Metric microtemperaments: Difference between revisions
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These are rank- | These are rank-2 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 # | * [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone]] | ||
* [[Semicomma family # | * ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell]] | ||
* [[Breedsmic temperaments # | * [[Tertiaseptal]], {2401/2400, 65625/65536} → [[Breedsmic temperaments #Tertiaseptal]] | ||
* [[Ragismic microtemperaments # | * ''[[Enneadecal]]'', {4375/4374, 703125/702464} → [[Ragismic microtemperaments #Enneadecal]] | ||
* [[Hemifamity temperaments # | * ''[[Undim]]'', {5120/5103, 390625/388962} → [[Hemifamity temperaments #Undim]] | ||
* [[Mirkwai clan # | * ''[[Grendel]]'', {6144/6125, 16875/16807} → [[Mirkwai clan #Grendel]] | ||
* [[Kleismic family # | * ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths]] | ||
* [[Schismatic family # | * ''[[Term]]'', {32805/32768, 250047/250000} → [[Schismatic family #Term]] | ||
* [[Wizmic microtemperaments # | * ''[[Qak]]'', {420175/419904, 703125/702464} → [[Wizmic microtemperaments #Qak]] | ||
== Luminal == | == Luminal == | ||
| Line 197: | Line 197: | ||
[[Badness]]: 0.048770 | [[Badness]]: 0.048770 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament collection]] | [[Category:Temperament collection]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Metric]] | [[Category:Metric microtemperaments| ]] <!-- main article --> | ||
[[Category:Microtemperament]] | |||
Revision as of 17:00, 4 July 2021
These are rank-2 temperaments that temper out the meter comma, 703125/702464 = [-11 2 7 -3⟩.
Temperaments not dicussed here include:
- Meantone, {81/80, 126/125} → Meantone family #Septimal meantone
- Triwell, {1029/1024, 235298/234375} → Semicomma family #Triwell
- Tertiaseptal, {2401/2400, 65625/65536} → Breedsmic temperaments #Tertiaseptal
- Enneadecal, {4375/4374, 703125/702464} → Ragismic microtemperaments #Enneadecal
- Undim, {5120/5103, 390625/388962} → Hemifamity temperaments #Undim
- Grendel, {6144/6125, 16875/16807} → Mirkwai clan #Grendel
- Marfifths, {10976/10935, 15625/15552} → Kleismic family #Marfifths
- Term, {32805/32768, 250047/250000} → Schismatic family #Term
- Qak, {420175/419904, 703125/702464} → Wizmic microtemperaments #Qak
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) 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) is related to 25ED5 tuning, and tempers out the hemfiness comma (saquadru-atriyo), 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) tempers out [-31 43 -16⟩ (quadla-quadquadgu) in the 5-limit; the meter and the euzenius comma, 78125000/78121827 as well as skeetsma (14348907/14336000, lalarutrigu) in the 7-limit. Osiris temperament (171&670, named after the eldest son of Geb) tempers out the same 5-limit comma as the geb, but with the breedsma rather than the meter tempered out.
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