Wizmic microtemperaments: Difference between revisions

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No need for cassawizmic because there is no canon androwizmic
- witcher (more properly addressed in amity family)
 
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{{Technical data page}}
{{Technical data page}}
This is a collection of [[Rank-2 temperament|rank-2]] [[microtemperament]]s which [[Tempering out|tempers out]] the [[wizma]], {{monzo|-6 -8 2 5}} = 420175/419904.
This is a collection of [[rank-2 temperament|rank-2]] [[microtemperament]]s which [[tempering out|temper out]] the [[wizma]] ({{monzo|legend=1| -6 -8 2 5 }}, [[ratio]]: 420175/419904).


Discussed elsewhere are:  
Temperaments discussed elsewhere are:  
* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth|Archytas clan]]
* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth|Archytas clan]]
* ''[[Gariwizmic]]'' (+33554432/33480783) → [[Garischismic clan #Gariwizmic|Garischismic clan]]
* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
* [[Oolong]] (+126/125) → [[Starling temperaments #Oolong|Starling temperaments]]
* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]]
* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen|Hemimean clan]]
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter|Hemifamity temperaments]]
* ''[[Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic|Porwell temperaments]]
* ''[[Hendecatonic (temperament)|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic|Porwell temperaments]]
* ''[[Sqrtphi]]'' (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi|Kleismic family]]
* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]]
* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]]
* ''[[Witcher]]'' (+1600000/1594323) → [[Amity family #Witcher|Amity family]]
* ''[[Fifthplus]]'' (+5625/65536) → [[Horwell temperaments #Fifthplus|Horwell temperaments]]
* [[Oolong]] (+126/125) → [[Starling temperaments #Oolong|Starling temperaments]]
* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]]
* ''[[Fifthplus]]'' (+65625/65536) → [[Horwell temperaments #Fifthplus|Horwell temperaments]]
* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck|Varunismic temperaments]]
* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen|Hemimean clan]]
* [[Sqrtphi]] (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi|Kleismic family]]
* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell|Semicomma family]]
* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell|Semicomma family]]
* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]]
* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]]


Considered below are qak, tokko, tertiathirds, witcher, and gariwizmic.  
Considered below are qak, tokko, and tertiathirds, in the order of increasing [[badness]].  


== Qak ==
== Qak ==
Qak tempers out the [[meter]] in addition to the wizma, and may be described as the {{nowrap| 50 & 171 }} temperament.
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


{{Mapping|legend=1| 1 27 11 40 | 0 -41 -14 -60 }}
{{Mapping|legend=1| 1 -14 -3 -20 | 0 41 14 60 }}
 
: mapping generators: ~2, ~125/96
: mapping generators: ~2, ~192/125


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 456.144
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0566{{c}}, ~125/96 = 456.1655{{c}}
: [[error map]]: {{val| +0.057 +0.039 -0.166 -0.027 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/96 = 456.1450{{c}}
: error map: {{val| 0.000 -0.009 -0.283 -0.125 }}


{{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 }}


[[Badness]]: 0.029267
[[Badness]] (Sintel): 0.741


== Tokko ==
== Tokko ==
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Tokko]].''
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Tokko (5-limit)]].''
 
Tokko tempers out the [[mitonisma]] in addition to the wizma, and may be described as the {{nowrap| 5 & 171 }} temperament.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 43: Line 52:
[[Comma list]]: 420175/419904, 5250987/5242880
[[Comma list]]: 420175/419904, 5250987/5242880


{{Mapping|legend=1| 1 12 56 -2 | 0 -13 -67 6 }}
{{Mapping|legend=1| 1 -1 -11 4 | 0 13 67 -6 }}
: mapping generators: ~2, ~147/128


: mapping generators: ~2, ~256/147
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.0850{{c}}, ~147/128 = 238.6157{{c}}
: [[error map]]: {{val| +0.085 -0.036 +0.004 -0.180 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~147/128 = 238.5997{{c}}
: error map: {{val| 0.000 -0.159 -0.133 -0.424 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 238.599
{{Optimal ET sequence|legend=1| 5, 161c, 166, 171, 1544d, 1715d, …, 2912dd, 3083cdd }}


{{Optimal ET sequence|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}
[[Badness]] (Sintel): 1.12
 
[[Badness]]: 0.044417


== Tertiathirds ==
== Tertiathirds ==
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.
Tertiathirds tempers out the quasiorwellisma, [[29360128/29296875]] in the 7-limit, and may be described as the {{nowrap| 121 & 149 }} temperament. It splits the interval of [[5/4]] into three [[14/13]] generators.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 60: Line 72:
[[Comma list]]: 420175/419904, 29360128/29296875
[[Comma list]]: 420175/419904, 29360128/29296875


{{Mapping|legend=1| 1 48 5 76 | 0 -52 -3 -82 }}
{{Mapping|legend=1| 1 -4 2 -6 | 0 52 3 82 }}
: mapping generators: ~2, ~3375/3136


: mapping generators: ~2, ~6272/3375
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.9305{{c}}, ~3375/3136 = 128.8804{{c}}
: [[error map]]: {{val| -0.070 +0.104 +0.188 -0.216 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3375/3136 = 128.8871{{c}}
: error map: {{val| 0.000 +0.173 +0.348 -0.085 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3375/3136 = 128.888
{{Optimal ET sequence|legend=1| 121, 149, 270, 2309c, 2579c }}


{{Optimal ET sequence|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
[[Badness]] (Sintel): 2.35
 
[[Badness]]: 0.093005


=== 11-limit ===
=== 11-limit ===
Line 75: Line 90:
Comma list: 3025/3024, 5632/5625, 117649/117612
Comma list: 3025/3024, 5632/5625, 117649/117612


Mapping: {{mapping| 1 48 5 76 107 | 0 -52 -3 -82 -116 }}
Mapping: {{mapping| 1 -4 2 -6 -9 | 0 52 3 82 116 }}


Optimal tuning (POTE): ~2 = 1\1, ~264/245 = 128.890
Optimal tunings:
* WE: ~2 = 1199.9251{{c}}, ~264/245 = 128.8818{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~264/245 = 128.8890{{c}}


{{Optimal ET sequence|legend=1| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }}
{{Optimal ET sequence|legend=0| 121, 149, 270 }}


Badness: 0.033322
Badness (Sintel): 1.10


=== 13-limit ===
=== 13-limit ===
Line 88: Line 105:
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224


Mapping: {{mapping| 1 48 5 76 107 76 | 0 -52 -3 -82 -116 -81 }}
Mapping: {{mapping| 1 -4 2 -6 -9 -5 | 0 52 3 82 116 81 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 128.890
Optimal tunings:
* WE: ~2 = 1199.9510{{c}}, ~14/13 = 128.8849{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 128.8896{{c}}


{{Optimal ET sequence|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
{{Optimal ET sequence|legend=0| 121, 149, 270 }}


Badness: 0.019494
Badness (Sintel): 0.806


=== 17-limit ===
=== 17-limit ===
Line 101: Line 120:
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: {{mapping| 1 48 5 76 107 76 63 | 0 -52 -3 -82 -116 -81 -66 }}
Mapping: {{mapping| 1 -4 2 -6 -9 -5 -3 | 0 52 3 82 116 81 66 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 128.891
Optimal tunings:
* WE: ~2 = 1199.8754{{c}}, ~14/13 = 128.8778{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 128.8898{{c}}


{{Optimal ET sequence|legend=1| 121, 149, 270 }}
{{Optimal ET sequence|legend=0| 121, 149, 270 }}


Badness: 0.019107
Badness (Sintel): 0.973


=== 19-limit ===
=== 19-limit ===
Line 114: Line 135:
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: {{mapping| 1 48 5 76 107 76 63 -2 | 0 -52 -3 -82 -116 -81 -66 7 }}
Mapping: {{mapping| 1 -4 2 -6 -9 -5 -3 5 | 0 52 3 82 116 81 66 -7 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 128.890
 
{{Optimal ET sequence|legend=1| 121, 149, 270 }}
 
Badness: 0.015621
 
== Witcher ==
{{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).
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 420175/419904, 1600000/1594323
 
{{Mapping|legend=1| 1 18 45 12 | 0 -25 -65 -14 }}
 
: mapping generators: ~2, ~63/40
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~80/63 = 412.098
 
{{Optimal ET sequence|legend=1| 99, 265, 364, 463, 562, 1025 }}
 
[[Badness]]: 0.080608
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 4375/4356, 1240029/1239040
 
Mapping: {{mapping| 1 18 45 12 77 | 0 -25 -65 -14 -112 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~80/63 = 412.079
 
{{Optimal ET sequence|legend=1| 99e, 166, 265 }}
 
Badness: 0.082607
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 729/728, 4375/4356, 10648/10647
 
Mapping: {{mapping| 1 18 45 12 77 93 | 0 -25 -65 -14 -112 -136 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~33/26 = 412.070
 
{{Optimal ET sequence|legend=1| 99ef, 166, 265, 431c, 696cc }}
 
Badness: 0.057980
 
=== Semiwitcher ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 41503/41472, 585640/583443
 
Mapping: {{mapping| 2 11 25 10 16 | 0 -25 -65 -14 -29 }}
 
: mapping generators: ~99/70, ~49/44
 
Optimal tuning (POTE): ~99/70 = 1\2, ~49/44 = 187.904
 
{{Optimal ET sequence|legend=1| 166, 198, 364, 562, 926, 1488bd, 2414bdd }}
 
Badness: 0.088189
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
 
Mapping: {{mapping| 2 11 25 10 16 24 | 0 -25 -65 -14 -29 -53 }}
 
Optimal tuning (POTE): ~99/70 = 1\2, ~39/35 = 187.904
 
{{Optimal ET sequence|legend=1| 166, 198, 364, 562, 926 }}
 
Badness: 0.038009
 
=== Hitch ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 117649/117612, 1600000/1594323
 
Mapping: {{mapping| 1 18 45 12 -10 | 0 -50 -130 -28 41 }}
 
: mapping generators: ~2, ~1120/891
 
Optimal tuning (POTE): ~2 = 1\1, ~1120/891 = 393.950
 
{{Optimal ET sequence|legend=1| 198, 463, 661, 1124bde }}
 
Badness: 0.093482
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
 
Mapping: {{mapping| 1 18 45 12 -10 71 | 0 -50 -130 -28 41 -205 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~1120/891 = 393.948
 
{{Optimal ET sequence|legend=1| 198, 463, 661 }}
 
Badness: 0.060716
 
==== Hitcher ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
 
Mapping: {{mapping| 1 18 45 12 -10 6 | 0 -50 -130 -28 41 -7 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~49/39 = 393.949
 
{{Optimal ET sequence|legend=1| 198, 463f, 661ff }}
 
Badness: 0.059591
 
== Gariwizmic ==
Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just. Unlike schismic, it finds 5/4 at the ''trans''diminished fourth (+45 fifths) minus a half pythagorean comma, or equivalently, at the ''trans''diminished octave (+39 fifths) minus a semioctave.
 
[[Subgroup]]: 2.3.5.7
 
Comma list: 420175/419904, [[33554432/33480783]]
 
{{Mapping|legend=1| 2 2 -41 22|0 1 39 -14}}
 
* mapping generators: ~46305/32768, ~3
[[Optimal tuning|Optimal tunings]]:
 
* [[WE]]: ~2 = 599.996{{c}}, ~3/2 = 702.177{{c}}
 
: [[error map]]: {{val|-0.069, 0.153, -0.021, -0.053}}
 
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6512{{c}}
 
: error map: {{val|0.000 0.261 0.114 0.149}}
 
{{Optimal ET sequence|legend=1|94, 176, 270, 364, 446, 634, 904}}
 
[[Badness]]: 2.225 (Sintel)
 
==== 11-limit ====
Subgroup: 2.3.5.7.11
 
Comma list: [[9801/9800]], [[19712/19683]], [[41503/41472]]
 
{{Mapping|legend=1| 2 2 -41 22 -20|0 1 39 -14 23}}
 
* mapping generators: ~99/70, ~3
 
* WE: ~99/70 = 599.979, ~3/2 = 702.194
: error map: {{val|-0.042 0.197 0.106 -0.001 -0.440}}
* CWE: ~99/70 = 1\2, ~3/2 = 702.218
: error map: {{val|0.000 0.263 0.185 0.123 -0.306}}
 
{{Optimal ET sequence|legend=0|94, 176, 270, 364, 446, 634, 904}}
 
[[Badness]]: 1.008 (Sintel)
 
==== 13-limit ====
Comma list: [[2080/2079]], [[1716/1715]], [[4096/4095]], [[35035/34992]]
 
{{Mapping|legend=1| 2 2 -41 22 -20 39|0 1 39 -14 23 -27}}
 
* mapping generators: ~99/70, ~3
 
[[Optimal tuning|Optimal tunings]]:
* WE: ~99/70 = 599.996, ~3/2 = 702.210
: error map: {{val|-0.008 0.246 0.035 0.146 -0.412 -0.353}}
* CWE: ~99/70 = 1\2, ~3/2 = 702.215
: error map: {{val|-0.000 0.260 0.054 0.170 -0.383 -0.321}}
 
{{Optimal ET sequence|legend=0|94, 176, 270, 364, 446, 634, 904}}
 
[[Badness]]: 0.822 (Sintel)
 
==== Subgroup: 2.3.5.7.11.13.19 ====
Comma list: [[2080/2079]], [[1540/1539]], [[1216/1215]], [[1716/1715]], [[1729/1728]]
 
{{Mapping|legend=1| 2 2 -41 22 -20 39 -43|0 1 39 -14 23 -27 44}}
 
* mapping generators: ~99/70, ~3


[[Optimal tuning|Optimal tunings]]:
Optimal tunings:  
* WE: ~99/70 = 599.996, ~3/2 = 702.210
* WE: ~2 = 1199.8964{{c}}, ~14/13 = 128.8793{{c}}
: error map: {{val|-0.006 0.250 0.057 0.147 -0.394 -0.355 -0.079}}
* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 128.8896{{c}}
* CWE: ~99/70 = 1\2, ~3/2 = 702.215
: error map: {{val|-0.000 0.260 0.070 0.165 -0.374 -0.332 -0.055}}


{{Optimal ET sequence|legend=0|94, 176, 270, 364, 446, 634, 904}}
{{Optimal ET sequence|legend=0| 121, 149, 270 }}


[[Badness]]: 0.655 (Sintel)
Badness (Sintel): 0.950


[[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]]

Latest revision as of 14:59, 3 June 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 microtemperaments which temper out the wizma (monzo: [-6 -8 2 5⟩, ratio: 420175/419904).

Temperaments discussed elsewhere are:

Considered below are qak, tokko, and tertiathirds, in the order of increasing badness.

Qak

Qak tempers out the meter in addition to the wizma, and may be described as the 50 & 171 temperament.

Subgroup: 2.3.5.7

Comma list: 420175/419904, 703125/702464

Mapping: [⟨1 -14 -3 -20], ⟨0 41 14 60]]

mapping generators: ~2, ~125/96

Optimal tunings:

  • WE: ~2 = 1200.0566 ¢, ~125/96 = 456.1655 ¢
error map: ⟨+0.057 +0.039 -0.166 -0.027]
  • CWE: ~2 = 1200.0000 ¢, ~125/96 = 456.1450 ¢
error map: ⟨0.000 -0.009 -0.283 -0.125]

Optimal ET sequence: 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd

Badness (Sintel): 0.741

Tokko

For the 5-limit version, see Syntonic–diatonic equivalence continuum #Tokko (5-limit).

Tokko tempers out the mitonisma in addition to the wizma, and may be described as the 5 & 171 temperament.

Subgroup: 2.3.5.7

Comma list: 420175/419904, 5250987/5242880

Mapping: [⟨1 -1 -11 4], ⟨0 13 67 -6]]

mapping generators: ~2, ~147/128

Optimal tunings:

  • WE: ~2 = 1200.0850 ¢, ~147/128 = 238.6157 ¢
error map: ⟨+0.085 -0.036 +0.004 -0.180]
  • CWE: ~2 = 1200.0000 ¢, ~147/128 = 238.5997 ¢
error map: ⟨0.000 -0.159 -0.133 -0.424]

Optimal ET sequence: 5, 161c, 166, 171, 1544d, 1715d, …, 2912dd, 3083cdd

Badness (Sintel): 1.12

Tertiathirds

Tertiathirds tempers out the quasiorwellisma, 29360128/29296875 in the 7-limit, and may be described as the 121 & 149 temperament. It splits the interval of 5/4 into three 14/13 generators.

Subgroup: 2.3.5.7

Comma list: 420175/419904, 29360128/29296875

Mapping: [⟨1 -4 2 -6], ⟨0 52 3 82]]

mapping generators: ~2, ~3375/3136

Optimal tunings:

  • WE: ~2 = 1199.9305 ¢, ~3375/3136 = 128.8804 ¢
error map: ⟨-0.070 +0.104 +0.188 -0.216]
  • CWE: ~2 = 1200.0000 ¢, ~3375/3136 = 128.8871 ¢
error map: ⟨0.000 +0.173 +0.348 -0.085]

Optimal ET sequence: 121, 149, 270, 2309c, 2579c

Badness (Sintel): 2.35

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 117649/117612

Mapping: [⟨1 -4 2 -6 -9], ⟨0 52 3 82 116]]

Optimal tunings:

  • WE: ~2 = 1199.9251 ¢, ~264/245 = 128.8818 ¢
  • CWE: ~2 = 1200.0000 ¢, ~264/245 = 128.8890 ¢

Optimal ET sequence: 121, 149, 270

Badness (Sintel): 1.10

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224

Mapping: [⟨1 -4 2 -6 -9 -5], ⟨0 52 3 82 116 81]]

Optimal tunings:

  • WE: ~2 = 1199.9510 ¢, ~14/13 = 128.8849 ¢
  • CWE: ~2 = 1200.0000 ¢, ~14/13 = 128.8896 ¢

Optimal ET sequence: 121, 149, 270

Badness (Sintel): 0.806

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224

Mapping: [⟨1 -4 2 -6 -9 -5 -3], ⟨0 52 3 82 116 81 66]]

Optimal tunings:

  • WE: ~2 = 1199.8754 ¢, ~14/13 = 128.8778 ¢
  • CWE: ~2 = 1200.0000 ¢, ~14/13 = 128.8898 ¢

Optimal ET sequence: 121, 149, 270

Badness (Sintel): 0.973

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125

Mapping: [⟨1 -4 2 -6 -9 -5 -3 5], ⟨0 52 3 82 116 81 66 -7]]

Optimal tunings:

  • WE: ~2 = 1199.8964 ¢, ~14/13 = 128.8793 ¢
  • CWE: ~2 = 1200.0000 ¢, ~14/13 = 128.8896 ¢

Optimal ET sequence: 121, 149, 270

Badness (Sintel): 0.950

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