Metric microtemperaments: Difference between revisions
+luminal |
m Cleanup for links |
||
| Line 1: | Line 1: | ||
These are rank-two temperaments that temper out the [[meter comma]], 703125/702464 = {{monzo|-11 2 7 -3}}. | These are rank-two temperaments that temper out the [[meter comma]], 703125/702464 = {{monzo|-11 2 7 -3}}. | ||
Temperaments not dicussed here include [[ | Temperaments not dicussed here include: | ||
* [[Meantone family #Septimal meantone|Septimal meantone]] | |||
* [[Semicomma family #Triwell|Triwell]] | |||
* [[Breedsmic temperaments #Tertiaseptal|Tertiaseptal]] | |||
* [[Ragismic microtemperaments #Enneadecal|Enneadecal]] | |||
* [[Hemifamity temperaments #Undim|Undim]] | |||
* [[Mirkwai clan #Grendel|Grendel]] | |||
* [[Kleismic family #Marfifths|Marfifths]] | |||
* [[Schismatic family #Term|Term]] | |||
* [[Wizmic microtemperaments #Qak|Qak]] | |||
= Luminal = | = Luminal = | ||
Revision as of 06:52, 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:
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