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Wizmic microtemperaments: Difference between revisions

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Discussed elsewhere are:  
Discussed elsewhere are:  
* [[Superpyth]], {64/63, 245/243} → [[Archytas clan #Superpyth|Archytas clan]]
* [[Superpyth]] (+64/63, or 245/243) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[Cloudtone]]'', {81/80, 16875/16384} → [[Meantone family #Cloudtone|Meantone family]]
* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* [[Oolong]], {126/125, 117649/116640} → [[Starling temperaments #Oolong|Starling temperaments]]
* [[Oolong]] (+126/125) → [[Starling temperaments #Oolong|Starling temperaments]]
* [[Wizard]], {225/224, 118098/117649} → [[Marvel temperaments #Wizard|Marvel temperaments]]
* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]
* ''[[Hemiseven]]'', {1029/1024, 19683/19600} → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* [[Ennealimmal]], {2401/2400, 4375/4374} → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
* ''[[Sengagen]]'', {3136/3125, 420175/419904} → [[Hemimean clan #Sengagen|Hemimean clan]]
* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen|Hemimean clan]]
* ''[[Septiquarter]]'', {5120/5103, 420175/419904} → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* ''[[Hendecatonic]]'', {6144/6125, 10976/10935} → [[Porwell temperaments #Hendecatonic|Porwell temperaments]]
* ''[[Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic|Porwell temperaments]]
* ''[[Sqrtphi]]'', {15625/15552, 16875/16807} → [[Kleismic family #Sqrtphi|Kleismic family]]
* ''[[Sqrtphi]]'' (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi|Kleismic family]]
* [[Tsaharuk]], {32805/32768, 420175/419904} → [[Schismatic family #Tsaharuk|Schismatic family]]
* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]]
* ''[[Fifthplus]]'', {65625/65536, 420175/419904} → [[Horwell temperaments #Fifthplus|Horwell temperaments]]
* ''[[Fifthplus]]'' (+5625/65536) → [[Horwell temperaments #Fifthplus|Horwell temperaments]]
* ''[[Octowerck]]'', {321489/320000, 420175/419904} → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* ''[[Quinwell]]'', {420175/419904, 2109375/2097152} → [[Semicomma family #Quinwell|Semicomma family]]
* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell|Semicomma family]]
* ''[[Decavish]]'', {420175/419904, 2202927104/2197265625} → [[Vishnuzmic family #Decavish|Vishnuzmic family]]
* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]]


Considered below are qak, tokko, tertiathirds, and witcher.  
Considered below are qak, tokko, tertiathirds, and witcher.  


== Qak ==
== Qak ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 420175/419904, 703125/702464
[[Comma list]]: 420175/419904, 703125/702464


[[Mapping]]: [{{val| 1 27 11 40 }}, {{val| 0 -41 -14 -60 }}]
{{Mapping|legend=1| 1 27 11 40 | 0 -41 -14 -60 }}


Mapping generators: ~2, ~192/125
: mapping generators: ~2, ~192/125


{{Multival|legend=1| 41 14 60 -73 -20 100 }}
{{Multival|legend=1| 41 14 60 -73 -20 100 }}


[[POTE generator]]: ~125/96 = 456.144
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 456.144


{{Optimal ET sequence|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
{{Optimal ET sequence|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
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== Tokko ==
== Tokko ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 420175/419904, 5250987/5242880
[[Comma list]]: 420175/419904, 5250987/5242880


[[Mapping]]: [{{val| 1 12 56 -2 }}, {{val| 0 -13 -67 6 }}]
{{Mapping|legend=1| 1 12 56 -2 | 0 -13 -67 6 }}


Mapping generators: ~2, ~256/147
: mapping generators: ~2, ~256/147


{{Multival|legend=1| 13 67 -6 76 -46 -202 }}
{{Multival|legend=1| 13 67 -6 76 -46 -202 }}


[[POTE generator]]: ~147/128 = 238.599
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 238.599


{{Optimal ET sequence|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}
{{Optimal ET sequence|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}
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The ''tertiathirds'' temperament (121&270) tempers out the quasiorwellisma, 29360128/29296875 in the 7-limit, as well as the wizma. This temperament splits the interval of 5/4 into three [[14/13]] generators.
The ''tertiathirds'' temperament (121&270) tempers out the quasiorwellisma, 29360128/29296875 in the 7-limit, as well as the wizma. This temperament splits the interval of 5/4 into three [[14/13]] generators.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 420175/419904, 29360128/29296875
[[Comma list]]: 420175/419904, 29360128/29296875


[[Mapping]]: [{{val| 1 48 5 76 }}, {{val| 0 -52 -3 -82 }}]
{{Mapping|legend=1| 1 48 5 76 | 0 -52 -3 -82 }}


Mapping generators: ~2, ~6272/3375
: mapping generators: ~2, ~6272/3375


{{Multival|legend=1| 52 3 82 -116 -16 182 }}
{{Multival|legend=1| 52 3 82 -116 -16 182 }}


[[POTE generator]]: ~3375/3136 = 128.888
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3375/3136 = 128.888


{{Optimal ET sequence|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
{{Optimal ET sequence|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
Line 78: Line 78:
Comma list: 3025/3024, 5632/5625, 117649/117612
Comma list: 3025/3024, 5632/5625, 117649/117612


Mapping: [{{val| 1 48 5 76 107 }}, {{val| 0 -52 -3 -82 -116 }}]
Mapping: {{mapping| 1 48 5 76 107 | 0 -52 -3 -82 -116 }}


POTE generator: ~264/245 = 128.890
Optimal tuning (POTE): ~2 = 1\1, ~264/245 = 128.890


{{Optimal ET sequence|legend=1| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }}
{{Optimal ET sequence|legend=1| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }}
Line 91: Line 91:
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224


Mapping: [{{val| 1 48 5 76 107 76 }}, {{val| 0 -52 -3 -82 -116 -81 }}]
Mapping: {{mapping| 1 48 5 76 107 76 | 0 -52 -3 -82 -116 -81 }}


POTE generator: ~14/13 = 128.890
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 128.890


{{Optimal ET sequence|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
{{Optimal ET sequence|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
Line 104: Line 104:
Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224
Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224


Mapping: [{{val| 1 48 5 76 107 76 63 }}, {{val| 0 -52 -3 -82 -116 -81 -66 }}]
Mapping: {{mapping| 1 48 5 76 107 76 63 | 0 -52 -3 -82 -116 -81 -66 }}


POTE generator: ~14/13 = 128.891
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 128.891


{{Optimal ET sequence|legend=1| 121, 149, 270 }}
{{Optimal ET sequence|legend=1| 121, 149, 270 }}
Line 117: Line 117:
Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125
Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125


Mapping: [{{val|1 48 5 76 107 76 63 -2}}, {{val|0 -52 -3 -82 -116 -81 -66 7}}]
Mapping: {{mapping| 1 48 5 76 107 76 63 -2 | 0 -52 -3 -82 -116 -81 -66 7 }}


POTE generator: ~14/13 = 128.890
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 128.890


{{Optimal ET sequence|legend=1| 121, 149, 270 }}
{{Optimal ET sequence|legend=1| 121, 149, 270 }}
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== Witcher ==
== Witcher ==
{{see also|Amity family}}
{{See also| Amity family }}


The witcher temperament (99&166) tempers out wizma (420175/419904) and the amity comma (1600000/1594323) as well as the ''hemfiness'' comma (4096000/4084101, saquinru-atriyo).
The witcher temperament (99 & 166) tempers out wizma (420175/419904) and the amity comma (1600000/1594323) as well as the ''hemfiness'' comma (4096000/4084101, saquinru-atriyo).


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 420175/419904, 1600000/1594323
[[Comma list]]: 420175/419904, 1600000/1594323


[[Mapping]]: [{{val| 1 18 45 12 }}, {{val| 0 -25 -65 -14 }}]
{{Mapping|legend=1| 1 18 45 12 | 0 -25 -65 -14 }}


Mapping generators: ~2, ~63/40
: mapping generators: ~2, ~63/40


{{Multival|legend=1| 25 65 14 45 -48 -150 }}
{{Multival|legend=1| 25 65 14 45 -48 -150 }}


[[POTE generator]]: ~80/63 = 412.098
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~80/63 = 412.098


{{Optimal ET sequence|legend=1| 99, 265, 364, 463, 562, 1025 }}
{{Optimal ET sequence|legend=1| 99, 265, 364, 463, 562, 1025 }}
Line 151: Line 151:
Comma list: 540/539, 4375/4356, 1240029/1239040
Comma list: 540/539, 4375/4356, 1240029/1239040


Mapping: [{{val| 1 18 45 12 77 }}, {{val| 0 -25 -65 -14 -112 }}]
Mapping: {{mapping| 1 18 45 12 77 | 0 -25 -65 -14 -112 }}


POTE generator: ~80/63 = 412.079
Optimal tuning (POTE): ~2 = 1\1, ~80/63 = 412.079


{{Optimal ET sequence|legend=1| 99e, 166, 265 }}
{{Optimal ET sequence|legend=1| 99e, 166, 265 }}
Line 164: Line 164:
Comma list: 540/539, 729/728, 4375/4356, 10648/10647
Comma list: 540/539, 729/728, 4375/4356, 10648/10647


Mapping: [{{val| 1 18 45 12 77 93 }}, {{val| 0 -25 -65 -14 -112 -136 }}]
Mapping: {{mapping| 1 18 45 12 77 93 | 0 -25 -65 -14 -112 -136 }}


POTE generator: ~33/26 = 412.070
Optimal tuning (POTE): ~2 = 1\1, ~33/26 = 412.070


{{Optimal ET sequence|legend=1| 99ef, 166, 265, 431c, 696cc }}
{{Optimal ET sequence|legend=1| 99ef, 166, 265, 431c, 696cc }}
Line 177: Line 177:
Comma list: 9801/9800, 41503/41472, 585640/583443
Comma list: 9801/9800, 41503/41472, 585640/583443


Mapping: [{{val| 2 11 25 10 16 }}, {{val| 0 -25 -65 -14 -29 }}]
Mapping: {{mapping| 2 11 25 10 16 | 0 -25 -65 -14 -29 }}


Mapping generators: ~99/70, ~49/44
: mapping generators: ~99/70, ~49/44


POTE generator: ~49/44 = 187.904
Optimal tuning (POTE): ~99/70 = 1\2, ~49/44 = 187.904


{{Optimal ET sequence|legend=1| 166, 198, 364, 562, 926, 1488bd, 2414bdd }}
{{Optimal ET sequence|legend=1| 166, 198, 364, 562, 926, 1488bd, 2414bdd }}
Line 192: Line 192:
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280


Mapping: [{{val| 2 11 25 10 16 24 }}, {{val| 0 -25 -65 -14 -29 -53 }}]
Mapping: {{mapping| 2 11 25 10 16 24 | 0 -25 -65 -14 -29 -53 }}


POTE generator: ~39/35 = 187.904
Optimal tuning (POTE): ~99/70 = 1\2, ~39/35 = 187.904


{{Optimal ET sequence|legend=1| 166, 198, 364, 562, 926 }}
{{Optimal ET sequence|legend=1| 166, 198, 364, 562, 926 }}
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Comma list: 3025/3024, 117649/117612, 1600000/1594323
Comma list: 3025/3024, 117649/117612, 1600000/1594323


Mapping: [{{val| 1 18 45 12 -10 }}, {{val| 0 -50 -130 -28 41 }}]
Mapping: {{mapping| 1 18 45 12 -10 | 0 -50 -130 -28 41 }}


Mapping generators: ~2, ~1120/891
: mapping generators: ~2, ~1120/891


POTE generator: ~1120/891 = 393.950
Optimal tuning (POTE): ~2 = 1\1, ~1120/891 = 393.950


{{Optimal ET sequence|legend=1| 198, 463, 661, 1124bde }}
{{Optimal ET sequence|legend=1| 198, 463, 661, 1124bde }}
Line 220: Line 220:
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323


Mapping: [{{val| 1 18 45 12 -10 71 }}, {{val| 0 -50 -130 -28 41 -205 }}]
Mapping: {{mapping| 1 18 45 12 -10 71 | 0 -50 -130 -28 41 -205 }}


POTE generator: ~1120/891 = 393.948
Optimal tuning (POTE): ~2 = 1\1, ~1120/891 = 393.948


{{Optimal ET sequence|legend=1| 198, 463, 661 }}
{{Optimal ET sequence|legend=1| 198, 463, 661 }}
Line 233: Line 233:
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561


Mapping: [{{val| 1 18 45 12 -10 6 }}, {{val| 0 -50 -130 -28 41 -7 }}]
Mapping: {{mapping| 1 18 45 12 -10 6 | 0 -50 -130 -28 41 -7 }}


POTE generator: ~49/39 = 393.949
Optimal tuning (POTE): ~2 = 1\1, ~49/39 = 393.949


{{Optimal ET sequence|legend=1| 198, 463f, 661ff }}
{{Optimal ET sequence|legend=1| 198, 463f, 661ff }}
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[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Wizmic microtemperaments| ]] <!-- main article -->
[[Category:Wizmic microtemperaments| ]] <!-- main article -->
[[Category:Wizmic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Microtemperaments]]
[[Category:Microtemperaments]]
Retrieved from "https://en.xen.wiki/w/Wizmic_microtemperaments"