Starling temperaments: Difference between revisions

This page discusses miscellaneous rank-2 temperaments tempering out [[126/125]], the starling comma or septimal semicomma.  

* ''[[Pater]]'', {16/15, 126/125} → [[Father family #Pater|Father family]]

* ''[[Flat]]'', {21/20, 25/24} → [[Dicot family #Flat|Dicot family]]

* ''[[Opossum]]'', {28/27, 126/125} → [[Trienstonic clan #Opossum|Trienstonic clan]]

* ''[[Diminished]]'', {36/35, 50/49} → [[Dimipent family #Diminished|Dimipent family]] / [[Jubilismic clan #Diminished|jubilismic clan]]

* [[Keemun]], {49/48, 126/125} → [[Kleismic family #Keemun|Kleismic family]]

* ''[[Augene]]'', {64/63, 126/125} → [[Augmented family #Augene|Augmented family]]

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

* [[Mavila]], {126/125, 135/128} → [[Pelogic family #Mavila|Pelogic family]]

* [[Sensi]], {126/125, 245/243}, [[Sensipent family #Sensi|Sensipent family]] / [[Sensamagic clan #Sensi|sensamagic clan]]

* ''[[Gilead]]'', {126/125, 343/324} → [[Shibboleth family #Gilead|Shibboleth family]]

* [[Muggles]], {126/125, 525/512} → [[Magic family #Muggles|Magic family]]

* ''[[Diaschismic]]'', {126/125, 2048/2025} → [[Diaschismic family #Diaschismic|Diaschismic family]]

* ''[[Wollemia]]'', {126/125, 2240/2187} → [[Tetracot family #Wollemia|Tetracot family]]

* ''[[Unicorn]]'', {126/125, 10976/10935} → [[Unicorn family #Unicorn|Unicorn family]]

* ''[[Coblack]]'', {126/125, 16807/16384} → [[Trisedodge family #Coblack|Trisedodge family]] / [[Cloudy clan #Coblack|cloudy clan]]

* ''[[Grackle]]'', {126/125, 32805/32768} → [[Schismatic family #Grackle|Schismatic family]]

* ''[[Worschmidt]]'', {126/125, 33075/32768} → [[Würschmidt family #Worschmidt|Würschmidt family]]

* ''[[Passionate]]'', {126/125, 131072/127575} → [[Passion family #Passionate|Passion family]]

* ''[[Vishnean]]'', {126/125, 540225/524288} → [[Vishnuzmic family #Vishnean|Vishnuzmic family]]

* ''[[Ditonic]]'', {126/125, 8751645/8388608} → [[Ditonmic family #Ditonic|Ditonmic family]]

* ''[[Muscogee]]'', {126/125, 33756345/33554432} → [[Mabila family #Muscogee|Mabila family]]

Since (6/5)³ = 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|12EDO]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.  

In addition to 126/125, myna tempers out [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the 27&31 temperament. It has 6/5 as a generator, and [[58edo|58EDO]] can be used as a tuning, with [[89edo|89EDO]] being a better one, and fans of round amounts in cents may like [[120edo|120EDO]]. It is also possible to tune myna with pure fifths by taking 6^1/10 as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.

Subgroup: 2.3.5.7

[[Comma list]]: 126/125, 1728/1715

[[Mapping]]: [{{val| 1 9 9 8 }}, {{val| 0 -10 -9 -7 }}]

Mapping generators: ~2, ~5/3

{{Multival|legend=1| 10 9 7 -9 -17 -9 }}

[[POTE generator]]: ~6/5 = 310.146

: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}]

: [[Eigenmonzo]]s (unchanged-intervals): 2, 3

{{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}

[[Badness]]: 0.027044

Mapping: [{{val| 1 9 9 8 22 }}, {{val| 0 -10 -9 -7 -25 }}]

POTE generator: ~6/5 = 310.144

{{Optimal ET sequence|legend=1| 27e, 31, 58, 89 }}

Badness: 0.016842

Mapping: [{{val| 1 9 9 8 22 0 }}, {{val| 0 -10 -9 -7 -25 5 }}]

POTE generator: ~6/5 = 310.276

{{Optimal ET sequence|legend=1| 27e, 31, 58 }}

Badness: 0.017125

Mapping: [{{val| 1 9 9 8 22 20 }}, {{val| 0 -10 -9 -7 -25 -22 }}]

POTE generator: ~6/5 = 310.381

{{Optimal ET sequence|legend=1| 27e, 31f, 58f }}

Badness: 0.027568

Comma list: 66/65, 105/104, 126/125, 540/539

Mapping: [{{val| 1 9 9 8 22 23 }}, {{val| 0 -10 -9 -7 -25 -26 }}]

POTE generator: ~6/5 = 309.804

{{Optimal ET sequence|legend=1| 27eff, 31 }}

Badness: 0.029868

Mapping: [{{val| 1 9 9 8 -1 }}, {{val| 0 -10 -9 -7 6 }}]

POTE generator: ~6/5 = 309.737

{{Optimal ET sequence|legend=1| 27, 31 }}

Badness: 0.033434

Mapping: [{{val| 1 9 9 8 2 }}, {{val| 0 -10 -9 -7 2 }}]

POTE generator: ~6/5 = 310.853

{{Optimal ET sequence|legend=1| 4, 23bc, 27e }}

Badness: 0.048687

== Valentine ==

Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3×7/5. In this respect it resembles miracle, with a generator of 3×5/7, and casablanca, with a generator of 5×7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the 31&46 temperament, and [[77edo|77EDO]], [[108edo|108EDO]] or [[185edo|185EDO]] make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)^1/9 as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as {{multival| 9 5 -3 7 … }}, tempering out 121/120 and 441/440; 46EDO has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^1/10.

Valentine is very closely related to [[Carlos Alpha]], the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.

Subgroup: 2.3.5

[[Comma list]]: 1990656/1953125

[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 9 5 }}]

[[POTE generator]]: ~25/24 = 78.039

{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 123 }}

 

 

 

[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 9 5 -3 }}]

 

 

[[POTE generator]]: ~21/20 = 77.864

 

* [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }}

: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]

: [[Eigenmonzo]]s (unchanged-intervals): 2, 7/6

: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]

[[Algebraic generator]]: smaller root of ''x''² - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.

 

{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 185, 262cd }}

 

[[Badness]]: 0.031056

Comma list: 121/120, 126/125, 176/175

Mapping: [{{val| 1 1 2 3 3 }}, {{val| 0 9 5 -3 7 }}]

Mapping generators: ~2, ~21/20

POTE generator: ~21/20 = 77.881

Minimax tuning:

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]

: Eigenmonzos (unchanged-intervals): 2, 11/7

Algebraic generator: positive root of 4''x''³ + 15''x''² - 21, or else Gontrand2, the smallest positive root of 4''x''⁷ - 8''x''⁶ + 5.

 

==== Dwynwen ====

Comma list: 91/90, 121/120, 126/125, 176/175

Mapping: [{{val| 1 1 2 3 3 2 }}, {{val| 0 9 5 -3 7 26 }}]

POTE generator: ~21/20 = 78.219

{{Optimal ET sequence|legend=1| 15, 31f, 46 }}

Badness: 0.023461

==== Lupercalia ====

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 105/104, 121/120, 126/125

Mapping: [{{val| 1 1 2 3 3 3 }}, {{val| 0 9 5 -3 7 11 }}]

POTE generator: ~21/20 = 77.709

{{Optimal ET sequence|legend=1| 15, 31, 77ff, 108eff, 139efff }}

Subgroup: 2.3.5.7.11.13

 

 

POTE generator: ~21/20 = 77.958

 

{{Optimal ET sequence|legend=1| 15f, 31, 46, 77 }}

 

 

===== 17-limit =====

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=== Hemivalentino ===

Comma list: 126/125, 243/242, 1029/1024

Mapping: [{{val| 1 1 2 3 2 }}, {{val| 0 18 10 -6 45 }}]

POTE generator: ~45/44 = 38.921

{{Optimal ET sequence|legend=1| 31, 92e, 123, 154, 185 }}

Badness: 0.061275

==== 13-limit ====

Comma list: 126/125, 196/195, 243/242, 1029/1024

Mapping: [{{val| 1 1 2 3 2 5 }}, {{val| 0 18 10 -6 45 -40 }}]

POTE generator: ~45/44 = 38.948

{{Optimal ET sequence|legend=1| 31, 92e, 123, 154 }}

Badness: 0.057919

==== Hemivalentoid ====

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 144/143, 243/242, 343/338

Mapping: [{{val| 1 1 2 3 2 4 }}, {{val| 0 18 10 -6 45 -9 }}]

 

 

 

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Nusecond]].''

 

Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&70. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. [[31edo|31EDO]] can be used as a tuning, or [[132edo|132EDO]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.

Subgroup: 2.3.5.7

[[Comma list]]: 126/125, 2430/2401

[[Mapping]]: [{{val| 1 3 4 5 }}, {{val| 0 -11 -13 -17 }}]

 

 

[[POTE generator]]: ~49/45 = 154.579

 

* [[7-odd-limit]]: ~49/45 = {{monzo| 4/13 0 -1/13 }}

: [[Eigenmonzo]]s (unchanged-intervals): 2, 5

* [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }}

 

 

[[Badness]]: 0.050389

Comma list: 99/98, 121/120, 126/125

Mapping: [{{val| 1 3 4 5 5 }}, {{val| 0 -11 -13 -17 -12 }}]

Mapping generators: ~2, ~11/10

POTE generator: ~11/10 = 154.645

: Eigenmonzos (unchanged-intervals): 2, 11/9

 

 

{{Optimal ET sequence|legend=1| 8d, 23de, 31, 101, 132ce, 163ce, 194cee }}

 

Badness: 0.025621

Comma list: 66/65, 99/98, 121/120, 126/125

Mapping: [{{val| 1 3 4 5 5 5 }}, {{val| 0 -11 -13 -17 -12 -10 }}]

POTE generator: ~11/10 = 154.478

{{Optimal ET sequence|legend=1| 8d, 23de, 31, 70f, 101ff }}

Badness: 0.023323

== Oolong ==

{{Main| Oolong }}

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Oolong]].''

Subgroup: 2.3.5.7

[[Comma list]]: 126/125, 117649/116640

[[Mapping]]: [{{val| 1 6 7 8 }}, {{val| 0 -17 -18 -20 }}]

{{Multival|legend=1| 17 18 20 -11 -16 -4 }}

[[POTE generator]]: ~6/5 = 311.679

{{Optimal ET sequence|legend=1| 27, 50, 77 }}

[[Badness]]: 0.073509

Comma list: 126/125, 176/175, 26411/26244

Mapping: [{{val| 1 6 7 8 18 }}, {{val| 0 -17 -18 -20 -56 }}]

POTE generator: ~6/5 = 311.587

{{Optimal ET sequence|legend=1| 27e, 77, 104c, 181c }}

Badness: 0.056915

Comma list: 126/125, 176/175, 196/195, 13013/12960

Mapping: [{{val| 1 6 7 8 18 5 }}, {{val| 0 -17 -18 -20 -56 -5 }}]

POTE generator: ~6/5 = 311.591

{{Optimal ET sequence|legend=1| 27e, 77, 104c, 181c }}

Badness: 0.035582

== Vines ==

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Vines]].''

Subgroup: 2.3.5.7

[[Comma list]]: 126/125, 84035/82944

[[Mapping]]: [{{val| 2 7 8 8 }}, {{val| 0 -8 -7 -5 }}]

[[POTE generator]]: ~6/5 = 312.602

 

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 126/125, 385/384, 2401/2376

Mapping: [{{val| 2 7 8 8 5 }}, {{val| 0 -8 -7 -5 4 }}]

POTE generator: ~6/5 = 312.601

{{Optimal ET sequence|legend=1| 42, 46, 96d, 142d, 238dd }}

Badness: 0.044499

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 196/195, 364/363, 385/384

Mapping: [{{val| 2 7 8 8 5 5 }}, {{val| 0 -8 -7 -5 4 5 }}]

POTE generator: ~6/5 = 312.564

{{Optimal ET sequence|legend=1| 42, 46, 96d, 238ddf }}

Badness: 0.029693

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Kumonga]].''

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 4 4 3 }}, {{val| 0 -13 -9 -1 }}]

 

{{Multival|legend=1| 13 9 1 -16 -35 -23 }}

[[POTE generator]]: ~8/7 = 222.797

[[Badness]]: 0.087500

Mapping: [{{val| 1 4 4 3 7 }}, {{val| 0 -13 -9 -1 -19 }}]

POTE generator: ~8/7 = 222.898

{{Optimal ET sequence|legend=1| 16, 27e, 43, 70e }}

Badness: 0.043336

Mapping: [{{val| 1 4 4 3 7 5 }}, {{val| 0 -13 -9 -1 -19 -7 }}]

POTE generator: ~8/7 = 222.961

{{Optimal ET sequence|legend=1| 16, 27e, 43, 70e, 113cdee }}

Badness: 0.028920

== Thuja ==

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Thuja]].''

Subgroup: 2.3.5.7

[[Comma list]]: 126/125, 65536/64827

[[Mapping]]: [{{val| 1 -4 0 7 }}, {{val| 0 12 5 -9 }}]

{{Multival|legend=1| 12 5 -9 -20 -48 -35 }}

[[POTE generator]]: ~175/128 = 558.605

{{Optimal ET sequence|legend=1| 15, 43, 58 }}

[[Badness]]: 0.088441

Comma list: 126/125, 176/175, 1344/1331

Mapping: [{{val| 1 -4 0 7 3 }}, {{val| 0 12 5 -9 1 }}]

POTE generator: ~11/8 = 558.620

{{Optimal ET sequence|legend=1| 15, 43, 58 }}

Badness: 0.033078

=== 13-limit ===

Comma list: 126/125, 144/143, 176/175, 364/363

Mapping: [{{val| 1 -4 0 7 3 -7 }}, {{val| 0 12 5 -9 1 23 }}]

POTE generator: ~11/8 = 558.589

{{Optimal ET sequence|legend=1| 15, 43, 58 }}

Badness: 0.022838

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

Comma list: 126/125, 144/143, 176/175, 221/220, 256/255

Mapping: [{{val| 1 -4 0 7 3 -7 12 }}, {{val| 0 12 5 -9 1 23 -17 }}]

POTE generator: ~11/8 = 558.509

{{Optimal ET sequence|legend=1| 15, 43, 58 }}

Badness: 0.022293

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220

Mapping: [{{val| 1 -4 0 7 3 -7 12 1 }}, {{val| 0 12 5 -9 1 23 -17 7 }}]

POTE generator: ~11/8 = 558.504

{{Optimal ET sequence|legend=1| 15, 43, 58h }}

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230

Mapping: [{{val| 1 -4 0 7 3 -7 12 1 5 }}, {{val| 0 12 5 -9 1 23 -17 7 -1 }}]

POTE generator: ~11/8 = 558.522

{{Optimal ET sequence|legend=1| 15, 43, 58hi }}

Badness: 0.016581

The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230

Mapping: [{{val| 1 -4 0 7 3 -7 12 1 5 3 }}, {{val| 0 12 5 -9 1 23 -17 7 -1 4 }}]

POTE generator: ~11/8 = 558.520

{{Optimal ET sequence|legend=1| 15, 43, 58hi }}

Badness: 0.013762

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Cypress]].''

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 7 10 15 }}, {{val| 0 -12 -17 -27 }}]

 

{{Multival|legend=1| 12 17 27 -1 9 15 }}

[[POTE generator]]: ~135/98 = 541.828

{{Optimal ET sequence|legend=1| 11cd, 20cd, 31, 206bcd, 237bcd, 268bcd, 299bcd, 330bbcd }}

[[Badness]]: 0.099801

Mapping: [{{val| 1 7 10 15 17 }}, {{val| 0 -12 -17 -27 -30 }}]

POTE generator: ~15/11 = 541.772

{{Optimal ET sequence|legend=1| 11cdee, 20cde, 31, 144cd, 175cd, 206bcde, 237bcde }}

Badness: 0.042719

Mapping: [{{val| 1 7 10 15 17 15 }}, {{val| 0 -12 -17 -27 -30 -25 }}]

POTE generator: ~15/11 = 541.778

{{Optimal ET sequence|legend=1| 11cdeef, 20cdef, 31 }}

Badness: 0.037849

== Bisemidim ==

Subgroup: 2.3.5.7

 

 

 

{{Multival|legend=1| 18 22 30 -7 -3 8 }}

 

 

{{Optimal ET sequence|legend=1| 50, 58, 108, 166c, 408ccc }}

 

[[Badness]]: 0.097786

 

=== 11-limit ===

 

 

Mapping: [{{val| 2 1 2 2 5 }}, {{val| 0 9 11 15 8 }}]

 

POTE generator: ~35/27 = 455.373

 

 

 

 

Mapping: [{{val| 2 1 2 2 5 5 }}, {{val| 0 9 11 15 8 10 }}]

POTE generator: ~35/27 = 455.347

{{Optimal ET sequence|legend=1| 50, 58, 166cef, 224ceeff }}

Badness: 0.023877

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Casablanca]].''

 

 

It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the 35/24 generator is particularly interesting; like 15/14 and 21/20, it represents an interval between one vertex of a [[hexany]] and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads. For another, if we add 385/384 to the list of commas, 35/24 is identified with 16/11, and casablanca is revealed as an 11-limit temperament with a very low complexity for 11 and not too high a one for 7; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit meantone.

 

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 12 10 5 }}, {{val| 0 -19 -14 -4 }}]

{{Multival|legend=1| 19 14 4 -22 -47 -30 }}

 

[[POTE generator]]: ~35/24 = 657.818

[[Badness]]: 0.101191

Mapping: [{{val| 1 12 10 5 4 }}, {{val| 0 -19 -14 -4 -1 }}]

POTE generator: ~16/11 = 657.923

{{Optimal ET sequence|legend=1| 11b, 20b, 31 }}

Badness: 0.067291

Mapping: [{{val| 1 12 10 5 4 7 }}, {{val| 0 -19 -14 -4 -1 -6 }}]

POTE generator: ~16/11 = 657.854

{{Optimal ET sequence|legend=1| 11b, 20b, 31 }}

Mapping: [{{val| 1 12 10 5 21 }}, {{val| 0 -19 -14 -4 -32 }}]

POTE generator: ~22/15 = 657.791

{{Optimal ET sequence|legend=1| 31, 73, 104c, 135c }}

Badness: 0.040539

Mapping: [{{val| 1 12 10 5 21 -10 }}, {{val| 0 -19 -14 -4 -32 25 }}]

POTE generator: ~22/15 = 657.756

{{Optimal ET sequence|legend=1| 31, 73, 104c, 135c, 239ccf }}

Badness: 0.040774

Mapping: [{{val| 1 12 10 5 21 7 }}, {{val| 0 -19 -14 -4 -32 -6 }}]

POTE generator: ~22/15 = 657.700

{{Optimal ET sequence|legend=1| 31, 104cff, 135cff }}

Badness: 0.041395

{{see also| High badness temperaments #Magus }}

Subgroup: 2.3.5.7

[[Mapping]]: [{{val| 1 -2 2 9 }}, {{val| 0 11 1 -19 }}]

{{Multival|legend=1| 11 1 -19 -24 -61 -47 }}

 

[[POTE generator]]: ~5/4 = 391.094

[[Badness]]: 0.110873