The Jacobins: Difference between revisions
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The main focus here will be on the 2.5.11.13 [[subgroup]], the subgroup 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]]. | The main focus here will be on the 2.5.11.13 [[subgroup]], the subgroup 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. 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. | Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments ― and it is consistent to distance 2 in the 2.5.11.13 subgroup, subgroup of the comma. 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 == | == Jacobin == | ||
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== Barton == | == Barton == | ||
{{Redirect| Barton | the musician | Jacob Barton }} | |||
{{See also| Chromatic pairs #Barton }} | {{See also| Chromatic pairs #Barton }} | ||
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[[Comma list]]: [[2200/2197]], [[6656/6655]] | [[Comma list]]: [[2200/2197]], [[6656/6655]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 6 3 6 | 0 -8 1 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 6 0 3 6 | 0 0 -8 0 1 -5 }} | ||
: gencom: [2 11/8; 2200/2197 6656/6655] | : gencom: [2 11/8; 2200/2197 6656/6655] | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.0822 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.0822 cents | ||
== Huguenot == | |||
Huguenot, named after French calvinists who fled to Ireland, tempers out the [[4225/4224|leprechaun comma]] together with the jacobin comma. | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 4225/4224, 6656/6655 | |||
{{Mapping|legend=1| 1 1 4 2 2 1 | 0 1 4 0 -3 -5 | 0 0 -5 0 4 7 | 0 0 0 1 0 0 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.009{{c}}, ~3/2 = 701.954{{c}}, ~96/55 = 964.312{{c}}, 7/4 = 968.809{{c}} | |||
: [[error map]]: {{val| 0.009, 0.008, -0.025, -0.000, 0.087, -0.102 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.953{{c}}, ~96/55 = 964.309{{c}}, 7/4 = 968.807{{c}} | |||
: error map: {{val| 0.000, -0.002, -0.045, -0.019, 0.058, -0.132 }} | |||
[[Support]]ing [[ET]]s: {{EDOs|87, 224, 270, 311, 494, 581, 764, 814, 1084, 1308}} | |||
[[Badness]]: 0.508 | |||
== Genojacobin == | == Genojacobin == | ||
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Comma list: 6656/6655, {{monzo|-17 -12 6 4 1 2}}, {{monzo|-12 2 17 -11 -1 1}} | Comma list: 6656/6655, {{monzo|-17 -12 6 4 1 2}}, {{monzo|-12 2 17 -11 -1 1}} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 4 14 19 -15 40 | 0 -5 -6 -10 4 6 | 0 0 -17 22 32 79 }} | ||
Sval mapping generators: ~2 = 1\1, ~3773/2700 = 579.594, ~290304/203125 = 619.783 | Sval mapping generators: ~2 = 1\1, ~3773/2700 = 579.594, ~290304/203125 = 619.783 | ||