Cataharry temperaments: Difference between revisions

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**Imported revision 541032676 - Original comment: **
 
 
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<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 is a collection of rank-2 temperaments tempering out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-02-15 16:01:40 UTC</tt>.<br>
* [[Godzilla]] (+49/48 or 81/80) → [[Meantone family #Godzilla|Meantone family]]
: The original revision id was <tt>541032676</tt>.<br>
* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
: The revision comment was: <tt></tt><br>
* ''[[Unicorn]]'' (+126/125) → [[Unicorn family #Septimal unicorn|Unicorn family]]
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]
<h4>Original Wikitext content:</h4>
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
<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">Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&gt; = 19683/19600.
* ''[[Buzzard]]'' (+1728/1715) → [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
* [[Harry]] (+2401/2400) → [[Breedsmic temperaments #Harry|Breedsmic temperaments]]
* [[Hamity]] (+2430/2401) → [[Amity family #Hamity|Amity family]]
* ''[[Subpental]]'' (+3136/3125) → [[Hemimean clan #Subpental|Hemimean clan]]
* ''[[Hemischis]]'' (+6144/6125) → [[Porwell temperaments #Hemischis|Porwell temperaments]]
* ''[[Mirkat]]'' (+16875/16807) → [[Mirkwai clan #Mirkat|Mirkwai clan]]
* ''[[Hours]]'' (+33075/32768) → [[Compton family #Hours|Compton family]]
* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
* ''[[Hemipental]]'' (+589824/588245) → [[Pental family #Hemipental|Pental family]]


=Swetneus=
== Swetneus ==
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.


Commas: 19683/19600, 50421/50000
[[Subgroup]]: 2.3.5.7


POTE generator: ~49/45 = 144.956
[[Comma list]]: 19683/19600, 50421/50000


Map: [|1 4 8 8&gt;, |0 -20 -47 -43&gt;]
{{Mapping|legend=1| 1 4 8 8 | 0 -20 -47 -43 }}
Wedgie: &lt;&lt;20 47 43 28 12 -32||
EDOs: 58, 91, 149, 505d, 654bd, 803bd
Badness: 0.1332


==11-limit==
Commas: 441/440, 3388/3375, 19683/19600


POTE generator: ~49/45 = 144.941
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 144.956


Map: [|1 4 8 8 13&gt;, |0 -20 -47 -43 -79&gt;]
{{Optimal ET sequence|legend=1| 58, 91, 149, 505d, 654bd, 803bd }}
EDOs: 58, 149, 207, 356e, 563cde, 919bcde
Badness: 0.0552


==13-limit==
[[Badness]]: 0.133168
Commas: 351/350, 441/440, 676/675, 847/845


POTE generator: ~49/45 = 144.939
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [|1 4 8 8 13 13&gt;, |0 -20 -47 -43 -79 -77&gt;]
Comma list: 441/440, 3388/3375, 19683/19600
EDOs: 58, 149, 207, 356e, 563cde, 919bcdef
 
Badness: 0.0289
Mapping: {{mapping| 1 4 8 8 13 | 0 -20 -47 -43 -79 }}
</pre></div>
 
<h4>Original HTML content:</h4>
Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941
<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 temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&amp;gt; = 19683/19600.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcde }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Swetneus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Swetneus&lt;/h1&gt;
 
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.&lt;br /&gt;
Badness: 0.055163
&lt;br /&gt;
 
Commas: 19683/19600, 50421/50000&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
POTE generator: ~49/45 = 144.956&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 351/350, 441/440, 676/675, 847/845
Map: [|1 4 8 8&amp;gt;, |0 -20 -47 -43&amp;gt;]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;20 47 43 28 12 -32||&lt;br /&gt;
Mapping: {{mapping| 1 4 8 8 13 13 | 0 -20 -47 -43 -79 -77 }}
EDOs: 58, 91, 149, 505d, 654bd, 803bd&lt;br /&gt;
 
Badness: 0.1332&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Swetneus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=1| 58, 149, 207, 356e, 563cde, 919bcdef }}
Commas: 441/440, 3388/3375, 19683/19600&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.028876
POTE generator: ~49/45 = 144.941&lt;br /&gt;
 
&lt;br /&gt;
== Majvamoid ==
Map: [|1 4 8 8 13&amp;gt;, |0 -20 -47 -43 -79&amp;gt;]&lt;br /&gt;
The ''majvamoid'' temperament (149 &amp; 183) is an extension of the [[Subgroup temperaments #No-sevens subgroup|majvam]] temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.
EDOs: 58, 149, 207, 356e, 563cde, 919bcde&lt;br /&gt;
 
Badness: 0.0552&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Swetneus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
[[Comma list]]: 19683/19600, 29360128/29296875
Commas: 351/350, 441/440, 676/675, 847/845&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 10 5 38 | 0 -22 -7 -92 }}
POTE generator: ~49/45 = 144.939&lt;br /&gt;
 
&lt;br /&gt;
 
Map: [|1 4 8 8 13 13&amp;gt;, |0 -20 -47 -43 -79 -77&amp;gt;]&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 459.031
EDOs: 58, 149, 207, 356e, 563cde, 919bcdef&lt;br /&gt;
 
Badness: 0.0289&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Optimal ET sequence|legend=1| 34d, 115d, 149, 183, 332, 515, 847, 1362bc }}
 
[[Badness]]: 0.207280
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 5632/5625, 19683/19600
 
Mapping: {{mapping| 1 10 5 38 31 | 0 -22 -7 -92 -72 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027
 
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332e, 515e, 698e }}
 
Badness: 0.065874
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 676/675, 1573/1568, 4225/4224
 
Mapping: {{mapping| 1 10 5 38 31 19 | 0 -22 -7 -92 -72 -40 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028
 
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef }}
 
Badness: 0.034696
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224
 
Mapping: {{mapping| 1 10 5 38 31 19 6 | 0 -22 -7 -92 -72 -40 -5 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027
 
{{Optimal ET sequence|legend=1| 34d, 149, 183, 332ef, 515ef, 698ef }}
 
Badness: 0.023302
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Cataharry| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:40, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 temperaments tempering out the cataharry comma, [-4 9 -2 -2⟩ = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:

Swetneus

The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 50421/50000

Mapping: [⟨1 4 8 8], ⟨0 -20 -47 -43]]


Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.956

Optimal ET sequence: 58, 91, 149, 505d, 654bd, 803bd

Badness: 0.133168

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3388/3375, 19683/19600

Mapping: [⟨1 4 8 8 13], ⟨0 -20 -47 -43 -79]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.941

Optimal ET sequence: 58, 149, 207, 356e, 563cde, 919bcde

Badness: 0.055163

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 676/675, 847/845

Mapping: [⟨1 4 8 8 13 13], ⟨0 -20 -47 -43 -79 -77]]

Optimal tuning (POTE): ~2 = 1\1, ~49/45 = 144.939

Optimal ET sequence: 58, 149, 207, 356e, 563cde, 919bcdef

Badness: 0.028876

Majvamoid

The majvamoid temperament (149 & 183) is an extension of the majvam temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 29360128/29296875

Mapping: [⟨1 10 5 38], ⟨0 -22 -7 -92]]


Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.031

Optimal ET sequence: 34d, 115d, 149, 183, 332, 515, 847, 1362bc

Badness: 0.207280

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 19683/19600

Mapping: [⟨1 10 5 38 31], ⟨0 -22 -7 -92 -72]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027

Optimal ET sequence: 34d, 149, 183, 332e, 515e, 698e

Badness: 0.065874

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 676/675, 1573/1568, 4225/4224

Mapping: [⟨1 10 5 38 31 19], ⟨0 -22 -7 -92 -72 -40]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.028

Optimal ET sequence: 34d, 149, 183, 332ef, 515ef

Badness: 0.034696

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224

Mapping: [⟨1 10 5 38 31 19 6], ⟨0 -22 -7 -92 -72 -40 -5]]

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 459.027

Optimal ET sequence: 34d, 149, 183, 332ef, 515ef, 698ef

Badness: 0.023302

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