
-* POTE: ~121/112 = 133.333, 343/198 = 950.9591 (~99/98 = 17.6258)
+* POTE: ~121/112 = 133.3333, 343/198 = 950.9591 (~99/98 = 17.6258)
 {{Optimal ET sequence|legend=0| 54, 63, 72, 135, 342, 477, 1089, 1566 }}