Metric microtemperaments: Difference between revisions
mNo edit summary |
+luminal |
||
| Line 2: | Line 2: | ||
Temperaments not dicussed here include [[Breedsmic temperaments #Tertiaseptal|tertiaseptal]], [[Ragismic microtemperaments #Enneadecal|enneadecal]], [[Schismatic family #Term|term]], [[Mirkwai clan #Grendel|grendel]], [[Hemifamity temperaments #Undim|undim]], [[Wizmic microtemperaments #Qak|qak]], [[Meantone family|meantone]], [[Kleismic family #Marfifths|marfifths]], and [[Semicomma family #Triwell|triwell]]. | Temperaments not dicussed here include [[Breedsmic temperaments #Tertiaseptal|tertiaseptal]], [[Ragismic microtemperaments #Enneadecal|enneadecal]], [[Schismatic family #Term|term]], [[Mirkwai clan #Grendel|grendel]], [[Hemifamity temperaments #Undim|undim]], [[Wizmic microtemperaments #Qak|qak]], [[Meantone family|meantone]], [[Kleismic family #Marfifths|marfifths]], and [[Semicomma family #Triwell|triwell]]. | ||
= Luminal = | |||
Luminal tempers out the [[meter comma|meter]] and the [[lux comma|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]]: [{{val| 1 0 5 8 }}, {{val| 0 29 -49 -95 }}] | |||
{{Multival|legend=1| 29 -49 -95 -145 -232 -82 }} | |||
[[POTE generator]]: ~8505/8192 = 65.5883 | |||
{{Val list|legend=1| 55d, 128, 183, 311, 494, 1299, 1793 }} | |||
[[Badness]]: 0.1348 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 131072/130977, 703125/702464 | |||
Mapping: [{{val| 1 0 5 8 1 }}, {{val| 0 29 -49 -95 45 }}] | |||
POTE generator: ~80/77 = 65.5881 | |||
Vals: {{val list| 55d, 128, 183, 311, 494, 1299, 1793, 2287d }} | |||
Badness: 0.03282 | |||
== 13-limit == | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2080/2079, 3025/3024, 4096/4095, 31250/31213 | |||
Mapping: [{{val| 1 0 5 8 1 -1 }}, {{val| 0 29 -49 -95 45 86 }}] | |||
POTE generator: ~27/26 = 65.5883 | |||
Vals: {{val list| 128, 183, 311, 494, 1299, 1793 }} | |||
Badness: 0.01685 | |||
== 17-limit == | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 1156/1155, 1275/1274, 2080/2079, 2431/2430, 4096/4095 | |||
Mapping: [{{val| 1 0 5 8 1 -1 6 }}, {{val| 0 29 -49 -95 45 86 -35 }}] | |||
POTE generator: ~27/26 = 65.5878 | |||
Vals: {{val list| 128, 183, 311, 494 }} | |||
Badness: 0.01467 | |||
= Decimetra = | = Decimetra = | ||
| Line 12: | Line 68: | ||
[[Mapping]]: [{{val|10 15 23 27}}, {{val|0 4 1 5}}] | [[Mapping]]: [{{val|10 15 23 27}}, {{val|0 4 1 5}}] | ||
{{Multival|legend=1|40 10 50 -77 -33 88}} | {{Multival|legend=1| 40 10 50 -77 -33 88 }} | ||
[[POTE generator]]: ~5/4 = 385.495 | [[POTE generator]]: ~5/4 = 385.495 | ||
Revision as of 06:32, 11 May 2021
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.
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: 0.1348
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: 0.03282
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: 0.01685
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: 0.01467
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