Metric microtemperaments: Difference between revisions

Line 2:

Temperaments not dicussed here include:

* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone]]

* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone|Meantone family]]

* ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell]]

* ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell|Semicomma family]]

* [[Tertiaseptal]], {2401/2400, 65625/65536} → [[Breedsmic temperaments #Tertiaseptal]]

* [[Tertiaseptal]], {2401/2400, 65625/65536} → [[Breedsmic temperaments #Tertiaseptal|Breedsmic temperaments]]

* ''[[Quintupole]]'', {4000/3969, 458752/455625} → [[~~Octagar temperaments~~ #Quintupole]]

* ''[[Quintupole]]'', {4000/3969, 458752/455625} → [[Quintaleap family #Quintupole|Quintaleap family]]

* ''[[Enneadecal]]'', {4375/4374, 703125/702464} → [[Ragismic microtemperaments #Enneadecal]]

* ''[[Enneadecal]]'', {4375/4374, 703125/702464} → [[Ragismic microtemperaments #Enneadecal|Ragismic microtemperaments]]

* ''[[Undim]]'', {5120/5103, 390625/388962} → [[Undim family #Septimal undim]]

* ''[[Undim]]'', {5120/5103, 390625/388962} → [[Undim family #Septimal undim|Undim family]]

* ''[[Grendel]]'', {6144/6125, 16875/16807} → [[Mirkwai clan #Grendel]]

* ''[[Grendel]]'', {6144/6125, 16875/16807} → [[Mirkwai clan #Grendel|Mirkwai clan]]

* ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths]]

* ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths|Kleismic family]]

* ''[[Term]]'', {32805/32768, 250047/250000} → [[Schismatic family #Term]]

* ''[[Term]]'', {32805/32768, 250047/250000} → [[Schismatic family #Term|Schismatic family]]

* ''[[Qak]]'', {420175/419904, 703125/702464} → [[Wizmic microtemperaments #Qak]]

* ''[[Qak]]'', {420175/419904, 703125/702464} → [[Wizmic microtemperaments #Qak|Wizmic microtemperaments]]

== Luminal ==

Line 76:

[[Comma list]]: 703125/702464, 823543/820125

[[Mapping]]: [{{val|10 ~~15 23 27~~}}, {{val|0 4 1 5}}]

[[Mapping]]: [{{val| 10 3 20 12 }}, {{val| 0 4 1 5 }}]

Line 91:

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

Mapping: [{{val|10 ~~15 23 27 35~~}}, {{val|0 4 1 5 -2}}]

Mapping: [{{val| 10 3 20 12 41 }}, {{val| 0 4 1 5 -2 }}]

POTE generator: ~5/4 = 385.396

Line 104:

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

Mapping: [{{val|10 ~~15 23 27 35~~ 37}}, {{val|0 4 1 5 -2 0}}]

Mapping: [{{val| 10 3 20 12 41 37 }}, {{val| 0 4 1 5 -2 0 }}]

POTE generator: ~5/4 = 385.419

Line 119:

[[Comma list]]: 703125/702464, 4096000/4084101

[[Mapping]]: [{{val|1 4 0 -1}}, {{val|0 -26 25 41}}]

[[Mapping]]: [{{val| 1 4 0 -1 }}, {{val| 0 -26 25 41 }}]

Line 134:

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

Mapping: [{{val|1 4 0 -1 -1}}, {{val|0 -26 25 41 48}}]

Mapping: [{{val| 1 4 0 -1 -1 }}, {{val| 0 -26 25 41 48 }}]

POTE generator: ~16/15 = 111.460

Line 147:

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

Mapping: [{{val|1 4 0 -1 -1 5}}, {{val|0 -26 25 41 48 -14}}]

Mapping: [{{val| 1 4 0 -1 -1 5 }}, {{val| 0 -26 25 41 48 -14 }}]

POTE generator: ~16/15 = 111.458

Line 160:

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

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

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

POTE generator: ~16/15 = 111.459

Line 173:

Subgroup: 2.3.5

[[Comma]]: {{monzo|-31 43 -16}}

[[Comma list]]: {{monzo| -31 43 -16 }}

[[Mapping]]: [{{val|1 -3 -10}}, {{val|0 16 43}}]

[[Mapping]]: [{{val| 1 -3 -10 }}, {{val| 0 16 43 }}]

[[POTE generator]]: ~8000/6561 = 343.868

Line 188:

[[Comma list]]: 703125/702464, 14348907/14336000

[[Mapping]]: [{{val|1 -3 -10 -29}}, {{val|0 16 43 111}}]

[[Mapping]]: [{{val| 1 -3 -10 -29 }}, {{val| 0 16 43 111 }}]

[[POTE generator]]: ~8000/6561 = 343.863

@@ Line 2: / Line 2: @@
 Temperaments not dicussed here include:
-* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone]]
+* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone|Meantone family]]
-* ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell]]
+* ''[[Triwell]]'', {1029/1024, 235298/234375} → [[Semicomma family #Triwell|Semicomma family]]
-* [[Tertiaseptal]], {2401/2400, 65625/65536} → [[Breedsmic temperaments #Tertiaseptal]]
+* [[Tertiaseptal]], {2401/2400, 65625/65536} → [[Breedsmic temperaments #Tertiaseptal|Breedsmic temperaments]]
-* ''[[Quintupole]]'', {4000/3969, 458752/455625} → [[Octagar temperaments #Quintupole]]
+* ''[[Quintupole]]'', {4000/3969, 458752/455625} → [[Quintaleap family #Quintupole|Quintaleap family]]
-* ''[[Enneadecal]]'', {4375/4374, 703125/702464} → [[Ragismic microtemperaments #Enneadecal]]
+* ''[[Enneadecal]]'', {4375/4374, 703125/702464} → [[Ragismic microtemperaments #Enneadecal|Ragismic microtemperaments]]
-* ''[[Undim]]'', {5120/5103, 390625/388962} → [[Undim family #Septimal undim]]
+* ''[[Undim]]'', {5120/5103, 390625/388962} → [[Undim family #Septimal undim|Undim family]]
-* ''[[Grendel]]'', {6144/6125, 16875/16807} → [[Mirkwai clan #Grendel]]
+* ''[[Grendel]]'', {6144/6125, 16875/16807} → [[Mirkwai clan #Grendel|Mirkwai clan]]
-* ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths]]
+* ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths|Kleismic family]]
-* ''[[Term]]'', {32805/32768, 250047/250000} → [[Schismatic family #Term]]
+* ''[[Term]]'', {32805/32768, 250047/250000} → [[Schismatic family #Term|Schismatic family]]
-* ''[[Qak]]'', {420175/419904, 703125/702464} → [[Wizmic microtemperaments #Qak]]
+* ''[[Qak]]'', {420175/419904, 703125/702464} → [[Wizmic microtemperaments #Qak|Wizmic microtemperaments]]
 == Luminal ==
@@ Line 76: / Line 76: @@
 [[Comma list]]: 703125/702464, 823543/820125
-[[Mapping]]: [{{val|10 15 23 27}}, {{val|0 4 1 5}}]
+[[Mapping]]: [{{val| 10 3 20 12 }}, {{val| 0 4 1 5 }}]
 {{Multival|legend=1| 40 10 50 -77 -33 88 }}
@@ Line 91: / Line 91: @@
 Comma list: 385/384, 9801/9800, 391314/390625
-Mapping: [{{val|10 15 23 27 35}}, {{val|0 4 1 5 -2}}]
+Mapping: [{{val| 10 3 20 12 41 }}, {{val| 0 4 1 5 -2 }}]
 POTE generator: ~5/4 = 385.396
@@ Line 104: / Line 104: @@
 Comma list: 385/384, 625/624, 847/845, 4459/4455
-Mapping: [{{val|10 15 23 27 35 37}}, {{val|0 4 1 5 -2 0}}]
+Mapping: [{{val| 10 3 20 12 41 37 }}, {{val| 0 4 1 5 -2 0 }}]
 POTE generator: ~5/4 = 385.419
@@ Line 119: / Line 119: @@
 [[Comma list]]: 703125/702464, 4096000/4084101
-[[Mapping]]: [{{val|1 4 0 -1}}, {{val|0 -26 25 41}}]
+[[Mapping]]: [{{val| 1 4 0 -1 }}, {{val| 0 -26 25 41 }}]
 {{Multival|legend=1|26 -25 -41 -100 -138 -25}}
@@ Line 134: / Line 134: @@
 Comma list: 1375/1372, 5632/5625, 35937/35840
-Mapping: [{{val|1 4 0 -1 -1}}, {{val|0 -26 25 41 48}}]
+Mapping: [{{val| 1 4 0 -1 -1 }}, {{val| 0 -26 25 41 48 }}]
 POTE generator: ~16/15 = 111.460
@@ Line 147: / Line 147: @@
 Comma list: 676/675, 1001/1000, 1375/1372, 4096/4095
-Mapping: [{{val|1 4 0 -1 -1 5}}, {{val|0 -26 25 41 48 -14}}]
+Mapping: [{{val| 1 4 0 -1 -1 5 }}, {{val| 0 -26 25 41 48 -14 }}]
 POTE generator: ~16/15 = 111.458
@@ Line 160: / Line 160: @@
 Comma list: 442/441, 561/560, 676/675, 715/714, 4096/4095
-Mapping: [{{val|1 4 0 -1 -1 5 0}}, {{val|0 -26 25 41 48 -14 44}}]
+Mapping: [{{val| 1 4 0 -1 -1 5 0 }}, {{val| 0 -26 25 41 48 -14 44 }}]
 POTE generator: ~16/15 = 111.459
@@ Line 173: / Line 173: @@
 Subgroup: 2.3.5
-[[Comma]]: {{monzo|-31 43 -16}}
+[[Comma list]]: {{monzo| -31 43 -16 }}
-[[Mapping]]: [{{val|1 -3 -10}}, {{val|0 16 43}}]
+[[Mapping]]: [{{val| 1 -3 -10 }}, {{val| 0 16 43 }}]
 [[POTE generator]]: ~8000/6561 = 343.868
@@ Line 188: / Line 188: @@
 [[Comma list]]: 703125/702464, 14348907/14336000
-[[Mapping]]: [{{val|1 -3 -10 -29}}, {{val|0 16 43 111}}]
+[[Mapping]]: [{{val| 1 -3 -10 -29 }}, {{val| 0 16 43 111 }}]
-{{Multival|legend=1|16 43 111 31 131 137}}
+{{Multival|legend=1| 16 43 111 31 131 137 }}
 [[POTE generator]]: ~8000/6561 = 343.863