Metric microtemperaments: Difference between revisions
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{{Val list|legend=1| 55d, 128, 183, 311, 494, 1299, 1793 }} | {{Val list|legend=1| 55d, 128, 183, 311, 494, 1299, 1793 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.134822 | ||
== 11-limit == | == 11-limit == | ||
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Vals: {{val list| 55d, 128, 183, 311, 494, 1299, 1793, 2287d }} | Vals: {{val list| 55d, 128, 183, 311, 494, 1299, 1793, 2287d }} | ||
Badness: 0. | Badness: 0.032816 | ||
== 13-limit == | == 13-limit == | ||
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Vals: {{val list| 128, 183, 311, 494, 1299, 1793 }} | Vals: {{val list| 128, 183, 311, 494, 1299, 1793 }} | ||
Badness: 0. | Badness: 0.016849 | ||
== 17-limit == | == 17-limit == | ||
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Vals: {{val list| 128, 183, 311, 494 }} | Vals: {{val list| 128, 183, 311, 494 }} | ||
Badness: 0. | Badness: 0.014674 | ||
= Decimetra = | = Decimetra = | ||
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Badness: 0.019205 | Badness: 0.019205 | ||
= Geb = | |||
The ''geb'' temperaent (171&506, named after the earth god of ancient Egyptian religion by [[User: Xenllium|Xenllium]]) tempers out the meter and the euzenius comma, 78125000/78121827 as well as 14348907/14336000 (lalarutrigu). | |||
{{See also|Breedsmic temperaments #Osiris}} | |||
Subgroup: 2.3.5 | |||
[[Comma]]: {{monzo|-31 43 -16}} | |||
[[Mapping]]: [{{val|1 -3 -10}}, {{val|0 16 43}}] | |||
[[POTE generator]]: ~8000/6561 = 343.868 | |||
{{Val list|legend=1| 7, 143c, 150c, 157, 164, 171, 506, 677, 848 }} | |||
[[Badness]]: 0.118577 | |||
== 7-limit == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 703125/702464, 14348907/14336000 | |||
[[Mapping]]: [{{val|1 -3 -10 -29}}, {{val|0 16 43 111}}] | |||
{{Multival|legend=1|16 43 111 31 131 137}} | |||
[[POTE generator]]: ~8000/6561 = 343.863 | |||
{{Val list|legend=1| 171, 1190, 1361, 1532, 1703, 1874, 2045, 2216, 4603bc }} | |||
[[Badness]]: 0.048770 | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Metric]] | [[Category:Metric]] | ||
Revision as of 13:23, 24 May 2021
These are rank-two temperaments that temper out the meter comma, 703125/702464 = [-11 2 7 -3⟩.
Temperaments not dicussed here include:
Luminal
Luminal tempers out the meter and the lux in the 7-limit, 3025/3024 in the 11-limit, 2080/2079, 4096/4095 in the 13-limit, and 1156/1155 and 2601/2600 in the 17-limit.
Subgroup: 2.3.5.7
Comma list: 703125/702464, 26843545600/26795786661
Mapping: [⟨1 0 5 8], ⟨0 29 -49 -95]]
Wedgie: ⟨⟨ 29 -49 -95 -145 -232 -82 ]]
POTE generator: ~8505/8192 = 65.5883
Badness: 0.134822
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 131072/130977, 703125/702464
Mapping: [⟨1 0 5 8 1], ⟨0 29 -49 -95 45]]
POTE generator: ~80/77 = 65.5881
Vals: Template:Val list
Badness: 0.032816
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 4096/4095, 31250/31213
Mapping: [⟨1 0 5 8 1 -1], ⟨0 29 -49 -95 45 86]]
POTE generator: ~27/26 = 65.5883
Vals: Template:Val list
Badness: 0.016849
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095
Mapping: [⟨1 0 5 8 1 -1 6], ⟨0 29 -49 -95 45 86 -35]]
POTE generator: ~27/26 = 65.5878
Vals: Template:Val list
Badness: 0.014674
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
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
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
Geb
The geb temperaent (171&506, named after the earth god of ancient Egyptian religion by Xenllium) tempers out the meter and the euzenius comma, 78125000/78121827 as well as 14348907/14336000 (lalarutrigu).
Subgroup: 2.3.5
Comma: [-31 43 -16⟩
Mapping: [⟨1 -3 -10], ⟨0 16 43]]
POTE generator: ~8000/6561 = 343.868
Badness: 0.118577
7-limit
Subgroup: 2.3.5.7
Comma list: 703125/702464, 14348907/14336000
Mapping: [⟨1 -3 -10 -29], ⟨0 16 43 111]]
Wedgie: ⟨⟨ 16 43 111 31 131 137 ]]
POTE generator: ~8000/6561 = 343.863
Badness: 0.048770