Starling temperaments: Difference between revisions

Revision as of 23:10, 27 April 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-04-27 23:10:26 UTC.

The original revision id was 326242790.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[toc]]
=Starling comma= 
This page discusses some of the temperaments tempering out [[126_125|126/125]], the [[starling comma]] or [[septimal semicomma]]. 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]] 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.

=Myna temperament= 
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, or in terms of its wedgie <<10 9 7 -9 -17 -9||. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[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.

[[Comma|Commas]]: 126/125, 1728/1715

7 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0 >, |9/10 9/10 0 0>, |17/10 7/10 0 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 3

[[POTE tuning|POTE generator]]: 310.146

Map: [<1 9 9 8|, <0 -10 -9 -7|]
[[Generator|Generators]]: 2, 5/3
EDOs: 27, 31, 58, 89
Badness: 0.0270

==11-limit== 
Commas: 126/125, 176/175, 243/242

[[POTE tuning|POTE generator]]: ~6/5 = 310.144

Map: [<1 9 9 8 22|, <0 -10 -9 -7 -25|]
EDOs: 31, 58, 89
Badness: 0.0168

==13-limit== 
Commas: 126/125, 144/143, 176/175, 196/195

[[POTE tuning|POTE generator]]: ~6/5 = 310.276

Map: [<1 9 9 8 22 0|, <0 -10 -9 -7 -25 5|]
EDOs: 27, 31, 58
Badness: 0.0171

==Minah==
Commas: 78/77, 91/90, 126/125, 176/175

POTE generator: ~6/5 = 310.381

Map: [<1 9 9 8 22 20|, <0 -10 -9 -7 -25 -22|]
EDOs: 27e, 31f, 58f, 116cef
Badness: 0.0276

==Myno==
Commas: 99/98, 126/125, 385/384

POTE generator: ~6/5 = 309.737

Map: [<1 9 9 8 -1|, <0 -10 -9 -7 6|]
EDOs: 27, 31
Badness: 0.0334

==Coleto==
Commas: 56/55, 100/99, 1728/1715

POTE generator: ~6/5 = 310.853

Map: [<1 9 9 8 2|, <0 -10 -9 -7 2|]
EDOs: 23bc, 27e
Badness: 0.0487

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3|Myna Music]] by [[Igliashon Jones]]

=Sensi temperament= 
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.

[[Comma|Commas]]: 126/125, 245/243

7-limit minimax
[|1 0 0 0>, |1/13 0 0 7/13>, |5/13 0 0 9/13>, |0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7

9-limit minimax
[|1 0 0 0>, |2/5 14/5 -7/5 0>,
|4/5 18/5 -9/5 0>, |3/5 26/5 -13/5 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/5

[[POTE tuning|POTE generator]]: ~9/7 = 443.383
Algebraic generator: Calista, the [[Algebraic number|real root]] of x^7-2x^2-1, at 340.6467 cents.

Map: [<1 6 8 11|, <0 -7 -9 -13|]
[[Generator|Generators]]: 2, 14/9
EDOs: 19, 27, 46, 249, 295
Badness: 0.0256

==Sensor== 
Commas: 126/125, 245/243, 385/384

[[POTE tuning|POTE generator]]: ~9/7 = 443.294

Map: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]
EDOs: 8, 19, 27, 46, 111, 157
Badness: 0.0379

===13-limit=== 
Commas: 91/90, 126/125, 169/168, 385/384

[[POTE tuning|POTE generator]]: ~9/7 = 443.321

Map: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]
EDOs: 8, 19, 27, 46, 157
Badness: 0.0256

==Sensis== 
Commas: 56/55, 100/99, 245/243

[[POTE tuning|POTE generator]]: 443.962

Map: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]
EDOs: 19, 27, 73, 100
Badness: 0.0287

===13-limit=== 
Commas: 56/55, 78/77, 91/90, 100/99

[[POTE tuning|POTE generator]]: 443.945

Map: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]
EDOs: 19, 27, 73, 100
Badness: 0.0200

==Sensus== 
Commas: 126/125, 176/175, 245/243

POTE generator: ~9/7 = 443.626

Map: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]
EDOs: 8, 19, 27, 46, 165
Badness: 0.0295

===13-limit=== 
Commas: 91/90, 126/125, 169/168, 352/351

POTE generator: ~9/7 = 443.559

Map: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]
EDOs: 8, 19, 27, 46, 303
Badness: 0.0208

=Valentine temperament= 
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]], [[108edo]] or [[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 <<9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et 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 "The 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.

[[Comma|Commas]]: 1029/1024, 126/125

[[Minimax tuning]]:
7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>,
|17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6

9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,
|47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>]
[[Eigenmonzo|Eigenmonzos]]: 2, 9/7

[[POTE tuning|POTE generator]]: 77.864

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

Map: [<1 1 2 3|, <0 9 5 -3|]
[[Generator|Generators]]: 2, 21/20
EDOs: 15, 31, 46, 77, 185, 262
Badness: 0.0311

==11-limit== 
[[Comma|Commas]]: 121/120, 126/125, 176/175

[[Minimax tuning]]:
[|1 0 0 0 0>, |1 0 0 -9/10 9/10>,
|2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/7

Minimax generator: (11/7)^(1/10) = 78.249
[[POTE tuning|POTE generator]]: 77.881

Algebraic generator: Gontrand2, the smallest positive root of 4x^7-8x^6+5, at 77.9989 cents.

Map: [<1 1 2 3 3|, <0 9 5 -3 7|]
[[Edo|Edos]]: [[15edo|15]], [[31edo|31]], [[46edo|46]], [[77edo|77]], [[108edo|108]], [[185edo|185]]
Badness: 0.0167

See also: [[Chords of valentine]]

==Dwynwen== 
Commas: 91/90, 121/120, 126/125, 176/175

POTE generator: ~21/20 = 78.219

Map: [<1 1 2 3 3 2|, <0 9 5 -3 7 26|]
EDOs: 15, 46
Badness: 0.0235

==Lupercalia== 
Commas: 66/65, 105/104, 121/120, 126/125

POTE generator: ~22/21 = 77.709

Map: [<1 1 2 3 3 3|, <0 9 5 -3 7 11|]
EDOs: 15, 31, 108, 139
Badness: 0.0213

==Valentino== 
Commas: 121/120, 126/125, 176/175, 196/195

POTE generator: ~22/21 = 77.958

Map: [<1 1 2 3 3 5|, <0 9 5 -3 7 -20|]
EDOs: 15, 31, 46, 77, 431
Badness: 0.0207

=Alicorn temperament= 
Commas: 126/125, 10976/10935

POTE generator: ~28/27 = 62.278

Map: [<1 2 3 4|, <0 -8 -13 -23|]
Wedgie: <<8 13 23 2 14 17||
EDOs: 19, 58, 77, 96
Badness: 0.0409

==11-limit== 
Commas: 126/125, 540/539, 896/891

POTE generator: ~28/27 = 62.101

Map: [<1 2 3 4 3|, <0 -8 -13 -23 9|]
EDOs: 19, 58
Badness: 0.0392

==13-limit== 
Commas: 126/125, 144/143, 196/195, 676/675

POTE generator: ~28/27 = 62.119

Map: [<1 2 3 4 3 5|, <0 -8 -13 -23 9 -25|]
EDOs: 19, 58

Badness: 0.0237

==Camahueto== 
Commas: 126/125, 10976/10935, 385/384

POTE generator: ~28/27 = 62.431

Map: [<1 2 3 4 2|, <0 -8 -13 -23 28|]
EDOs: 19, 58, 77, 96
Badness: 0.0659

===13-limit=== 
Commas: 126/125, 196/195, 385/384, 676/675

POTE generator: ~28/27 = 62.434

Map: [<1 2 3 4 2 5|, <0 -8 -13 -23 28 -25|]
EDOs: 19, 58, 77
Badness: 0.0362


=Casablanca temperament= 
Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, <<19 14 4 -22 -47 -30||, or as 31&73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.

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|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.

Commas: 126/125, 589824/588245

POTE generator: ~35/24 = 657.818

Map: [<1 12 10 5|, <0 -19 -14 -4|]
EDOs: 9, 11, 31, 135, 166
Badness: 0.1012

==11-limit== 
Commas: 126/125, 385/384, 2420/2401

POTE generator: ~16/11 = 657.923

Map: [<1 12 10 5 4|, |0 -19 -14 -4 -1>]
EDOs: 9, 11, 31, 259, 549
Badness: 0.0623

==Marrakesh== 
Commas: 126/125, 176/175, 14641/14580

POTE generator: ~22/15 = 657.791

Map: [<1 12 10 5 21|, |0 -19 -14 -4 -32>]
EDOs: 9, 11, 20, 31, 42, 73
Badness: 0.0405

===13-limit=== 
126/125, 176/175, 196/195, 17303/17280

POTE generator: ~22/15 = 657.756

Map: [<1 12 10 5 21 -10|, |0 -19 -14 -4 -32 25>]
EDOs: 31, 73, 104c, 135c, 239cf
Badness: 0.0408

===Murakuc=== 
Commas: 126/125, 144/143, 176/175, 1540/1521

POTE generator: ~22/15 = 657.700

Map: [<1 12 10 5 21 7|, |0 -19 -14 -4 -32 -6>]
EDOs: 31, 73f, 104cf
Badness: 0.0414

=Nusecond temperament= 
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&70, or in terms of its wedgie as <<11 13 17 -5 -4 3||. 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]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[Patent val|patent vals]] 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.

[[Comma|Commas]]: 126/125, 2430/2401

7-limit minimax
[|1 0 0 0>, |-5/13 0 11/13 0>, |0 0 1 0>, |-3/13 0 17/13 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 5

9-limit minimax
[|1 0 0 0>, |0 1 0 0>, |5/11 13/11 0 0>, |4/11 17/11 0 0>]
[[Eigenmonzo|Eigenmonzos]]: 2, 3

[[POTE tuning|POTE generator]]: 154.579

Map: [<1 3 4 5|, <0 -11 -13 -17|]
[[Generator|Generators]]: 2, 49/45
EDOs: 7, 8, 31, 101, 132, 163
Badness: 0.0504

==11-limit== 
[[Comma|Commas]]: 99/98, 121/120, 126/125

11-limit minimax
[|1 0 0 0 0>, |19/10 11/5 0 0 -11/10>,
|27/10 13/5 0 0 -13/10>, |33/10 17/5 0 0 -17/10>,
|19/5 12/5 0 0 -6/5>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/9

[[POTE tuning|POTE generator]]: ~11/10 = 154.645
Algebraic generator: [[Algebraic number|positive root]] of 15x^2-10x-7, or (5+sqrt(130))/15, at 154.6652 cents. The recurrence converges very quickly.

Map: [<1 3 4 5 5|, <0 -11 -13 -17 -12|]
[[Generator|Generators]]: 2, 11/10
EDOs: 7, 8, 31, 101, 194
Badness: 0.0256

==13-limit==
Commas: 66/65 99/98 121/120 126/125

POTE generator: ~11/10 = 154.478

Map: [<1 3 4 5 5 5|, <0 -11 -13 -17 -12 -10|]
EDOs: 31, 70f, 101f
Badness: 0.0233

=Thuja= 
Commas: 126/125, 65536/64827

POTE generator: ~175/128 = 558.605

Map: [<1 8 5 -2|, <0 -12 -5 9|]
Wedgie: <<12 5 -9 -20 -48 -35||
EDOs: 15, 43, 58
Badness: 0.0884

==11-limit== 
Commas: 126/125, 176/175, 1344/1331

POTE generator: ~11/8 = 558.620

Map: [<1 8 5 -2 4|, <0 -12 -5 9 -1|]
EDOs: 15, 43, 58
Badness: 0.0331

==13-limit== 
Commas: 126/125, 144/143, 176/175, 364/363

POTE generator: ~11/8 = 558.589

Map: [<1 8 5 -2 4 16|, <0 -12 -5 9 -1 -23|]
EDOs: 15, 43, 58
Badness: 0.0228

=Bisemidim=
Commas: 126/125, 118098/117649

POTE generator: ~35/27 = 455.445

Map: [<2 1 2 2|, <0 9 11 15|]
Wedgie: <<18 22 30 -7 -3 8||
EDOs: 50, 58, 108, 166c, 408c
Badness: 0.0978

==11-limit==
Commas: 126/125, 540/539, 1344/1331

POTE generator: ~35/27 = 455.373

Map: [<2 1 2 2 5|, <0 9 11 15 8|]
EDOs: 50, 58, 108, 166ce, 224ce
Badness: 0.0412

==13-limit==
Commas: 126/125, 144/143, 196/195, 364/363

POTE generator: ~35/27 = 455.347

Map: [<2 1 2 2 5 5|, <0 9 11 15 8 10|]
EDOs: 50, 58, 166cef, 224cef
Badness: 0.0239

=Kumonga=
Commas: 126/125, 12288/12005

POTE generator: ~8/7 = 222.797

Map: [<1 4 4 3|, <0 -13 -9 -1|]
Wedgie: <<13 9 1 -16 -35 -23||
EDOs: 16, 27, 43, 70, 167cd
Badness: 0.0875

==11-limit==
Commas: 126/125, 176/175, 864/847

POTE generator: ~8/7 = 222.898

Map: [<1 4 4 3 7|, <0 -13 -9 -1 -19|]
EDOs: 16, 27e, 43, 70e
Badness: 0.0433

==13-limit==
Commas: 78/77, 126/125, 144/143, 176/175

POTE generator: ~8/7 = 222.961

Map: [<1 4 4 3 7 5|, <0 -13 -9 -1 -19 -7|]
EDOs: 16, 27e, 43, 70e, 113cde
Badness: 0.0289

Original HTML content:

<html><head><title>Starling temperaments</title></head><body><!-- ws:start:WikiTextTocRule:82:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 1em;"><a href="#Starling comma">Starling comma</a></div>
<!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 1em;"><a href="#Myna temperament">Myna temperament</a></div>
<!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 2em;"><a href="#Myna temperament-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Myna temperament-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Myna temperament-Minah">Minah</a></div>
<!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 2em;"><a href="#Myna temperament-Myno">Myno</a></div>
<!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Myna temperament-Coleto">Coleto</a></div>
<!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 1em;"><a href="#Sensi temperament">Sensi temperament</a></div>
<!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensor">Sensor</a></div>
<!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensor-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensis">Sensis</a></div>
<!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensis-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#Sensi temperament-Sensus">Sensus</a></div>
<!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 3em;"><a href="#Sensi temperament-Sensus-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 1em;"><a href="#Valentine temperament">Valentine temperament</a></div>
<!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Valentine temperament-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Dwynwen">Dwynwen</a></div>
<!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Lupercalia">Lupercalia</a></div>
<!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Valentine temperament-Valentino">Valentino</a></div>
<!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 1em;"><a href="#Alicorn temperament">Alicorn temperament</a></div>
<!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Alicorn temperament-Camahueto">Camahueto</a></div>
<!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 3em;"><a href="#Alicorn temperament-Camahueto-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 1em;"><a href="#Casablanca temperament">Casablanca temperament</a></div>
<!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Casablanca temperament-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 2em;"><a href="#Casablanca temperament-Marrakesh">Marrakesh</a></div>
<!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 3em;"><a href="#Casablanca temperament-Marrakesh-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 3em;"><a href="#Casablanca temperament-Marrakesh-Murakuc">Murakuc</a></div>
<!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 1em;"><a href="#Nusecond temperament">Nusecond temperament</a></div>
<!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 2em;"><a href="#Nusecond temperament-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Nusecond temperament-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Thuja">Thuja</a></div>
<!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Thuja-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Thuja-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Bisemidim">Bisemidim</a></div>
<!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Bisemidim-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Bisemidim-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Kumonga">Kumonga</a></div>
<!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Kumonga-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Kumonga-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --></div>
<!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Starling comma"></a><!-- ws:end:WikiTextHeadingRule:0 -->Starling comma</h1>
 This page discusses some of the temperaments tempering out <a class="wiki_link" href="/126_125">126/125</a>, the <a class="wiki_link" href="/starling%20comma">starling comma</a> or <a class="wiki_link" href="/septimal%20semicomma">septimal semicomma</a>. Since (6/5)^3 = 126/125 * 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the <a class="wiki_link" href="/starling%20tetrad">starling tetrad</a>, 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 <a class="wiki_link" href="/12edo">12edo</a> 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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Myna temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Myna temperament</h1>
 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&amp;31 temperament, or in terms of its wedgie &lt;&lt;10 9 7 -9 -17 -9||. It has 6/5 as a generator, and <a class="wiki_link" href="/58edo">58edo</a> can be used as a tuning, with <a class="wiki_link" href="/89edo">89edo</a> being a better one, and fans of round amounts in cents may like <a class="wiki_link" href="/120edo">120edo</a>. 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.<br />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 1728/1715<br />
<br />
7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |0 1 0 0 &gt;, |9/10 9/10 0 0&gt;, |17/10 7/10 0 0&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 310.146<br />
<br />
Map: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 5/3<br />
EDOs: 27, 31, 58, 89<br />
Badness: 0.0270<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Myna temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
 Commas: 126/125, 176/175, 243/242<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 310.144<br />
<br />
Map: [&lt;1 9 9 8 22|, &lt;0 -10 -9 -7 -25|]<br />
EDOs: 31, 58, 89<br />
Badness: 0.0168<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Myna temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
 Commas: 126/125, 144/143, 176/175, 196/195<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 310.276<br />
<br />
Map: [&lt;1 9 9 8 22 0|, &lt;0 -10 -9 -7 -25 5|]<br />
EDOs: 27, 31, 58<br />
Badness: 0.0171<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Myna temperament-Minah"></a><!-- ws:end:WikiTextHeadingRule:8 -->Minah</h2>
Commas: 78/77, 91/90, 126/125, 176/175<br />
<br />
POTE generator: ~6/5 = 310.381<br />
<br />
Map: [&lt;1 9 9 8 22 20|, &lt;0 -10 -9 -7 -25 -22|]<br />
EDOs: 27e, 31f, 58f, 116cef<br />
Badness: 0.0276<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Myna temperament-Myno"></a><!-- ws:end:WikiTextHeadingRule:10 -->Myno</h2>
Commas: 99/98, 126/125, 385/384<br />
<br />
POTE generator: ~6/5 = 309.737<br />
<br />
Map: [&lt;1 9 9 8 -1|, &lt;0 -10 -9 -7 6|]<br />
EDOs: 27, 31<br />
Badness: 0.0334<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Myna temperament-Coleto"></a><!-- ws:end:WikiTextHeadingRule:12 -->Coleto</h2>
Commas: 56/55, 100/99, 1728/1715<br />
<br />
POTE generator: ~6/5 = 310.853<br />
<br />
Map: [&lt;1 9 9 8 2|, &lt;0 -10 -9 -7 2|]<br />
EDOs: 23bc, 27e<br />
Badness: 0.0487<br />
<br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3" rel="nofollow">Myna Music</a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Sensi temperament"></a><!-- ws:end:WikiTextHeadingRule:14 -->Sensi temperament</h1>
 Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. <a class="wiki_link" href="/46edo">46edo</a> is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.<br />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 245/243<br />
<br />
7-limit minimax<br />
[|1 0 0 0&gt;, |1/13 0 0 7/13&gt;, |5/13 0 0 9/13&gt;, |0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br />
<br />
9-limit minimax<br />
[|1 0 0 0&gt;, |2/5 14/5 -7/5 0&gt;,<br />
|4/5 18/5 -9/5 0&gt;, |3/5 26/5 -13/5 0&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/5<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.383<br />
Algebraic generator: Calista, the <a class="wiki_link" href="/Algebraic%20number">real root</a> of x^7-2x^2-1, at 340.6467 cents.<br />
<br />
Map: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 14/9<br />
EDOs: 19, 27, 46, 249, 295<br />
Badness: 0.0256<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Sensi temperament-Sensor"></a><!-- ws:end:WikiTextHeadingRule:16 -->Sensor</h2>
 Commas: 126/125, 245/243, 385/384<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.294<br />
<br />
Map: [&lt;1 6 8 11 -6|, &lt;0 -7 -9 -13 15|]<br />
EDOs: 8, 19, 27, 46, 111, 157<br />
Badness: 0.0379<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Sensi temperament-Sensor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h3>
 Commas: 91/90, 126/125, 169/168, 385/384<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 443.321<br />
<br />
Map: [&lt;1 6 8 11 -6 10|, &lt;0 -7 -9 -13 15 -10|]<br />
EDOs: 8, 19, 27, 46, 157<br />
Badness: 0.0256<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Sensi temperament-Sensis"></a><!-- ws:end:WikiTextHeadingRule:20 -->Sensis</h2>
 Commas: 56/55, 100/99, 245/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.962<br />
<br />
Map: [&lt;1 6 8 11 6|, &lt;0 -7 -9 -13 -4|]<br />
EDOs: 19, 27, 73, 100<br />
Badness: 0.0287<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Sensi temperament-Sensis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h3>
 Commas: 56/55, 78/77, 91/90, 100/99<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 443.945<br />
<br />
Map: [&lt;1 6 8 11 6 10|, &lt;0 -7 -9 -13 -4 -10|]<br />
EDOs: 19, 27, 73, 100<br />
Badness: 0.0200<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Sensi temperament-Sensus"></a><!-- ws:end:WikiTextHeadingRule:24 -->Sensus</h2>
 Commas: 126/125, 176/175, 245/243<br />
<br />
POTE generator: ~9/7 = 443.626<br />
<br />
Map: [&lt;1 6 8 11 23|, &lt;0 -7 -9 -13 -31|]<br />
EDOs: 8, 19, 27, 46, 165<br />
Badness: 0.0295<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Sensi temperament-Sensus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h3>
 Commas: 91/90, 126/125, 169/168, 352/351<br />
<br />
POTE generator: ~9/7 = 443.559<br />
<br />
Map: [&lt;1 6 8 11 23 10|, &lt;0 -7 -9 -13 -31 -10|]<br />
EDOs: 8, 19, 27, 46, 303<br />
Badness: 0.0208<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Valentine temperament"></a><!-- ws:end:WikiTextHeadingRule:28 -->Valentine temperament</h1>
 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 <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice of 7-limit tetrads</a>. Valentine can also be described as the 31&amp;46 temperament, and <a class="wiki_link" href="/77edo">77edo</a>, <a class="wiki_link" href="/108edo">108edo</a> or <a class="wiki_link" href="/185edo">185edo</a> 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 &lt;&lt;9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et has a valentine generator 3/46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^(1/10).<br />
<br />
Valentine is very closely related to <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a>, 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 <em>Beauty in the Beast</em> 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 &quot;The melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before&quot;, 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.<br />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 126/125<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
7-limit: [|1 0 0 0&gt;, |5/2 3/4 0 -3/4&gt;,<br />
|17/6 5/12 0 -5/12&gt;, [5/2 -1/4 0 1/4&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br />
<br />
9-limit: [|1 0 0 0&gt;, |10/7 6/7 0 -3/7&gt;,<br />
|47/21 10/21 0 -5/21&gt;, |20/7 -2/7 0 1/7&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.864<br />
<br />
Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">smaller root</a> of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.<br />
<br />
Map: [&lt;1 1 2 3|, &lt;0 9 5 -3|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 21/20<br />
EDOs: 15, 31, 46, 77, 185, 262<br />
Badness: 0.0311<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Valentine temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2>
 <a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br />
[|1 0 0 0 0&gt;, |1 0 0 -9/10 9/10&gt;,<br />
|2 0 0 -1/2 1/2&gt;, |3 0 0 3/10 -3/10&gt;, |3 0 0 -7/10 7/10&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/7<br />
<br />
Minimax generator: (11/7)^(1/10) = 78.249<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.881<br />
<br />
Algebraic generator: Gontrand2, the smallest positive root of 4x^7-8x^6+5, at 77.9989 cents.<br />
<br />
Map: [&lt;1 1 2 3 3|, &lt;0 9 5 -3 7|]<br />
<a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/77edo">77</a>, <a class="wiki_link" href="/108edo">108</a>, <a class="wiki_link" href="/185edo">185</a><br />
Badness: 0.0167<br />
<br />
See also: <a class="wiki_link" href="/Chords%20of%20valentine">Chords of valentine</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Valentine temperament-Dwynwen"></a><!-- ws:end:WikiTextHeadingRule:32 -->Dwynwen</h2>
 Commas: 91/90, 121/120, 126/125, 176/175<br />
<br />
POTE generator: ~21/20 = 78.219<br />
<br />
Map: [&lt;1 1 2 3 3 2|, &lt;0 9 5 -3 7 26|]<br />
EDOs: 15, 46<br />
Badness: 0.0235<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Valentine temperament-Lupercalia"></a><!-- ws:end:WikiTextHeadingRule:34 -->Lupercalia</h2>
 Commas: 66/65, 105/104, 121/120, 126/125<br />
<br />
POTE generator: ~22/21 = 77.709<br />
<br />
Map: [&lt;1 1 2 3 3 3|, &lt;0 9 5 -3 7 11|]<br />
EDOs: 15, 31, 108, 139<br />
Badness: 0.0213<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Valentine temperament-Valentino"></a><!-- ws:end:WikiTextHeadingRule:36 -->Valentino</h2>
 Commas: 121/120, 126/125, 176/175, 196/195<br />
<br />
POTE generator: ~22/21 = 77.958<br />
<br />
Map: [&lt;1 1 2 3 3 5|, &lt;0 9 5 -3 7 -20|]<br />
EDOs: 15, 31, 46, 77, 431<br />
Badness: 0.0207<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Alicorn temperament"></a><!-- ws:end:WikiTextHeadingRule:38 -->Alicorn temperament</h1>
 Commas: 126/125, 10976/10935<br />
<br />
POTE generator: ~28/27 = 62.278<br />
<br />
Map: [&lt;1 2 3 4|, &lt;0 -8 -13 -23|]<br />
Wedgie: &lt;&lt;8 13 23 2 14 17||<br />
EDOs: 19, 58, 77, 96<br />
Badness: 0.0409<br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Alicorn temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2>
 Commas: 126/125, 540/539, 896/891<br />
<br />
POTE generator: ~28/27 = 62.101<br />
<br />
Map: [&lt;1 2 3 4 3|, &lt;0 -8 -13 -23 9|]<br />
EDOs: 19, 58<br />
Badness: 0.0392<br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Alicorn temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2>
 Commas: 126/125, 144/143, 196/195, 676/675<br />
<br />
POTE generator: ~28/27 = 62.119<br />
<br />
Map: [&lt;1 2 3 4 3 5|, &lt;0 -8 -13 -23 9 -25|]<br />
EDOs: 19, 58<br />
<br />
Badness: 0.0237<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Alicorn temperament-Camahueto"></a><!-- ws:end:WikiTextHeadingRule:44 -->Camahueto</h2>
 Commas: 126/125, 10976/10935, 385/384<br />
<br />
POTE generator: ~28/27 = 62.431<br />
<br />
Map: [&lt;1 2 3 4 2|, &lt;0 -8 -13 -23 28|]<br />
EDOs: 19, 58, 77, 96<br />
Badness: 0.0659<br />
<br />
<!-- ws:start:WikiTextHeadingRule:46:&lt;h3&gt; --><h3 id="toc23"><a name="Alicorn temperament-Camahueto-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h3>
 Commas: 126/125, 196/195, 385/384, 676/675<br />
<br />
POTE generator: ~28/27 = 62.434<br />
<br />
Map: [&lt;1 2 3 4 2 5|, &lt;0 -8 -13 -23 28 -25|]<br />
EDOs: 19, 58, 77<br />
Badness: 0.0362<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Casablanca temperament"></a><!-- ws:end:WikiTextHeadingRule:48 -->Casablanca temperament</h1>
 Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, &lt;&lt;19 14 4 -22 -47 -30||, or as 31&amp;73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.<br />
<br />
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 <a class="wiki_link" href="/Hexany">hexany</a> 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.<br />
<br />
Commas: 126/125, 589824/588245<br />
<br />
POTE generator: ~35/24 = 657.818<br />
<br />
Map: [&lt;1 12 10 5|, &lt;0 -19 -14 -4|]<br />
EDOs: 9, 11, 31, 135, 166<br />
Badness: 0.1012<br />
<br />
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Casablanca temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2>
 Commas: 126/125, 385/384, 2420/2401<br />
<br />
POTE generator: ~16/11 = 657.923<br />
<br />
Map: [&lt;1 12 10 5 4|, |0 -19 -14 -4 -1&gt;]<br />
EDOs: 9, 11, 31, 259, 549<br />
Badness: 0.0623<br />
<br />
<!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Casablanca temperament-Marrakesh"></a><!-- ws:end:WikiTextHeadingRule:52 -->Marrakesh</h2>
 Commas: 126/125, 176/175, 14641/14580<br />
<br />
POTE generator: ~22/15 = 657.791<br />
<br />
Map: [&lt;1 12 10 5 21|, |0 -19 -14 -4 -32&gt;]<br />
EDOs: 9, 11, 20, 31, 42, 73<br />
Badness: 0.0405<br />
<br />
<!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc27"><a name="Casablanca temperament-Marrakesh-13-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->13-limit</h3>
 126/125, 176/175, 196/195, 17303/17280<br />
<br />
POTE generator: ~22/15 = 657.756<br />
<br />
Map: [&lt;1 12 10 5 21 -10|, |0 -19 -14 -4 -32 25&gt;]<br />
EDOs: 31, 73, 104c, 135c, 239cf<br />
Badness: 0.0408<br />
<br />
<!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="Casablanca temperament-Marrakesh-Murakuc"></a><!-- ws:end:WikiTextHeadingRule:56 -->Murakuc</h3>
 Commas: 126/125, 144/143, 176/175, 1540/1521<br />
<br />
POTE generator: ~22/15 = 657.700<br />
<br />
Map: [&lt;1 12 10 5 21 7|, |0 -19 -14 -4 -32 -6&gt;]<br />
EDOs: 31, 73f, 104cf<br />
Badness: 0.0414<br />
<br />
<!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Nusecond temperament"></a><!-- ws:end:WikiTextHeadingRule:58 -->Nusecond temperament</h1>
 Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;70, or in terms of its wedgie as &lt;&lt;11 13 17 -5 -4 3||. 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. <a class="wiki_link" href="/31edo">31edo</a> can be used as a tuning, or <a class="wiki_link" href="/132edo">132edo</a> with a val which is the sum of the <a class="wiki_link" href="/Patent%20val">patent vals</a> 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.<br />
<br />
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 2430/2401<br />
<br />
7-limit minimax<br />
[|1 0 0 0&gt;, |-5/13 0 11/13 0&gt;, |0 0 1 0&gt;, |-3/13 0 17/13 0&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 5<br />
<br />
9-limit minimax<br />
[|1 0 0 0&gt;, |0 1 0 0&gt;, |5/11 13/11 0 0&gt;, |4/11 17/11 0 0&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 3<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 154.579<br />
<br />
Map: [&lt;1 3 4 5|, &lt;0 -11 -13 -17|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 49/45<br />
EDOs: 7, 8, 31, 101, 132, 163<br />
Badness: 0.0504<br />
<br />
<!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Nusecond temperament-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2>
 <a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 126/125<br />
<br />
11-limit minimax<br />
[|1 0 0 0 0&gt;, |19/10 11/5 0 0 -11/10&gt;,<br />
|27/10 13/5 0 0 -13/10&gt;, |33/10 17/5 0 0 -17/10&gt;,<br />
|19/5 12/5 0 0 -6/5&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/10 = 154.645<br />
Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 15x^2-10x-7, or (5+sqrt(130))/15, at 154.6652 cents. The recurrence converges very quickly.<br />
<br />
Map: [&lt;1 3 4 5 5|, &lt;0 -11 -13 -17 -12|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 11/10<br />
EDOs: 7, 8, 31, 101, 194<br />
Badness: 0.0256<br />
<br />
<!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Nusecond temperament-13-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->13-limit</h2>
Commas: 66/65 99/98 121/120 126/125<br />
<br />
POTE generator: ~11/10 = 154.478<br />
<br />
Map: [&lt;1 3 4 5 5 5|, &lt;0 -11 -13 -17 -12 -10|]<br />
EDOs: 31, 70f, 101f<br />
Badness: 0.0233<br />
<br />
<!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Thuja"></a><!-- ws:end:WikiTextHeadingRule:64 -->Thuja</h1>
 Commas: 126/125, 65536/64827<br />
<br />
POTE generator: ~175/128 = 558.605<br />
<br />
Map: [&lt;1 8 5 -2|, &lt;0 -12 -5 9|]<br />
Wedgie: &lt;&lt;12 5 -9 -20 -48 -35||<br />
EDOs: 15, 43, 58<br />
Badness: 0.0884<br />
<br />
<!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Thuja-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->11-limit</h2>
 Commas: 126/125, 176/175, 1344/1331<br />
<br />
POTE generator: ~11/8 = 558.620<br />
<br />
Map: [&lt;1 8 5 -2 4|, &lt;0 -12 -5 9 -1|]<br />
EDOs: 15, 43, 58<br />
Badness: 0.0331<br />
<br />
<!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Thuja-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2>
 Commas: 126/125, 144/143, 176/175, 364/363<br />
<br />
POTE generator: ~11/8 = 558.589<br />
<br />
Map: [&lt;1 8 5 -2 4 16|, &lt;0 -12 -5 9 -1 -23|]<br />
EDOs: 15, 43, 58<br />
Badness: 0.0228<br />
<br />
<!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Bisemidim"></a><!-- ws:end:WikiTextHeadingRule:70 -->Bisemidim</h1>
Commas: 126/125, 118098/117649<br />
<br />
POTE generator: ~35/27 = 455.445<br />
<br />
Map: [&lt;2 1 2 2|, &lt;0 9 11 15|]<br />
Wedgie: &lt;&lt;18 22 30 -7 -3 8||<br />
EDOs: 50, 58, 108, 166c, 408c<br />
Badness: 0.0978<br />
<br />
<!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Bisemidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2>
Commas: 126/125, 540/539, 1344/1331<br />
<br />
POTE generator: ~35/27 = 455.373<br />
<br />
Map: [&lt;2 1 2 2 5|, &lt;0 9 11 15 8|]<br />
EDOs: 50, 58, 108, 166ce, 224ce<br />
Badness: 0.0412<br />
<br />
<!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Bisemidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2>
Commas: 126/125, 144/143, 196/195, 364/363<br />
<br />
POTE generator: ~35/27 = 455.347<br />
<br />
Map: [&lt;2 1 2 2 5 5|, &lt;0 9 11 15 8 10|]<br />
EDOs: 50, 58, 166cef, 224cef<br />
Badness: 0.0239<br />
<br />
<!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc38"><a name="Kumonga"></a><!-- ws:end:WikiTextHeadingRule:76 -->Kumonga</h1>
Commas: 126/125, 12288/12005<br />
<br />
POTE generator: ~8/7 = 222.797<br />
<br />
Map: [&lt;1 4 4 3|, &lt;0 -13 -9 -1|]<br />
Wedgie: &lt;&lt;13 9 1 -16 -35 -23||<br />
EDOs: 16, 27, 43, 70, 167cd<br />
Badness: 0.0875<br />
<br />
<!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Kumonga-11-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->11-limit</h2>
Commas: 126/125, 176/175, 864/847<br />
<br />
POTE generator: ~8/7 = 222.898<br />
<br />
Map: [&lt;1 4 4 3 7|, &lt;0 -13 -9 -1 -19|]<br />
EDOs: 16, 27e, 43, 70e<br />
Badness: 0.0433<br />
<br />
<!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Kumonga-13-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->13-limit</h2>
Commas: 78/77, 126/125, 144/143, 176/175<br />
<br />
POTE generator: ~8/7 = 222.961<br />
<br />
Map: [&lt;1 4 4 3 7 5|, &lt;0 -13 -9 -1 -19 -7|]<br />
EDOs: 16, 27e, 43, 70e, 113cde<br />
Badness: 0.0289</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-27 22:27:50 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-27 23:10:26 UTC</tt>.<br>
-: The original revision id was <tt>326236072</tt>.<br>
+: The original revision id was <tt>326242790</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 43: / Line 43: @@
 EDOs: 27, 31, 58
 Badness: 0.0171
+==Minah==
+Commas: 78/77, 91/90, 126/125, 176/175
+POTE generator: ~6/5 = 310.381
+Map: [&lt;1 9 9 8 22 20|, &lt;0 -10 -9 -7 -25 -22|]
+EDOs: 27e, 31f, 58f, 116cef
+Badness: 0.0276
 ==Myno==
@@ Line 436: / Line 445: @@
 Map: [&lt;1 4 4 3 7 5|, &lt;0 -13 -9 -1 -19 -7|]
 EDOs: 16, 27e, 43, 70e, 113cde
-Badness: 0.0289
+Badness: 0.0289</pre></div>
-</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Starling temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:80:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Starling comma"&gt;Starling comma&lt;/a&gt;&lt;/div&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Starling temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:82:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Starling comma"&gt;Starling comma&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Myna temperament"&gt;Myna temperament&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Myna temperament"&gt;Myna temperament&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-Myno"&gt;Myno&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-Minah"&gt;Minah&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-Coleto"&gt;Coleto&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-Myno"&gt;Myno&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sensi temperament"&gt;Sensi temperament&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Myna temperament-Coleto"&gt;Coleto&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensi temperament-Sensor"&gt;Sensor&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Sensi temperament"&gt;Sensi temperament&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensi temperament-Sensor-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensi temperament-Sensor"&gt;Sensor&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensi temperament-Sensis"&gt;Sensis&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensi temperament-Sensor-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensi temperament-Sensis-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensi temperament-Sensis"&gt;Sensis&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensi temperament-Sensus"&gt;Sensus&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensi temperament-Sensis-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensi temperament-Sensus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Sensi temperament-Sensus"&gt;Sensus&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Valentine temperament"&gt;Valentine temperament&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Sensi temperament-Sensus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Valentine temperament"&gt;Valentine temperament&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-Dwynwen"&gt;Dwynwen&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-Lupercalia"&gt;Lupercalia&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-Dwynwen"&gt;Dwynwen&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-Valentino"&gt;Valentino&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-Lupercalia"&gt;Lupercalia&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Alicorn temperament"&gt;Alicorn temperament&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Valentine temperament-Valentino"&gt;Valentino&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alicorn temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Alicorn temperament"&gt;Alicorn temperament&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alicorn temperament-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alicorn temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alicorn temperament-Camahueto"&gt;Camahueto&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alicorn temperament-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Alicorn temperament-Camahueto-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alicorn temperament-Camahueto"&gt;Camahueto&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Casablanca temperament"&gt;Casablanca temperament&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Alicorn temperament-Camahueto-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Casablanca temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Casablanca temperament"&gt;Casablanca temperament&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Casablanca temperament-Marrakesh"&gt;Marrakesh&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Casablanca temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Casablanca temperament-Marrakesh-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Casablanca temperament-Marrakesh"&gt;Marrakesh&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Casablanca temperament-Marrakesh-Murakuc"&gt;Murakuc&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Casablanca temperament-Marrakesh-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Nusecond temperament"&gt;Nusecond temperament&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Casablanca temperament-Marrakesh-Murakuc"&gt;Murakuc&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Nusecond temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Nusecond temperament"&gt;Nusecond temperament&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Nusecond temperament-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Nusecond temperament-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Thuja"&gt;Thuja&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Nusecond temperament-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thuja-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Thuja"&gt;Thuja&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thuja-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thuja-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bisemidim"&gt;Bisemidim&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thuja-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bisemidim-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bisemidim"&gt;Bisemidim&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bisemidim-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bisemidim-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Kumonga"&gt;Kumonga&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bisemidim-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Kumonga-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Kumonga"&gt;Kumonga&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Kumonga-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Kumonga-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Kumonga-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Starling comma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Starling comma&lt;/h1&gt;
+&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Starling comma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Starling comma&lt;/h1&gt;
   This page discusses some of the temperaments tempering out &lt;a class="wiki_link" href="/126_125"&gt;126/125&lt;/a&gt;, the &lt;a class="wiki_link" href="/starling%20comma"&gt;starling comma&lt;/a&gt; or &lt;a class="wiki_link" href="/septimal%20semicomma"&gt;septimal semicomma&lt;/a&gt;. Since (6/5)^3 = 126/125 * 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the &lt;a class="wiki_link" href="/starling%20tetrad"&gt;starling tetrad&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 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.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 517: / Line 526: @@
 Badness: 0.0171&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Myna temperament-Myno"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Myno&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Myna temperament-Minah"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Minah&lt;/h2&gt;
+Commas: 78/77, 91/90, 126/125, 176/175&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~6/5 = 310.381&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 9 9 8 22 20|, &amp;lt;0 -10 -9 -7 -25 -22|]&lt;br /&gt;
+EDOs: 27e, 31f, 58f, 116cef&lt;br /&gt;
+Badness: 0.0276&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Myna temperament-Myno"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Myno&lt;/h2&gt;
 Commas: 99/98, 126/125, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 526: / Line 544: @@
 Badness: 0.0334&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Myna temperament-Coleto"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Coleto&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Myna temperament-Coleto"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Coleto&lt;/h2&gt;
 Commas: 56/55, 100/99, 1728/1715&lt;br /&gt;
 &lt;br /&gt;
@@ Line 537: / Line 555: @@
 &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3" rel="nofollow"&gt;Myna Music&lt;/a&gt; by &lt;a class="wiki_link" href="/Igliashon%20Jones"&gt;Igliashon Jones&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Sensi temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sensi temperament&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Sensi temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Sensi temperament&lt;/h1&gt;
   Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&amp;amp;27 temperament. It has as a generator half of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt; is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 559: / Line 577: @@
 Badness: 0.0256&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Sensi temperament-Sensor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Sensor&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Sensi temperament-Sensor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Sensor&lt;/h2&gt;
   Commas: 126/125, 245/243, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 568: / Line 586: @@
 Badness: 0.0379&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Sensi temperament-Sensor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Sensi temperament-Sensor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h3&gt;
   Commas: 91/90, 126/125, 169/168, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 577: / Line 595: @@
 Badness: 0.0256&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Sensi temperament-Sensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Sensis&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Sensi temperament-Sensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Sensis&lt;/h2&gt;
   Commas: 56/55, 100/99, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 586: / Line 604: @@
 Badness: 0.0287&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Sensi temperament-Sensis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Sensi temperament-Sensis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h3&gt;
   Commas: 56/55, 78/77, 91/90, 100/99&lt;br /&gt;
 &lt;br /&gt;
@@ Line 595: / Line 613: @@
 Badness: 0.0200&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Sensi temperament-Sensus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Sensus&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Sensi temperament-Sensus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Sensus&lt;/h2&gt;
   Commas: 126/125, 176/175, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 604: / Line 622: @@
 Badness: 0.0295&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Sensi temperament-Sensus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Sensi temperament-Sensus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h3&gt;
   Commas: 91/90, 126/125, 169/168, 352/351&lt;br /&gt;
 &lt;br /&gt;
@@ Line 613: / Line 631: @@
 Badness: 0.0208&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Valentine temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Valentine temperament&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Valentine temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Valentine temperament&lt;/h1&gt;
   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 &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;lattice of 7-limit tetrads&lt;/a&gt;. Valentine can also be described as the 31&amp;amp;46 temperament, and &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt;, &lt;a class="wiki_link" href="/108edo"&gt;108edo&lt;/a&gt; or &lt;a class="wiki_link" href="/185edo"&gt;185edo&lt;/a&gt; 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 &amp;lt;&amp;lt;9 5 -3 7 ... ||, tempering out 121/120 and 441/440; 46et has a valentine generator 3/46 which is only 0.0117 cents sharp of the minimax generator, (11/7)^(1/10).&lt;br /&gt;
 &lt;br /&gt;
@@ Line 638: / Line 656: @@
 Badness: 0.0311&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Valentine temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Valentine temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
   &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 121/120, 126/125, 176/175&lt;br /&gt;
 &lt;br /&gt;
@@ Line 657: / Line 675: @@
 See also: &lt;a class="wiki_link" href="/Chords%20of%20valentine"&gt;Chords of valentine&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Valentine temperament-Dwynwen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Dwynwen&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Valentine temperament-Dwynwen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Dwynwen&lt;/h2&gt;
   Commas: 91/90, 121/120, 126/125, 176/175&lt;br /&gt;
 &lt;br /&gt;
@@ Line 666: / Line 684: @@
 Badness: 0.0235&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Valentine temperament-Lupercalia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Lupercalia&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Valentine temperament-Lupercalia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Lupercalia&lt;/h2&gt;
   Commas: 66/65, 105/104, 121/120, 126/125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 675: / Line 693: @@
 Badness: 0.0213&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Valentine temperament-Valentino"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Valentino&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Valentine temperament-Valentino"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Valentino&lt;/h2&gt;
   Commas: 121/120, 126/125, 176/175, 196/195&lt;br /&gt;
 &lt;br /&gt;
@@ Line 684: / Line 702: @@
 Badness: 0.0207&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Alicorn temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Alicorn temperament&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Alicorn temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Alicorn temperament&lt;/h1&gt;
   Commas: 126/125, 10976/10935&lt;br /&gt;
 &lt;br /&gt;
@@ Line 694: / Line 712: @@
 Badness: 0.0409&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Alicorn temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Alicorn temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
   Commas: 126/125, 540/539, 896/891&lt;br /&gt;
 &lt;br /&gt;
@@ Line 703: / Line 721: @@
 Badness: 0.0392&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Alicorn temperament-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Alicorn temperament-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
   Commas: 126/125, 144/143, 196/195, 676/675&lt;br /&gt;
 &lt;br /&gt;
@@ Line 713: / Line 731: @@
 Badness: 0.0237&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Alicorn temperament-Camahueto"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Camahueto&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Alicorn temperament-Camahueto"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Camahueto&lt;/h2&gt;
   Commas: 126/125, 10976/10935, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 722: / Line 740: @@
 Badness: 0.0659&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc22"&gt;&lt;a name="Alicorn temperament-Camahueto-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc23"&gt;&lt;a name="Alicorn temperament-Camahueto-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h3&gt;
   Commas: 126/125, 196/195, 385/384, 676/675&lt;br /&gt;
 &lt;br /&gt;
@@ Line 732: / Line 750: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Casablanca temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Casablanca temperament&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Casablanca temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Casablanca temperament&lt;/h1&gt;
   Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, &amp;lt;&amp;lt;19 14 4 -22 -47 -30||, or as 31&amp;amp;73. 74/135 or 91/166 supply good tunings for the generator, and 20 and 31 note MOS are available.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 745: / Line 763: @@
 Badness: 0.1012&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Casablanca temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Casablanca temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;11-limit&lt;/h2&gt;
   Commas: 126/125, 385/384, 2420/2401&lt;br /&gt;
 &lt;br /&gt;
@@ Line 754: / Line 772: @@
 Badness: 0.0623&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Casablanca temperament-Marrakesh"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Marrakesh&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Casablanca temperament-Marrakesh"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Marrakesh&lt;/h2&gt;
   Commas: 126/125, 176/175, 14641/14580&lt;br /&gt;
 &lt;br /&gt;
@@ Line 763: / Line 781: @@
 Badness: 0.0405&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc26"&gt;&lt;a name="Casablanca temperament-Marrakesh-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Casablanca temperament-Marrakesh-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;13-limit&lt;/h3&gt;
 /125, 176/175, 196/195, 17303/17280&lt;br /&gt;
 &lt;br /&gt;
@@ Line 772: / Line 790: @@
 Badness: 0.0408&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Casablanca temperament-Marrakesh-Murakuc"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Murakuc&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="Casablanca temperament-Marrakesh-Murakuc"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Murakuc&lt;/h3&gt;
   Commas: 126/125, 144/143, 176/175, 1540/1521&lt;br /&gt;
 &lt;br /&gt;
@@ Line 781: / Line 799: @@
 Badness: 0.0414&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="Nusecond temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Nusecond temperament&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Nusecond temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Nusecond temperament&lt;/h1&gt;
   Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&amp;amp;70, or in terms of its wedgie as &amp;lt;&amp;lt;11 13 17 -5 -4 3||. 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. &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; can be used as a tuning, or &lt;a class="wiki_link" href="/132edo"&gt;132edo&lt;/a&gt; with a val which is the sum of the &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; 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.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 801: / Line 819: @@
 Badness: 0.0504&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Nusecond temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Nusecond temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;11-limit&lt;/h2&gt;
   &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 99/98, 121/120, 126/125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 818: / Line 836: @@
 Badness: 0.0256&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Nusecond temperament-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Nusecond temperament-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;13-limit&lt;/h2&gt;
 Commas: 66/65 99/98 121/120 126/125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 827: / Line 845: @@
 Badness: 0.0233&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="Thuja"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Thuja&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Thuja"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Thuja&lt;/h1&gt;
   Commas: 126/125, 65536/64827&lt;br /&gt;
 &lt;br /&gt;
@@ Line 837: / Line 855: @@
 Badness: 0.0884&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Thuja-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Thuja-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;11-limit&lt;/h2&gt;
   Commas: 126/125, 176/175, 1344/1331&lt;br /&gt;
 &lt;br /&gt;
@@ Line 846: / Line 864: @@
 Badness: 0.0331&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Thuja-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Thuja-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;13-limit&lt;/h2&gt;
   Commas: 126/125, 144/143, 176/175, 364/363&lt;br /&gt;
 &lt;br /&gt;
@@ Line 855: / Line 873: @@
 Badness: 0.0228&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="Bisemidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Bisemidim&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Bisemidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Bisemidim&lt;/h1&gt;
 Commas: 126/125, 118098/117649&lt;br /&gt;
 &lt;br /&gt;
@@ Line 865: / Line 883: @@
 Badness: 0.0978&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Bisemidim-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Bisemidim-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;11-limit&lt;/h2&gt;
 Commas: 126/125, 540/539, 1344/1331&lt;br /&gt;
 &lt;br /&gt;
@@ Line 874: / Line 892: @@
 Badness: 0.0412&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Bisemidim-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Bisemidim-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;13-limit&lt;/h2&gt;
 Commas: 126/125, 144/143, 196/195, 364/363&lt;br /&gt;
 &lt;br /&gt;
@@ Line 883: / Line 901: @@
 Badness: 0.0239&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="Kumonga"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;Kumonga&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc38"&gt;&lt;a name="Kumonga"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Kumonga&lt;/h1&gt;
 Commas: 126/125, 12288/12005&lt;br /&gt;
 &lt;br /&gt;
@@ Line 893: / Line 911: @@
 Badness: 0.0875&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Kumonga-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Kumonga-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;11-limit&lt;/h2&gt;
 Commas: 126/125, 176/175, 864/847&lt;br /&gt;
 &lt;br /&gt;
@@ Line 902: / Line 920: @@
 Badness: 0.0433&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Kumonga-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Kumonga-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;13-limit&lt;/h2&gt;
 Commas: 78/77, 126/125, 144/143, 176/175&lt;br /&gt;
 &lt;br /&gt;

Starling temperaments: Difference between revisions

Revision as of 23:10, 27 April 2012

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search