Starling temperaments: Difference between revisions

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Temperaments discussed in families and clans are:
Temperaments discussed in families and clans are:
* ''[[Brutus]]'' (+10/9) → [[Very low accuracy temperaments #Brutus|Very low accuracy temperaments]]
* ''[[Pater]]'' (+16/15) → [[Father family #Pater|Father family]]
* ''[[Pater]]'' (+16/15) → [[Father family #Pater|Father family]]
* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone|Meantone family]]
* ''[[Mavling]]'' (+135/128) → [[Mavila family #Mavling|Mavila family]]
* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle|Schismatic family]]
* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie|Dicot family]]
* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie|Dicot family]]
* ''[[Opossum]]'' (+28/27) → [[Trienstonic clan #Opossum|Trienstonic clan]]
* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
* [[Augene]] (+64/63) → [[Augmented family #Augene|Augmented family]]
* [[Opossum]] (+28/27) → [[Trienstonic clan #Opossum|Trienstonic clan]]
* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]
* [[Muggles]] (+525/512) → [[Magic family #Muggles|Magic family]]
* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate|Passion family]]
* ''[[Ripple]]'' (+405/392) → [[Ripple family #Septimal ripple|Ripple family]]
* [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]]
* [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]]
* [[Augene]] (+64/63) → [[Augmented family #Augene|Augmented family]]
* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone|Meantone family]]
* [[Mavila]] (+135/128) → [[Pelogic family #Mavila|Pelogic family]]
* [[Sensi]] (+245/243), [[Sensipent family #Sensi|Sensipent family]]
* [[Sensi]] (+245/243), [[Sensipent family #Sensi|Sensipent family]]
* [[Muggles]] (+525/512) → [[Magic family #Muggles|Magic family]]
* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine|Gamelismic clan]]
* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]
* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn|Unicorn family]]
* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn|Unicorn family]]
* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]] / [[Cloudy clan #Coblack|cloudy clan]]
* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle|Schismatic family]]
* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt|Würschmidt family]]
* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt|Würschmidt family]]
* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine|Gamelismic clan]]
* ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee|Mabila family]]
* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja|Buzzardsmic clan]]
* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja|Buzzardsmic clan]]
* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate|Passion family]]
* ''[[Paraguay]]'' (+12005/11664) → [[Parakleismic family #Paraguay|Parakleismic family]]
* ''[[Vishnean]]'' (+540225/524288) → [[Vishnuzmic family #Vishnean|Vishnuzmic family]]
* ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton|Ditonmic family]]
* ''[[Ditonic]]'' (+8751645/8388608) → [[Ditonmic family #Ditonic|Ditonmic family]]
* ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean|Vishnu family]]
* ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee|Mabila family]]
* ''[[Bisemidim]]'' (+118098/117649) → [[Stearnsmic clan #Bisemidim|Stearnsmic clan]]
* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]]


Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].  
Considered below are myna, nusecond, oolong, vines, kumonga, cypress, casablanca, amigo, supersensi, and cobalt, sorted by increasing [[badness]].  


Since {{nowrap|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo]] established itself as the standard tuning, it is actually three stacked minor thirds and an augmented second, contrary to the popular belief that it is four stacked minor thirds.  
Since {{nowrap|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord.  


== Myna ==
== Myna ==
Line 67: Line 71:
Comma list: 126/125, 176/175, 243/242
Comma list: 126/125, 176/175, 243/242


Mapping: {{mapping| 1 -1 0 1 -3 | 0 10 9 7 25 }}
{{Mapping|legend=0| 1 -1 0 1 -3 | 0 10 9 7 25 }}


Optimal tunings:  
Optimal tunings:  
Line 82: Line 86:
Comma list: 126/125, 144/143, 176/175, 196/195
Comma list: 126/125, 144/143, 176/175, 196/195


Mapping: {{mapping| 1 -1 0 1 -3 5 | 0 10 9 7 25 -5 }}
{{Mapping|legend=0| 1 -1 0 1 -3 5 | 0 10 9 7 25 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 97: Line 101:
Comma list: 78/77, 91/90, 126/125, 176/175
Comma list: 78/77, 91/90, 126/125, 176/175


Mapping: {{mapping| 1 -1 0 1 -3 -2 | 0 10 9 7 25 22 }}
{{Mapping|legend=0| 1 -1 0 1 -3 -2 | 0 10 9 7 25 22 }}


Optimal tunings:  
Optimal tunings:  
Line 112: Line 116:
Comma list: 66/65, 105/104, 126/125, 243/242
Comma list: 66/65, 105/104, 126/125, 243/242


Mapping: {{mapping| 1 -1 0 1 -3 -3 | 0 10 9 7 25 26 }}
{{Mapping|legend=0| 1 -1 0 1 -3 -3 | 0 10 9 7 25 26 }}


Optimal tunings:  
Optimal tunings:  
Line 127: Line 131:
Comma list: 99/98, 126/125, 385/384
Comma list: 99/98, 126/125, 385/384


Mapping: {{mapping| 1 -1 0 1 5 | 0 10 9 7 -6 }}
{{Mapping|legend=0| 1 -1 0 1 5 | 0 10 9 7 -6 }}


Optimal tunings:  
Optimal tunings:  
Line 142: Line 146:
Comma list: 56/55, 100/99, 1728/1715
Comma list: 56/55, 100/99, 1728/1715


Mapping: {{mapping| 1 -1 0 1 4 | 0 10 9 7 -2 }}
{{Mapping|legend=0| 1 -1 0 1 4 | 0 10 9 7 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 189: Line 193:
Comma list: 99/98, 121/120, 126/125
Comma list: 99/98, 121/120, 126/125


Mapping: {{mapping| 1 -8 -9 -12 -7 | 0 11 13 17 12 }}
{{Mapping|legend=0| 1 -8 -9 -12 -7 | 0 11 13 17 12 }}


Optimal tunings:  
Optimal tunings:  
Line 211: Line 215:
Comma list: 66/65, 99/98, 121/120, 126/125
Comma list: 66/65, 99/98, 121/120, 126/125


Mapping: {{mapping| 1 -8 -9 -12 -7 -5 | 0 11 13 17 12 10 }}
{{Mapping|legend=0| 1 -8 -9 -12 -7 -5 | 0 11 13 17 12 10 }}


Optimal tunings:  
Optimal tunings:  
Line 247: Line 251:
Comma list: 126/125, 176/175, 26411/26244
Comma list: 126/125, 176/175, 26411/26244


Mapping: {{mapping| 1 -11 -11 -12 -38 | 0 17 18 20 56 }}
{{Mapping|legend=0| 1 -11 -11 -12 -38 | 0 17 18 20 56 }}


Optimal tunings:  
Optimal tunings:  
Line 262: Line 266:
Comma list: 126/125, 176/175, 196/195, 13013/12960
Comma list: 126/125, 176/175, 196/195, 13013/12960


Mapping: {{mapping| 1 -11 -11 -12 -38 0 | 0 17 18 20 56 5 }}
{{Mapping|legend=0| 1 -11 -11 -12 -38 0 | 0 17 18 20 56 5 }}


Optimal tunings:  
Optimal tunings:  
Line 299: Line 303:
Comma list: 126/125, 385/384, 2401/2376
Comma list: 126/125, 385/384, 2401/2376


Mapping: {{mapping| 2 -1 1 3 9 | 0 8 7 5 -4 }}
{{Mapping|legend=0| 2 -1 1 3 9 | 0 8 7 5 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 314: Line 318:
Comma list: 126/125, 196/195, 364/363, 385/384
Comma list: 126/125, 196/195, 364/363, 385/384


Mapping: {{mapping| 2 -1 1 3 9 10 | 0 8 7 5 -4 -5 }}
{{Mapping|legend=0| 2 -1 1 3 9 10 | 0 8 7 5 -4 -5 }}


Optimal tunings:  
Optimal tunings:  
Line 325: Line 329:


== Xenial ==
== Xenial ==
{{Main| Xenial }}
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''


Named by [[User:Xenllium|Xenllium]] in 2026, xenial may be described as the {{nowrap| 19 & 70 }} temperament, splitting the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2|perfect fifth]] above 7 octaves, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.
Named by [[User:Xenllium|Xenllium]] in 2026, xenial may be described as the {{nowrap| 19 & 70 }} temperament, splitting the [[8/3|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2|perfect fifth]] above 7 [[octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 342: Line 347:
: error map: {{val| 0.000 -1.644 +3.162 -1.021 }}
: error map: {{val| 0.000 -1.644 +3.162 -1.021 }}


{{Optimal ET sequence|legend=1| 19, 70, 89 }}
{{Optimal ET sequence|legend=1| 19, 51cd, 70, 89 }}


[[Badness]] (Sintel): 2.13
[[Badness]] (Sintel): 2.13
Line 351: Line 356:
Comma list: 126/125, 540/539, 16384/16335
Comma list: 126/125, 540/539, 16384/16335


Mapping: {{mapping| 1 -6 -12 -25 22 | 0 9 17 33 -22 }}
{{Mapping|legend=0| 1 -6 -12 -25 22 | 0 9 17 33 -22 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.614{{c}}, ~9/5 = 1010.872{{c}}
* WE: ~2 = 1199.6137{{c}}, ~9/5 = 1010.8717{{c}}
* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.192{{c}}
* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.1915{{c}}


{{Optimal ET sequence|legend=0| 19, 70, 89 }}
{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}


Badness (Sintel): 2.31
Badness (Sintel): 2.31
Line 366: Line 371:
Comma list: 126/125, 169/168, 540/539, 729/728
Comma list: 126/125, 169/168, 540/539, 729/728


Mapping: {{mapping| 1 -6 -12 -25 22 -14 | 0 9 17 33 -22 21 }}
{{Mapping|legend=0| 1 -6 -12 -25 22 -14 | 0 9 17 33 -22 21 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.856{{c}}, ~9/5 = 1011.091{{c}}
* WE: ~2 = 1199.8559{{c}}, ~9/5 = 1011.0911{{c}}
* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.210{{c}}
* CWE: ~2 = 1200.000{{c}}, ~9/5 = 1011.2102{{c}}


{{Optimal ET sequence|legend=0| 19, 70, 89 }}
{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}


Badness (Sintel): 1.98
Badness (Sintel): 1.98
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 126/125, 169/168, 221/220, 256/255, 540/539
{{Mapping|legend=0| 1 -6 -12 -25 22 -14 26 | 0 9 17 33 -22 21 -26 }}
Optimal tunings:
* WE: ~2 = 1199.6970{{c}}, ~9/5 = 1010.9792{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2323{{c}}
{{Optimal ET sequence|legend=0| 19, 51cd, 70, 89 }}
Badness (Sintel): 2.06
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 126/125, 169/168, 171/170, 221/220, 256/255, 540/539
{{Mapping|legend=0| 1 -6 -12 -25 22 -14 26 27 | 0 9 17 33 -22 21 -26 -27 }}
Optimal tunings:
* WE: ~2 = 1199.7741{{c}}, ~9/5 = 1011.0334{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2230{{c}}
{{Optimal ET sequence|legend=0| 19, 51cdh, 70, 89 }}
Badness (Sintel): 2.03
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 126/125, 162/161, 169/168, 171/170, 208/207, 221/220, 231/230
{{Mapping|legend=0| 1 -6 -12 -25 22 -14 26 27 2 | 0 9 17 33 -22 21 -26 -27 3 }}
Optimal tunings:
* WE: ~2 = 1199.6628{{c}}, ~9/5 = 1010.9415{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/5 = 1011.2245{{c}}
{{Optimal ET sequence|legend=0| 19, 51cdh, 70, 89 }}
Badness (Sintel): 1.93


== Kumonga ==
== Kumonga ==
Line 401: Line 451:
Comma list: 126/125, 176/175, 864/847
Comma list: 126/125, 176/175, 864/847


Mapping: {{mapping| 1 -9 -5 2 -12 | 0 13 9 1 19 }}
{{Mapping|legend=0| 1 -9 -5 2 -12 | 0 13 9 1 19 }}


Optimal tunings:  
Optimal tunings:  
Line 416: Line 466:
Comma list: 78/77, 126/125, 144/143, 176/175
Comma list: 78/77, 126/125, 144/143, 176/175


Mapping: {{mapping| 1 -9 -5 2 -12 -2 | 0 13 9 1 19 7 }}
{{Mapping|legend=0| 1 -9 -5 2 -12 -2 | 0 13 9 1 19 7 }}


Optimal tunings:  
Optimal tunings:  
Line 425: Line 475:


Badness (Sintel): 1.19
Badness (Sintel): 1.19
== Bisemidim ==
Bisemidim tempers out [[118098/117649]] and may be described as the {{nowrap| 50 & 58 }} temperament. It has a [[semi-octave]] period and a [[~]][[49/45]] generator. Nine generators minus a period give the [[3/2|perfect fifth]], so the [[ploidacot]] for the temperament is diploid alpha-enneacot. [[108edo]] and [[166edo]] in the 166cef val may be recommended as tunings.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 126/125, 118098/117649
{{Mapping|legend=1| 2 1 2 2 | 0 9 11 15 }}
: mapping generators: ~343/243, ~49/45
[[Optimal tuning]]s:
* [[WE]]: ~343/243 = 599.8915{{c}}, ~49/45 = 144.5293{{c}}
: [[error map]]: {{val| -0.217 -1.299 +3.292 -1.103 }}
* [[CWE]]: ~343/243 = 600.0000{{c}}, ~49/45 = 144.5351{{c}}
: error map: {{val| 0.000 -1.139 +3.572 -0.799 }}
{{Optimal ET sequence|legend=1| 50, 58, 108, 166c, 408ccc }}
[[Badness]] (Sintel): 2.47
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 126/125, 540/539, 1344/1331
Mapping: {{mapping| 2 1 2 2 5 | 0 9 11 15 8 }}
Optimal tunings:
* WE: ~99/70 = 599.6360{{c}}, ~12/11 = 144.5388{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~12/11 = 144.5623{{c}}
{{Optimal ET sequence|legend=0| 50, 58, 108, 166ce, 224cee }}
Badness (Sintel): 1.36
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 196/195, 364/363
Mapping: {{mapping| 2 1 2 2 5 5 | 0 9 11 15 8 10 }}
Optimal tunings:
* WE: ~55/39 = 599.5217{{c}}, ~12/11 = 144.5375{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~12/11 = 144.5698{{c}}
{{Optimal ET sequence|legend=0| 50, 58, 166cef, 224ceeff }}
Badness (Sintel): 0.987


== Cypress ==
== Cypress ==
Line 500: Line 500:
Comma list: 99/98, 126/125, 243/242
Comma list: 99/98, 126/125, 243/242


Mapping: {{mapping| 1 -5 -7 -12 -13 | 0 12 17 27 30 }}
{{Mapping|legend=0| 1 -5 -7 -12 -13 | 0 12 17 27 30 }}


Optimal tunings:  
Optimal tunings:  
Line 515: Line 515:
Comma list: 66/65, 99/98, 126/125, 243/242
Comma list: 66/65, 99/98, 126/125, 243/242


Mapping: {{mapping| 1 -5 -7 -12 -13 -10 | 0 12 17 27 30 25 }}
{{Mapping|legend=0| 1 -5 -7 -12 -13 -10 | 0 12 17 27 30 25 }}


Optimal tunings:  
Optimal tunings:  
Line 558: Line 558:
Comma list: 126/125, 385/384, 2420/2401
Comma list: 126/125, 385/384, 2420/2401


Mapping: {{mapping| 1 -7 -4 1 3 | 0 19 14 4 1 }}
{{Mapping|legend=0| 1 -7 -4 1 3 | 0 19 14 4 1 }}


Optimal tunings:  
Optimal tunings:  
Line 573: Line 573:
Comma list: 126/125, 196/195, 385/384, 2420/2401
Comma list: 126/125, 196/195, 385/384, 2420/2401


Mapping: {{mapping| 1 -7 -4 1 3 1 | 0 19 14 4 1 6 }}
{{Mapping|legend=0| 1 -7 -4 1 3 1 | 0 19 14 4 1 6 }}


Optimal tunings:  
Optimal tunings:  
Line 588: Line 588:
Comma list: 126/125, 176/175, 14641/14580
Comma list: 126/125, 176/175, 14641/14580


Mapping: {{mapping| 1 -7 -4 1 -11 | 0 19 14 4 32 }}
{{Mapping|legend=0| 1 -7 -4 1 -11 | 0 19 14 4 32 }}


Optimal tunings:  
Optimal tunings:  
Line 603: Line 603:
Comma list: 126/125, 176/175, 196/195, 14641/14580
Comma list: 126/125, 176/175, 196/195, 14641/14580


Mapping: {{mapping| 1 -7 -4 1 -11 15 | 0 19 14 4 32 -25 }}
{{Mapping|legend=0| 1 -7 -4 1 -11 15 | 0 19 14 4 32 -25 }}


Optimal tunings:  
Optimal tunings:  
Line 618: Line 618:
Comma list: 126/125, 144/143, 176/175, 1540/1521
Comma list: 126/125, 144/143, 176/175, 1540/1521


Mapping: {{mapping| 1 -7 -4 1 -11 1 | 0 19 14 4 32 6 }}
{{Mapping|legend=0| 1 -7 -4 1 -11 1 | 0 19 14 4 32 6 }}


Optimal tunings:  
Optimal tunings:  
Line 653: Line 653:
Comma list: 126/125, 176/175, 16384/16335
Comma list: 126/125, 176/175, 16384/16335


Mapping: {{mapping| 1 -2 2 9 9 | 0 11 1 -19 -17 }}
{{Mapping|legend=0| 1 -2 2 9 9 | 0 11 1 -19 -17 }}


Optimal tunings:  
Optimal tunings:  
Line 668: Line 668:
Comma list: 126/125, 169/168, 176/175, 364/363
Comma list: 126/125, 169/168, 176/175, 364/363


Mapping: {{mapping| 1 -2 2 9 9 5 | 0 11 1 -19 -17 -4 }}
{{Mapping|legend=0| 1 -2 2 9 9 5 | 0 11 1 -19 -17 -4 }}


Optimal tunings:  
Optimal tunings:  
Line 677: Line 677:


Badness (Sintel): 1.27
Badness (Sintel): 1.27
== Gilead ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].''
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 126/125, 343/324
{{Mapping|legend=1| 1 -5 -5 -6 | 0 9 10 12 }}
: mapping generators: ~2, ~5/3
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.4516{{c}}, ~5/3 = 879.6394{{c}}
: [[error map]]: {{val| +1.452 +7.542 +2.823 -21.862 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 878.7223{{c}}
: error map: {{val| 0.000 +6.545 +0.909 -24.159 }}
{{Optimal ET sequence|legend=1| 11cd, 15, 41dd }}
[[Badness]] (Sintel): 2.92


== Supersensi ==
== Supersensi ==
Line 723: Line 703:
Comma list: 99/98, 126/125, 864/847
Comma list: 99/98, 126/125, 864/847


Mapping: {{mapping| 1 -4 -4 -5 -1 | 0 15 17 21 12 }}
{{Mapping|legend=0| 1 -4 -4 -5 -1 | 0 15 17 21 12 }}


Optimal tunings:  
Optimal tunings:  
Line 738: Line 718:
Comma list: 78/77, 99/98, 126/125, 144/143
Comma list: 78/77, 99/98, 126/125, 144/143


Mapping: {{mapping| 1 -4 -4 -5 -1 -3 | 0 15 17 21 12 18 }}
{{Mapping|legend=0| 1 -4 -4 -5 -1 -3 | 0 15 17 21 12 18 }}


Optimal tunings:  
Optimal tunings:  
Line 753: Line 733:
Comma list: 78/77, 99/98, 120/119, 126/125, 144/143
Comma list: 78/77, 99/98, 120/119, 126/125, 144/143


Mapping: {{mapping| 1 -4 -4 -5 -1 -3 0 | 0 15 17 21 12 18 11 }}
{{Mapping|legend=0| 1 -4 -4 -5 -1 -3 0 | 0 15 17 21 12 18 11 }}


Optimal tunings:  
Optimal tunings:  
Line 792: Line 772:
Comma list: 126/125, 540/539, 21609/21296
Comma list: 126/125, 540/539, 21609/21296


Mapping: {{mapping| 27 0 20 33 8 | 0 1 1 1 2 }}
{{Mapping|legend=0| 27 0 20 33 8 | 0 1 1 1 2 }}


Optimal tunings:  
Optimal tunings:  
Line 807: Line 787:
Comma list: 126/125, 144/143, 196/195, 21609/21296
Comma list: 126/125, 144/143, 196/195, 21609/21296


Mapping: {{mapping| 27 0 20 33 8 100 | 0 1 1 1 2 0 }}
{{Mapping|legend=0| 27 0 20 33 8 100 | 0 1 1 1 2 0 }}


Optimal tunings:  
Optimal tunings:  
Line 822: Line 802:
Comma list: 126/125, 144/143, 189/187, 196/195, 1452/1445
Comma list: 126/125, 144/143, 189/187, 196/195, 1452/1445


Mapping: {{mapping| 27 0 20 33 8 100 79 | 0 1 1 1 2 0 2 }}
{{Mapping|legend=0| 27 0 20 33 8 100 79 | 0 1 1 1 2 0 2 }}


Optimal tunings:  
Optimal tunings:  
Line 837: Line 817:
Comma list: 126/125, 144/143, 171/170, 189/187, 196/195, 969/968
Comma list: 126/125, 144/143, 171/170, 189/187, 196/195, 969/968


Mapping: {{mapping| 27 0 20 33 8 100 79 99 | 0 1 1 1 2 0 2 1 }}
{{Mapping|legend=0| 27 0 20 33 8 100 79 99 | 0 1 1 1 2 0 2 1 }}


Optimal tunings:  
Optimal tunings:  
Line 852: Line 832:
Comma list: 126/125, 144/143, 196/195, 221/220, 12005/11968
Comma list: 126/125, 144/143, 196/195, 221/220, 12005/11968


Mapping: {{mapping| 27 0 20 33 8 100 -18 | 0 1 1 1 2 0 3 }}
{{Mapping|legend=0| 27 0 20 33 8 100 -18 | 0 1 1 1 2 0 3 }}


Optimal tunings:  
Optimal tunings:  
Line 867: Line 847:
Comma list: 126/125, 144/143, 196/195, 210/209, 221/220, 1088/1083
Comma list: 126/125, 144/143, 196/195, 210/209, 221/220, 1088/1083


Mapping: {{mapping| 27 0 20 33 8 100 -18 72 | 0 1 1 1 2 0 3 1 }}
{{Mapping|legend=0| 27 0 20 33 8 100 -18 72 | 0 1 1 1 2 0 3 1 }}


Optimal tunings:  
Optimal tunings:  
Line 882: Line 862:
Comma list: 126/125, 169/168, 540/539, 975/968
Comma list: 126/125, 169/168, 540/539, 975/968


Mapping: {{mapping| 27 0 20 33 8 57 | 0 1 1 1 2 1 }}
{{Mapping|legend=0| 27 0 20 33 8 57 | 0 1 1 1 2 1 }}


Optimal tunings:  
Optimal tunings:  
Line 894: Line 874:
== References ==
== References ==


[[Category:Starling temperaments| ]] <!-- main article -->
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Starling temperaments| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]