Metric microtemperaments

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Revision as of 06:38, 3 May 2021 by Xenllium (talk | contribs) (Created page with "These are rank-two temperaments that temper out the meter comma, 703125/702464 = {{monzo|-11 2 7 -3}}. Temperaments not dicussed here include Breedsmic temperaments #Te...")
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These are rank-two temperaments that temper out the meter comma, 703125/702464 = [-11 2 7 -3.

Temperaments not dicussed here include tertiaseptal, enneadecal, term, grendel, undim, qak, meantone, marfifths, and triwell.

Decimetra

The decimetra temperament (50&140, named by Xenllium) tempers out the Procyon comma, 823543/820125 = [0 -8 -3 7 as well as linus comma.

Subgroup: 2.3.5.7

Comma list: 703125/702464, 823543/820125

Mapping: [10 15 23 27], 0 4 1 5]]

Wedgie⟨⟨ 40 10 50 -77 -33 88 ]]

POTE generator: ~5/4 = 385.495

Template:Val list

Badness: 0.121818

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 9801/9800, 391314/390625

Mapping: [10 15 23 27 35], 0 4 1 5 -2]]

POTE generator: ~5/4 = 385.396

Vals: Template:Val list

Badness: 0.056915

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 625/624, 847/845, 4459/4455

Mapping: [10 15 23 27 35 37], 0 4 1 5 -2 0]]

POTE generator: ~5/4 = 385.419

Vals: Template:Val list

Badness: 0.029297

Stockhausenic

The stockhausenic temperament (140&183, named by Xenllium) is related to 25ED5 tuning, and tempers out the hemfiness comma (saquadru-atriyo, named by Xenllium), 4096000/4084101 = [15 -5 3 -5.

Subgroup: 2.3.5.7

Comma list: 703125/702464, 4096000/4084101

Mapping: [1 4 0 -1], 0 -26 25 41]]

Wedgie⟨⟨ 26 -25 -41 -100 -138 -25 ]]

POTE generator: ~16/15 = 111.453

Template:Val list

Badness: 0.088753

11-limit

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 5632/5625, 35937/35840

Mapping: [1 4 0 -1 -1], 0 -26 25 41 48]]

POTE generator: ~16/15 = 111.460

Vals: Template:Val list

Badness: 0.056043

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1375/1372, 4096/4095

Mapping: [1 4 0 -1 -1 5], 0 -26 25 41 48 -14]]

POTE generator: ~16/15 = 111.458

Vals: Template:Val list

Badness: 0.029947

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 442/441, 561/560, 676/675, 715/714, 4096/4095

Mapping: [1 4 0 -1 -1 5 0], 0 -26 25 41 48 -14 44]

POTE generator: ~16/15 = 111.459

Vals: Template:Val list

Badness: 0.019205