Starling temperaments: Difference between revisions

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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-06-~~23 17~~:42:08 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-29 13:08:27 UTC</tt>.<br>

: The original revision id was <tt>~~238467149~~</tt>.<br>

: The original revision id was <tt>239348455</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>

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">~~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 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.

<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]

==Myna temperament==

=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 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.

Line 24:

Line 27:

Badness: 0.0270

===11-limit===

==11-limit==

Commas: 126/125, 176/175, 243/242

Line 33:

Line 36:

Badness: 0.0168

===13-limit===

==13-limit==

Commas: 126/125, 144/143, 176/175, 196/195

Line 44:

Line 47:

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

==Sensi temperament==

=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.

Line 66:

Line 69:

Badness: 0.0256

===Sensor===

==Sensor==

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

Line 75:

Line 78:

Badness: 0.0379

====13-limit====

===13-limit===

Commas: 91/90, 126/125, 169/168, 385/384

Line 84:

Line 87:

Badness: 0.0256

===Sensis===

==Sensis==

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

Line 93:

Line 96:

Badness: 0.0287

====13-limit====

===13-limit===

Commas: 56/55, 78/77, 91/90, 100/99

Line 102:

Line 105:

Badness: 0.0200

===Sensus===

==Sensus==

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

Line 111:

Line 114:

Badness: 0.0295

====13-limit====

===13-limit===

Commas: 91/90, 126/125, 169/168, 352/351

Line 120:

Line 123:

Badness: 0.0208

==Valentine temperament==

=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).

Line 145:

Line 148:

Badness: 0.0311

===11-limit===

==11-limit==

[[Comma|Commas]]: 121/120, 126/125, 176/175

Line 162:

Line 165:

Badness: 0.0167

===Dynwen===

==Dynwen==

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

Line 171:

Line 174:

Badness: 0.0235

===Lupercalia===

==Lupercalia==

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

Line 180:

Line 183:

Badness: 0.0213

===Valentino===

==Valentino==

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

Line 189:

Line 192:

Badness: 0.0207

==Casablanca temperament==

=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.

Line 202:

Line 205:

Badness: 0.1012

===11-limit===

==11-limit==

Commas: 126/125, 385/384, 2420/2401

Line 209:

Line 212:

Badness: 0.0623

==Nusecond temperament==

=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.

Line 229:

Line 232:

Badness: 0.0504

===11-limit===

==11-limit==

[[Comma|Commas]]: 99/98, 121/120, 126/125

Line 246:

Line 249:

Badness: 0.0256</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"><html><head><title>Starling temperaments</title></head><body>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 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 />

<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"><html><head><title>Starling temperaments</title></head><body><a href="#Starling comma">Starling comma</a> | <a href="#Myna temperament">Myna temperament</a> | <a href="#Sensi temperament">Sensi temperament</a> | <a href="#Valentine temperament">Valentine temperament</a> | <a href="#Casablanca temperament">Casablanca temperament</a> | <a href="#Nusecond temperament">Nusecond temperament</a>

<br />

<h1 id="toc0"><a name="Starling comma"></a>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 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 />

<h2 id="~~toc0~~"><a name="x-Myna temperament"></a>Myna temperament</h2>

<h1 id="toc1"><a name="Myna temperament"></a>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 />

Line 264:

Line 270:

Badness: 0.0270<br />

<br />

<h3 id="~~toc1~~"><a name="x-Myna temperament-11-limit"></a>11-limit</h3>

<h2 id="toc2"><a name="Myna temperament-11-limit"></a>11-limit</h2>

Commas: 126/125, 176/175, 243/242<br />

<br />

Line 273:

Line 279:

Badness: 0.0168<br />

<br />

<h3 id="~~toc2~~"><a name="x-Myna temperament-13-limit"></a>13-limit</h3>

<h2 id="toc3"><a name="Myna temperament-13-limit"></a>13-limit</h2>

Commas: 126/125, 144/143, 176/175, 196/195<br />

<br />

Line 284:

Line 290:

<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 />

<h2 id="~~toc3~~"><a name="x-Sensi temperament"></a>Sensi temperament</h2>

<h1 id="toc4"><a name="Sensi temperament"></a>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 />

Line 306:

Line 312:

Badness: 0.0256<br />

<br />

<h3 id="~~toc4~~"><a name="x-Sensi temperament-Sensor"></a>Sensor</h3>

<h2 id="toc5"><a name="Sensi temperament-Sensor"></a>Sensor</h2>

Commas: 126/125, 245/243, 385/384<br />

<br />

Line 315:

Line 321:

Badness: 0.0379<br />

<br />

<h4 id="~~toc5~~"><a name="x-Sensi temperament-Sensor-13-limit"></a>13-limit</h4>

<h3 id="toc6"><a name="Sensi temperament-Sensor-13-limit"></a>13-limit</h3>

Commas: 91/90, 126/125, 169/168, 385/384<br />

<br />

Line 324:

Line 330:

Badness: 0.0256<br />

<br />

<h3 id="~~toc6~~"><a name="x-Sensi temperament-Sensis"></a>Sensis</h3>

<h2 id="toc7"><a name="Sensi temperament-Sensis"></a>Sensis</h2>

Commas: 56/55, 100/99, 245/243<br />

<br />

Line 333:

Line 339:

Badness: 0.0287<br />

<br />

<h4 id="~~toc7~~"><a name="x-Sensi temperament-Sensis-13-limit"></a>13-limit</h4>

<h3 id="toc8"><a name="Sensi temperament-Sensis-13-limit"></a>13-limit</h3>

Commas: 56/55, 78/77, 91/90, 100/99<br />

<br />

Line 342:

Line 348:

Badness: 0.0200<br />

<br />

<h3 id="~~toc8~~"><a name="x-Sensi temperament-Sensus"></a>Sensus</h3>

<h2 id="toc9"><a name="Sensi temperament-Sensus"></a>Sensus</h2>

Commas: 126/125, 176/175, 245/243<br />

<br />

Line 351:

Line 357:

Badness: 0.0295<br />

<br />

<h4 id="~~toc9~~"><a name="x-Sensi temperament-Sensus-13-limit"></a>13-limit</h4>

<h3 id="toc10"><a name="Sensi temperament-Sensus-13-limit"></a>13-limit</h3>

Commas: 91/90, 126/125, 169/168, 352/351<br />

<br />

Line 360:

Line 366:

Badness: 0.0208<br />

<br />

<h2 id="~~toc10~~"><a name="x-Valentine temperament"></a>Valentine temperament</h2>

<h1 id="toc11"><a name="Valentine temperament"></a>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 />

Line 385:

Line 391:

Badness: 0.0311<br />

<br />

<h3 id="~~toc11~~"><a name="x-Valentine temperament-11-limit"></a>11-limit</h3>

<h2 id="toc12"><a name="Valentine temperament-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br />

<br />

Line 402:

Line 408:

Badness: 0.0167<br />

<br />

<h3 id="~~toc12~~"><a name="x-Valentine temperament-Dynwen"></a>Dynwen</h3>

<h2 id="toc13"><a name="Valentine temperament-Dynwen"></a>Dynwen</h2>

Commas: 91/90, 121/120, 126/125, 176/175<br />

<br />

Line 411:

Line 417:

Badness: 0.0235<br />

<br />

<h3 id="~~toc13~~"><a name="x-Valentine temperament-Lupercalia"></a>Lupercalia</h3>

<h2 id="toc14"><a name="Valentine temperament-Lupercalia"></a>Lupercalia</h2>

Commas: 66/65, 105/104, 121/120, 126/125<br />

<br />

Line 420:

Line 426:

Badness: 0.0213<br />

<br />

<h3 id="~~toc14~~"><a name="x-Valentine temperament-Valentino"></a>Valentino</h3>

<h2 id="toc15"><a name="Valentine temperament-Valentino"></a>Valentino</h2>

Commas: 121/120, 126/125, 176/175, 196/195<br />

<br />

Line 429:

Line 435:

Badness: 0.0207<br />

<br />

<h2 id="~~toc15~~"><a name="x-Casablanca temperament"></a>Casablanca temperament</h2>

<h1 id="toc16"><a name="Casablanca temperament"></a>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 />

Line 442:

Line 448:

Badness: 0.1012<br />

<br />

<h3 id="~~toc16~~"><a name="x-Casablanca temperament-11-limit"></a>11-limit</h3>

<h2 id="toc17"><a name="Casablanca temperament-11-limit"></a>11-limit</h2>

Commas: 126/125, 385/384, 2420/2401<br />

<br />

Line 449:

Line 455:

Badness: 0.0623<br />

<br />

<h2 id="~~toc17~~"><a name="x-Nusecond temperament"></a>Nusecond temperament</h2>

<h1 id="toc18"><a name="Nusecond temperament"></a>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 />

Line 469:

Line 475:

Badness: 0.0504<br />

<br />

<h3 id="~~toc18~~"><a name="x-Nusecond temperament-11-limit"></a>11-limit</h3>

<h2 id="toc19"><a name="Nusecond temperament-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 99/98, 121/120, 126/125<br />

<br />

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-06-23 17:42:08 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-29 13:08:27 UTC</tt>.<br>
-: The original revision id was <tt>238467149</tt>.<br>
+: The original revision id was <tt>239348455</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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 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.
+<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
-==Myna temperament==
+=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 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&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 [[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.
@@ Line 24: / Line 27: @@
 Badness: 0.0270
-===11-limit===
+==11-limit==
 Commas: 126/125, 176/175, 243/242
@@ Line 33: / Line 36: @@
 Badness: 0.0168
-===13-limit===
+==13-limit==
 Commas: 126/125, 144/143, 176/175, 196/195
@@ Line 44: / Line 47: @@
 [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3|Myna Music]] by [[Igliashon Jones]]
-==Sensi temperament==
+=Sensi temperament=
 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. [[46edo]] is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available.
@@ Line 66: / Line 69: @@
 Badness: 0.0256
-===Sensor===
+==Sensor==
 Commas: 126/125, 245/243, 385/384
@@ Line 75: / Line 78: @@
 Badness: 0.0379
-====13-limit====
+===13-limit===
 Commas: 91/90, 126/125, 169/168, 385/384
@@ Line 84: / Line 87: @@
 Badness: 0.0256
-===Sensis===
+==Sensis==
 Commas: 56/55, 100/99, 245/243
@@ Line 93: / Line 96: @@
 Badness: 0.0287
-====13-limit====
+===13-limit===
 Commas: 56/55, 78/77, 91/90, 100/99
@@ Line 102: / Line 105: @@
 Badness: 0.0200
-===Sensus===
+==Sensus==
 Commas: 126/125, 176/175, 245/243
@@ Line 111: / Line 114: @@
 Badness: 0.0295
-====13-limit====
+===13-limit===
 Commas: 91/90, 126/125, 169/168, 352/351
@@ Line 120: / Line 123: @@
 Badness: 0.0208
-==Valentine temperament==
+=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&amp;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 &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).
@@ Line 145: / Line 148: @@
 Badness: 0.0311
-===11-limit===
+==11-limit==
 [[Comma|Commas]]: 121/120, 126/125, 176/175
@@ Line 162: / Line 165: @@
 Badness: 0.0167
-===Dynwen===
+==Dynwen==
 Commas: 91/90, 121/120, 126/125, 176/175
@@ Line 171: / Line 174: @@
 Badness: 0.0235
-===Lupercalia===
+==Lupercalia==
 Commas: 66/65, 105/104, 121/120, 126/125
@@ Line 180: / Line 183: @@
 Badness: 0.0213
-===Valentino===
+==Valentino==
 Commas: 121/120, 126/125, 176/175, 196/195
@@ Line 189: / Line 192: @@
 Badness: 0.0207
-==Casablanca temperament==
+=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, &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.
@@ Line 202: / Line 205: @@
 Badness: 0.1012
-===11-limit===
+==11-limit==
 Commas: 126/125, 385/384, 2420/2401
@@ Line 209: / Line 212: @@
 Badness: 0.0623
-==Nusecond temperament==
+=Nusecond temperament=
 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. [[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.
@@ Line 229: / Line 232: @@
 Badness: 0.0504
-===11-limit===
+==11-limit==
 [[Comma|Commas]]: 99/98, 121/120, 126/125
@@ Line 246: / Line 249: @@
 Badness: 0.0256</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;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 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;
+<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:40:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;a href="#Starling comma"&gt;Starling comma&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt; | &lt;a href="#Myna temperament"&gt;Myna temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt; | &lt;a href="#Sensi temperament"&gt;Sensi temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Valentine temperament"&gt;Valentine temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Casablanca temperament"&gt;Casablanca temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Nusecond temperament"&gt;Nusecond temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;
+&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;br /&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 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;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Myna temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Myna temperament&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Myna temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Myna temperament&lt;/h1&gt;
 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;amp;31 temperament, or in terms of its wedgie &amp;lt;&amp;lt;10 9 7 -9 -17 -9||. It has 6/5 as a generator, and &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; can be used as a tuning, with &lt;a class="wiki_link" href="/89edo"&gt;89edo&lt;/a&gt; being a better one, and fans of round amounts in cents may like &lt;a class="wiki_link" href="/120edo"&gt;120edo&lt;/a&gt;. 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.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 264: / Line 270: @@
 Badness: 0.0270&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Myna temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Myna temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 Commas: 126/125, 176/175, 243/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 273: / Line 279: @@
 Badness: 0.0168&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Myna temperament-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Myna temperament-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
 Commas: 126/125, 144/143, 176/175, 196/195&lt;br /&gt;
 &lt;br /&gt;
@@ Line 284: / Line 290: @@
 &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:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Sensi temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Sensi temperament&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Sensi temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&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 306: / Line 312: @@
 Badness: 0.0256&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Sensi temperament-Sensor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Sensor&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Sensi temperament-Sensor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Sensor&lt;/h2&gt;
 Commas: 126/125, 245/243, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 315: / Line 321: @@
 Badness: 0.0379&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc5"&gt;&lt;a name="x-Sensi temperament-Sensor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h4&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Sensi temperament-Sensor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h3&gt;
 Commas: 91/90, 126/125, 169/168, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 324: / Line 330: @@
 Badness: 0.0256&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Sensi temperament-Sensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sensis&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Sensi temperament-Sensis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Sensis&lt;/h2&gt;
 Commas: 56/55, 100/99, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 333: / Line 339: @@
 Badness: 0.0287&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc7"&gt;&lt;a name="x-Sensi temperament-Sensis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h4&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Sensi temperament-Sensis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
 Commas: 56/55, 78/77, 91/90, 100/99&lt;br /&gt;
 &lt;br /&gt;
@@ Line 342: / Line 348: @@
 Badness: 0.0200&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="x-Sensi temperament-Sensus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Sensus&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Sensi temperament-Sensus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Sensus&lt;/h2&gt;
 Commas: 126/125, 176/175, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 351: / Line 357: @@
 Badness: 0.0295&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc9"&gt;&lt;a name="x-Sensi temperament-Sensus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h4&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Sensi temperament-Sensus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h3&gt;
 Commas: 91/90, 126/125, 169/168, 352/351&lt;br /&gt;
 &lt;br /&gt;
@@ Line 360: / Line 366: @@
 Badness: 0.0208&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Valentine temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Valentine temperament&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Valentine temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&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 385: / Line 391: @@
 Badness: 0.0311&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x-Valentine temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Valentine temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&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 402: / Line 408: @@
 Badness: 0.0167&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="x-Valentine temperament-Dynwen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Dynwen&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Valentine temperament-Dynwen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Dynwen&lt;/h2&gt;
 Commas: 91/90, 121/120, 126/125, 176/175&lt;br /&gt;
 &lt;br /&gt;
@@ Line 411: / Line 417: @@
 Badness: 0.0235&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="x-Valentine temperament-Lupercalia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Lupercalia&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Valentine temperament-Lupercalia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Lupercalia&lt;/h2&gt;
 Commas: 66/65, 105/104, 121/120, 126/125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 420: / Line 426: @@
 Badness: 0.0213&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="x-Valentine temperament-Valentino"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Valentino&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Valentine temperament-Valentino"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Valentino&lt;/h2&gt;
 Commas: 121/120, 126/125, 176/175, 196/195&lt;br /&gt;
 &lt;br /&gt;
@@ Line 429: / Line 435: @@
 Badness: 0.0207&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="x-Casablanca temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Casablanca temperament&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Casablanca temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&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 442: / Line 448: @@
 Badness: 0.1012&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x-Casablanca temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Casablanca temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
 Commas: 126/125, 385/384, 2420/2401&lt;br /&gt;
 &lt;br /&gt;
@@ Line 449: / Line 455: @@
 Badness: 0.0623&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="x-Nusecond temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Nusecond temperament&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Nusecond temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&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 469: / Line 475: @@
 Badness: 0.0504&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="x-Nusecond temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Nusecond temperament-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&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;