Cataharry family: Difference between revisions

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~~<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>2012-02-18 04:05:44 UTC</tt>.<br>~~

~~: The original revision id was <tt>302948328</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">[[toc]]

The cataharry family of rank ~~three temperaments~~ tempers out the cataharry comma, 19683/19600.

The '''cataharry family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the [[cataharry comma]], 19683/19600.

~~Comma~~: ~~19683/19600~~

== Cataharry ==

[[Subgroup]]: 2.3.5.7

~~7 and 9 limit minimax~~

[[Comma list]]: [[19683/19600]]

[~~|1 0 0 0>, |4/9 0 2/9 2/9>,~~

~~|0 0 1 0>, |0 0 0 1>~~]

~~Eigenmonzos~~: ~~2, 8~~/~~7, 5/4~~

~~Map: [<~~1 0 0 -2|~~, <~~0 2 0 9|~~, <~~0 0 1 -1|]

~~Generators~~: 2, 140/81, 5

~~Edos~~: 19, 24, 48, 53~~, 58~~, 72, 130, 202, ~~457~~, 587~~, 659, 717~~

: mapping generators: ~2, ~140/81, ~5

[[Minimax tuning]]:

* [[7-odd-limit|7-]] and [[9-odd-limit]]:

: {{monzo list| 1 0 0 0 | 4/9 0 2/9 2/9 | 0 0 1 0 | 0 0 0 1 }}

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7

{{Optimal ET sequence|legend=1| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}

[[Badness]]: 0.301 × 10<sup>-3</sup>

[[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7

== Albus ==

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 540/539, 8019/8000

: mapping generators: ~2, ~140/81, ~5

[[Minimax tuning]]:

* [[11-odd-limit]]

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo| 5 0 7/2 -2 -3/2 }}, {{monzo| 5 0 5/2 -1 -3/2 }}, {{monzo| 5 0 5/2 -2 -1/2 }}]

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5

{{Optimal ET sequence|legend=1| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}

[[Badness]]: 0.621 × 10<sup>-3</sup>

==~~11 limit children~~==

=== Madagascar ===

Subgroup: 2.3.5.7.11.13

~~==Albus==~~

Comma list: 351/350, 540/539, 676/675

~~Commas~~: 540/539, ~~8019~~/~~8000~~

~~Minimax tuning~~

Mapping: {{mapping| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}

[|1 0 0 ~~0 0>, |8/3 0 4/3~~ -2/3 -~~2/3>,~~

|5 0 ~~7/2 -~~2 -3~~/2>,~~ |5 0 ~~5/2~~ -1 -3~~/2>,~~

~~|5 0 5/2 -2 -~~1~~/2>]~~

~~Eigenmonzos: 2, 11/10, 7/5~~

~~Map~~: [~~<1 0~~ 0 -2 6|~~, <~~0 2 0 9 -~~12|, <0 0~~ 1 -1 3|]

[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]

~~Generators: 2, 140/81, 5~~

~~Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640~~

~~Badness: 0.000621~~

==~~=Madagascar===~~

Lattice basis:

~~Commas~~: ~~351~~/~~350~~, ~~540~~/~~539, 676/675~~

: 15/13 length = 0.3019, 26/25 length = 0.9477

: Angle (15/13, 26/25) = 81.6476

13 and 15 limit ~~minimax~~

Minimax tuning:

[|1 0 0 0 0 0~~>~~, |8/3 0 4/3 -2/3 -2/3 0~~>~~,

* 13- and 15-odd-limit

|5 0 7/2 -2 -3/2 0~~>~~, |5 0 5/2 -1 -3/2 0~~>~~,

: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo| 5 0 7/2 -2 -3/2 0 }}, {{monzo| 5 0 5/2 -1 -3/2 0 }}, {{monzo| 5 0 5/2 -2 -1/2 0 }}, {{monzo| 8 0 11/2 -3 -5/2 0 }}]

|5 0 5/2 -2 -1/2 0~~>~~, |8 0 11/2 -3 -5/2 0~~>~~]

: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5

~~Eigenmonzos~~: 2, 11~~/10, 7~~/5

~~Lattice basis: 15/13 0.3019 26/25 0.9477~~

{{Optimal ET sequence|legend=1| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}

~~Angle(15/13, 26/25)~~ = ~~81.6476~~

~~Map to lattice: [<0 -2 -3 -6 3 -6~~|, ~~<0 0 -1 1 -3 -1|]~~

~~Map~~: ~~[<1~~ 0 ~~0 -2 6 -1|, <0 2 0 9~~ -12 3~~|, <0 0 1 -1 3 1|]~~

Badness: 0.560 × 10<sup>-3</sup>

~~Generators: 2, 26~~/~~15, 5~~

~~Edos: 19, 53, 58, 72, 111, 130, 183, 313~~

Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11

~~Badness: 0.000560~~

~~[[Spectrum of a temperament|Spectrum]]~~: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11

Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3

[[madagascar19]]

Scales: [[madagascar19]]

== Snape ==

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 441/440, 19683/19600

{{Optimal ET sequence|legend=1| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}

[[Badness]]: 0.988 × 10<sup>-3</sup>

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 676/675

Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}

{{Optimal ET sequence|legend=1| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}

Badness: 0.786 × 10<sup>-3</sup>

== Hagrid ==

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 243/242, 9801/9800

: mapping generators: ~99/70, ~140/81, ~5

[[Badness]]: 1.116 × 10<sup>-3</sup>

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 364/363

Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}

: mapping generators: ~99/70, ~26/15, ~5

Badness: 0.876 × 10<sup>-3</sup>

== Draco ==

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 176/175, 19683/19600

=~~=Snape==~~

{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}

~~Commas: 19683/19600~~, ~~441/440~~

13-~~limit~~

[[Badness]]: 1.934 × 10<sup>-3</sup>

~~Commas: 351/350, 441/440, 729~~/~~728~~

==~~Hagrid~~==

=== 13-limit ===

~~Commas~~: ~~243/242, 9801/9800~~

Subgroup: 2.3.5.7.11.13

~~13-limit~~

Comma list: 176/175, 351/350, 676/675

~~Commas~~: ~~243~~/~~242~~, 351/350, ~~729~~/~~728~~

~~==Draco==~~

Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}

~~Commas~~: ~~19683/19600, 176/175~~

~~Map: [<~~1 ~~0 0 -2 -6|, <0 2 0 9 9~~|, ~~<0 0 1 -1 1|]~~

{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cdf }}

~~EDOs:~~ 24, 34d, 53, 58, 111, ~~357cd, 468cd~~

~~Badness: 0.001934~~

13-~~limit~~

Badness: 0.999 × 10<sup>-3</sup>

~~Commas: 176/175, 351/350, 676~~/~~675~~

~~Map~~: ~~[<1 0 0 -2 -6 -1|, <0 2 0 9 9 3|, <0 0 1 -1 1 1|~~]

[[Category:Temperament families]]

~~EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf~~

[[Category:Pages with mostly numerical content]]

~~Badness~~: ~~0.000999</pre></div>~~

[[Category:Cataharry family| ]]

~~<h4>Original HTML~~ content~~:</h4>~~

[[Category:Cataharry| ]]

~~<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>Cataharry family</title></head><body><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 2em;"><a href="#x-11 limit children">11 limit children</a></div>

[[Category:Rank 3]]

~~<div style="margin-left: 2em;"><a href="#x-Albus">Albus</a></div>~~

~~<div style="margin-left: 3em;"><a href="#x-Albus-Madagascar">Madagascar</a></div>~~

~~<div style="margin-left: 2em;"><a href="#x-Snape">Snape</a></div>~~

~~<div style="margin-left: 2em;"><a href="#x-Hagrid">Hagrid</a></div>~~

~~<div style="margin-left: 2em;"><a href="#x-Draco">Draco</a></div>~~

~~</div>~~

~~<br />~~

~~The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.<br />~~

~~<br />~~

~~Comma: 19683/19600<br />~~

~~<br />~~

~~7 and 9 limit minimax<br />~~

[|~~1 0 0 0&gt;, |4/9 0 2/9 2/9&gt;, <br />~~

~~|0 0 1 0&gt;, |0 0 0 1&gt;~~]~~<br />~~

~~Eigenmonzos: 2, 8/7, 5/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 0 -2|, &lt;0 2 0 9|, &lt;0 0 1 -1|~~]~~<br />~~

~~Generators: 2, 140/81, 5<br />~~

~~Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7<br />~~

~~<br />~~

~~<h2 id="toc0"><a name="x-11 limit children"></a><~~!-- ~~ws:end:WikiTextHeadingRule:0~~ --~~>11 limit children</h2>~~

~~<br />~~

~~<h2 id="toc1"><a name="x-Albus"></a>Albus</h2>~~

~~Commas: 540/539, 8019/8000<br />~~

~~<br />~~

~~Minimax tuning<br />~~

~~[|1 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3&gt;, <br />~~

~~|5 0 7/2 -2 -3/2&gt;,~~ |~~5 0 5/2 -1 -3/2&gt;, <br />~~

~~|5 0 5/2 -2 -1/2&gt;~~]~~<br />~~

~~Eigenmonzos: 2, 11/10, 7/5<br />~~

~~<br />~~

~~Map: [&lt;1 0 0 -2 6|, &lt;0 2 0 9 -12|, &lt;0 0 1 -1 3|~~]~~<br />~~

~~Generators: 2, 140/81, 5<br />~~

~~Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640<br />~~

~~Badness: 0.000621<br />~~

~~<br />~~

~~<~~!-- ~~ws:start:WikiTextHeadingRule:4:&lt;h3&gt;~~ --~~><h3 id="toc2"><a name="x-Albus-Madagascar"></a>Madagascar</h3>~~

~~Commas: 351/350, 540/539, 676/675<br />~~

~~<br />~~

~~13 and 15 limit minimax<br />~~

~~[|1 0 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3 0&gt;, <br />~~

~~|5 0 7/2 -2 -3/2 0&gt;, |5 0 5/2 -1 -3/2 0&gt;, <br />~~

~~|5 0 5/2 -2 -1/2 0&gt;, |8 0 11/2 -3 -5/2 0&gt;]<br />~~

~~Eigenmonzos: 2, 11/10, 7/5<br />~~

~~<br />~~

~~Lattice basis: 15/13 0.3019 26/25 0.9477<br />~~

~~Angle(15/13, 26/25) = 81.6476<br />~~

~~Map to lattice:~~ [~~&lt;0 -2 -3 -6 3 -6|, &lt;0 0 -1 1 -3 -1|]<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 0 -2 6 -1|, &lt;0 2 0 9 -12 3|, &lt;0 0 1 -1 3 1|]<br />~~

~~Generators: 2, 26/15, 5<br />~~

~~Edos: 19, 53, 58, 72, 111, 130, 183, 313<br />~~

~~Badness: 0.000560<br />~~

<a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11<br />

~~<br />~~

~~Projection pairs~~: 3 ~~676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3<br />~~

~~<br />~~

~~<a class="wiki_link" href="/madagascar19">madagascar19</a><br />~~

~~<br />~~

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

~~Commas: 19683/19600, 441/440<br />~~

~~<br />~~

~~13-limit<br />~~

~~Commas: 351/350, 441/440, 729/728<br />~~

~~<br />~~

~~<h2 id="toc4"><a name="x-Hagrid"></a>Hagrid</h2>~~

~~Commas: 243/242, 9801/9800<br />~~

~~<br />~~

~~13-limit<br />~~

~~Commas: 243/242, 351/350, 729/728<br />~~

~~<br />~~

~~<h2 id="toc5"><a name="x-Draco"></a>Draco</h2>~~

~~Commas: 19683/19600, 176/175<br />~~

~~<br />~~

~~Map: [&lt;1 0 0 -2 -6|, &lt;0 2 0 9 9|, &lt;0 0 1 -1 1|~~]~~<br />~~

~~EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd<br />~~

~~Badness: 0.001934<br />~~

~~<br />~~

~~13-limit<br />~~

~~Commas: 176/175, 351/350, 676/675<br />~~

~~<br />~~

~~Map: [&lt;1 0 0 -2 -6 -1|, &lt;0 2 0 9 9 3|, &lt;0 0 1 -1 1 1|~~]~~<br />~~

~~EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf<br />~~

~~Badness: 0.000999</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Technical data page}}
-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>2012-02-18 04:05:44 UTC</tt>.<br>
-: The original revision id was <tt>302948328</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">[[toc]]
-The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.
+The '''cataharry family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the [[cataharry comma]], 19683/19600.
-Comma: 19683/19600
+== Cataharry ==
+[[Subgroup]]: 2.3.5.7
-and 9 limit minimax
+[[Comma list]]: [[19683/19600]]
-[|1 0 0 0&gt;, |4/9 0 2/9 2/9&gt;,
-|0 0 1 0&gt;, |0 0 0 1&gt;]
-Eigenmonzos: 2, 8/7, 5/4
-Map: [&lt;1 0 0 -2|, &lt;0 2 0 9|, &lt;0 0 1 -1|]
+{{Mapping|legend=1| 1 0 0 -2 | 0 2 0 9 | 0 0 1 -1 }}
-Generators: 2, 140/81, 5
-Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717
+: mapping generators: ~2, ~140/81, ~5
+[[Minimax tuning]]:
+* [[7-odd-limit|7-]] and [[9-odd-limit]]:
+: {{monzo list| 1 0 0 0 | 4/9 0 2/9 2/9 | 0 0 1 0 | 0 0 0 1 }}
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
+{{Optimal ET sequence|legend=1| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}
+[[Badness]]: 0.301 × 10<sup>-3</sup>
 [[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7
+== Albus ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 540/539, 8019/8000
+{{Mapping|legend=1| 1 0 0 -2 6 | 0 2 0 9 -12 | 0 0 1 -1 3 }}
+: mapping generators: ~2, ~140/81, ~5
+[[Minimax tuning]]:
+* [[11-odd-limit]]
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo| 5 0 7/2 -2 -3/2 }}, {{monzo| 5 0 5/2 -1 -3/2 }}, {{monzo| 5 0 5/2 -2 -1/2 }}]
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5
+{{Optimal ET sequence|legend=1| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}
+[[Badness]]: 0.621 × 10<sup>-3</sup>
-==11 limit children==
+=== Madagascar ===
+Subgroup: 2.3.5.7.11.13
-==Albus==
+Comma list: 351/350, 540/539, 676/675
-Commas: 540/539, 8019/8000
-Minimax tuning
+Mapping: {{mapping| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}
-[|1 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3&gt;,
-|5 0 7/2 -2 -3/2&gt;, |5 0 5/2 -1 -3/2&gt;,
-|5 0 5/2 -2 -1/2&gt;]
-Eigenmonzos: 2, 11/10, 7/5
-Map: [&lt;1 0 0 -2 6|, &lt;0 2 0 9 -12|, &lt;0 0 1 -1 3|]
+[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]
-Generators: 2, 140/81, 5
-Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640
-Badness: 0.000621
-===Madagascar===
+Lattice basis:
-Commas: 351/350, 540/539, 676/675
+: 15/13 length = 0.3019, 26/25 length = 0.9477
+: Angle (15/13, 26/25) = 81.6476
-and 15 limit minimax
+Minimax tuning:
-[|1 0 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3 0&gt;,
+* 13- and 15-odd-limit
-|5 0 7/2 -2 -3/2 0&gt;, |5 0 5/2 -1 -3/2 0&gt;,
+: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo| 5 0 7/2 -2 -3/2 0 }}, {{monzo| 5 0 5/2 -1 -3/2 0 }}, {{monzo| 5 0 5/2 -2 -1/2 0 }}, {{monzo| 8 0 11/2 -3 -5/2 0 }}]
-|5 0 5/2 -2 -1/2 0&gt;, |8 0 11/2 -3 -5/2 0&gt;]
+: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5
-Eigenmonzos: 2, 11/10, 7/5
-Lattice basis: 15/13 0.3019 26/25 0.9477
+{{Optimal ET sequence|legend=1| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}
-Angle(15/13, 26/25) = 81.6476
-Map to lattice: [&lt;0 -2 -3 -6 3 -6|, &lt;0 0 -1 1 -3 -1|]
-Map: [&lt;1 0 0 -2 6 -1|, &lt;0 2 0 9 -12 3|, &lt;0 0 1 -1 3 1|]
+Badness: 0.560 × 10<sup>-3</sup>
-Generators: 2, 26/15, 5
-Edos: 19, 53, 58, 72, 111, 130, 183, 313
+Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11
-Badness: 0.000560
-[[Spectrum of a temperament|Spectrum]]: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11
 Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3
-[[madagascar19]]
+Scales: [[madagascar19]]
+== Snape ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 441/440, 19683/19600
+{{Mapping|legend=1| 1 0 0 -2 -7 | 0 2 0 9 22 | 0 0 1 -1 -3 }}
+{{Optimal ET sequence|legend=1| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}
+[[Badness]]: 0.988 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 441/440, 676/675
+Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}
+{{Optimal ET sequence|legend=1| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}
+Badness: 0.786 × 10<sup>-3</sup>
+== Hagrid ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 243/242, 9801/9800
+{{Mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 0 0 1 -1 0 }}
+: mapping generators: ~99/70, ~140/81, ~5
+{{Optimal ET sequence|legend=1| 24, 34d, 48, 58, 72, 130, 202 }}
+[[Badness]]: 1.116 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 351/350, 364/363
+Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}
+: mapping generators: ~99/70, ~26/15, ~5
+{{Optimal ET sequence|legend=1| 24, 34d, 58, 72, 130 }}
+Badness: 0.876 × 10<sup>-3</sup>
+== Draco ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 176/175, 19683/19600
+{{Mapping|legend=1| 1 0 0 -2 -6 | 0 2 0 9 9 | 0 0 1 -1 1 }}
-==Snape==
+{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}
-Commas: 19683/19600, 441/440
--limit
+[[Badness]]: 1.934 × 10<sup>-3</sup>
-Commas: 351/350, 441/440, 729/728
-==Hagrid==
+=== 13-limit ===
-Commas: 243/242, 9801/9800
+Subgroup: 2.3.5.7.11.13
--limit
+Comma list: 176/175, 351/350, 676/675
-Commas: 243/242, 351/350, 729/728
-==Draco==
+Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}
-Commas: 19683/19600, 176/175
-Map: [&lt;1 0 0 -2 -6|, &lt;0 2 0 9 9|, &lt;0 0 1 -1 1|]
+{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cdf }}
-EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd
-Badness: 0.001934
--limit
+Badness: 0.999 × 10<sup>-3</sup>
-Commas: 176/175, 351/350, 676/675
-Map: [&lt;1 0 0 -2 -6 -1|, &lt;0 2 0 9 9 3|, &lt;0 0 1 -1 1 1|]
+[[Category:Temperament families]]
-EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf
+[[Category:Pages with mostly numerical content]]
-Badness: 0.000999</pre></div>
+[[Category:Cataharry family| ]] <!-- main article -->
-<h4>Original HTML content:</h4>
+[[Category:Cataharry| ]] <!-- key article -->
-<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;Cataharry family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-11 limit children"&gt;11 limit children&lt;/a&gt;&lt;/div&gt;
+[[Category:Rank 3]]
-&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Albus"&gt;Albus&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#x-Albus-Madagascar"&gt;Madagascar&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Snape"&gt;Snape&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Hagrid"&gt;Hagrid&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Draco"&gt;Draco&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
-The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.&lt;br /&gt;
-&lt;br /&gt;
-Comma: 19683/19600&lt;br /&gt;
-&lt;br /&gt;
-and 9 limit minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |4/9 0 2/9 2/9&amp;gt;, &lt;br /&gt;
-|0 0 1 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 8/7, 5/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 -2|, &amp;lt;0 2 0 9|, &amp;lt;0 0 1 -1|]&lt;br /&gt;
-Generators: 2, 140/81, 5&lt;br /&gt;
-Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7&lt;br /&gt;
-&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-11 limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11 limit children&lt;/h2&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Albus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Albus&lt;/h2&gt;
-Commas: 540/539, 8019/8000&lt;br /&gt;
-&lt;br /&gt;
-Minimax tuning&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |8/3 0 4/3 -2/3 -2/3&amp;gt;, &lt;br /&gt;
-|5 0 7/2 -2 -3/2&amp;gt;, |5 0 5/2 -1 -3/2&amp;gt;, &lt;br /&gt;
-|5 0 5/2 -2 -1/2&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 11/10, 7/5&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 -2 6|, &amp;lt;0 2 0 9 -12|, &amp;lt;0 0 1 -1 3|]&lt;br /&gt;
-Generators: 2, 140/81, 5&lt;br /&gt;
-Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640&lt;br /&gt;
-Badness: 0.000621&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-Albus-Madagascar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Madagascar&lt;/h3&gt;
- Commas: 351/350, 540/539, 676/675&lt;br /&gt;
-&lt;br /&gt;
-and 15 limit minimax&lt;br /&gt;
-[|1 0 0 0 0 0&amp;gt;, |8/3 0 4/3 -2/3 -2/3 0&amp;gt;, &lt;br /&gt;
-|5 0 7/2 -2 -3/2 0&amp;gt;, |5 0 5/2 -1 -3/2 0&amp;gt;, &lt;br /&gt;
-|5 0 5/2 -2 -1/2 0&amp;gt;, |8 0 11/2 -3 -5/2 0&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 11/10, 7/5&lt;br /&gt;
-&lt;br /&gt;
-Lattice basis: 15/13 0.3019 26/25 0.9477&lt;br /&gt;
-Angle(15/13, 26/25) = 81.6476&lt;br /&gt;
-Map to lattice: [&amp;lt;0 -2 -3 -6 3 -6|, &amp;lt;0 0 -1 1 -3 -1|]&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 -2 6 -1|, &amp;lt;0 2 0 9 -12 3|, &amp;lt;0 0 1 -1 3 1|]&lt;br /&gt;
-Generators: 2, 26/15, 5&lt;br /&gt;
-Edos: 19, 53, 58, 72, 111, 130, 183, 313&lt;br /&gt;
-Badness: 0.000560&lt;br /&gt;
-&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11&lt;br /&gt;
-&lt;br /&gt;
-Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/madagascar19"&gt;madagascar19&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-Snape"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Snape&lt;/h2&gt;
-Commas: 19683/19600, 441/440&lt;br /&gt;
-&lt;br /&gt;
--limit&lt;br /&gt;
-Commas: 351/350, 441/440, 729/728&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="x-Hagrid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hagrid&lt;/h2&gt;
-Commas: 243/242, 9801/9800&lt;br /&gt;
-&lt;br /&gt;
--limit&lt;br /&gt;
-Commas: 243/242, 351/350, 729/728&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="x-Draco"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Draco&lt;/h2&gt;
-Commas: 19683/19600, 176/175&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 -2 -6|, &amp;lt;0 2 0 9 9|, &amp;lt;0 0 1 -1 1|]&lt;br /&gt;
-EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd&lt;br /&gt;
-Badness: 0.001934&lt;br /&gt;
-&lt;br /&gt;
--limit&lt;br /&gt;
-Commas: 176/175, 351/350, 676/675&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 -2 -6 -1|, &amp;lt;0 2 0 9 9 3|, &amp;lt;0 0 1 -1 1 1|]&lt;br /&gt;
-EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf&lt;br /&gt;
-Badness: 0.000999&lt;/body&gt;&lt;/html&gt;</pre></div>