The Jacobins: Difference between revisions

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'''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].

The main focus here will be on the 2.5.11.13 [[subgroup]], as the jacobin comma ~~can be entrenched in~~ other temperaments like [[vidar]].

The main focus here will be on the 2.5.11.13 [[subgroup]], the subgorup of the comma. Besides, in the full 13-limit the jacobin comma often functions as a part of a basis of other temperaments of other families and groups, like [[vidar]].

Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments.

Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments. Since 1789edo has a bad approximation to the 3rd harmonic, 2.5.7.11.13 is also the main subgroup for many temperaments, and 7-limit extensions to 2.5.11.13 temperaments are named "septimal ..." after the original temperament.

== Jacobin-naiadic ==

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[[Optimal tuning]] ([[CTE]]): ~11/8 = 551.370

Vals: {{EDOs| 37, 1789 }}

=== Septimal onzonic ===

Septimal onzonic in between the 2.5.11.13 subgroup adds the mapping for 7.

Subgroup: 2.5.7.11.13

Comma list: 6656/6655, 200126927/200000000, 41322093568/41259765625

Sval mapping: [{{val| 1 74 114 3 74 }}, {{val| 0 -156 -242 1 -153 }}]

Optimal tuning (CTE): ~11/8 = 551.369

Vals: {{EDOs| 37, 1789 }}

@@ Line 1: / Line 1: @@
 '''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].
-The main focus here will be on the 2.5.11.13 [[subgroup]], as the jacobin comma can be entrenched in other temperaments like [[vidar]].
+The main focus here will be on the 2.5.11.13 [[subgroup]], the subgorup of the comma. Besides, in the full 13-limit the jacobin comma often functions as a part of a basis of other temperaments of other families and groups, like [[vidar]].
-Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments.
+Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments. Since 1789edo has a bad approximation to the 3rd harmonic, 2.5.7.11.13 is also the main subgroup for many temperaments, and 7-limit extensions to 2.5.11.13 temperaments are named "septimal ..." after the original temperament.
 == Jacobin-naiadic ==
@@ Line 29: / Line 29: @@
 [[Optimal tuning]] ([[CTE]]): ~11/8 = 551.370
+Vals: {{EDOs| 37, 1789 }}
+=== Septimal onzonic ===
+Septimal onzonic in between the 2.5.11.13 subgroup adds the mapping for 7.
+Subgroup: 2.5.7.11.13
+Comma list: 6656/6655, 200126927/200000000, 41322093568/41259765625
+Sval mapping: [{{val| 1 74 114 3 74 }}, {{val| 0 -156 -242 1 -153 }}]
+Optimal tuning (CTE): ~11/8 = 551.369
 Vals: {{EDOs| 37, 1789 }}