Cataharry temperaments: Difference between revisions

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**Imported revision 541032744 - Original comment: **
Switch to Sintel's badness, WE & CWE tunings. Improve intro to each entry
 
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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 temperament|rank-2]] '''cataharry temperaments''', which [[tempering out|temper out]] the [[cataharry comma]] ({{monzo|legend=1| -4 9 -2 -2 }}, [[ratio]]: 19683/19600). For the family of [[rank-3 temperament]]s, see [[Cataharry family]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-02-15 16:02:29 UTC</tt>.<br>
: The original revision id was <tt>541032744</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|flat]]


Cataharry temperaments temper out the cataharry comma, |-4 9 -2 -2&gt; = 19683/19600.
Discussed elsewhere are:
* ''[[Mite]]'' (+27/25) → [[Bug family #Mite|Bug family]]
* [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]]
* ''[[Immunized]]'' (+64/63) → [[Immunity family #Immunized|Immunity family]]
* ''[[Hemischis]]'' (+6144/6125) → [[Schismatic family #Hemischis|Schismatic family]]
* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Septimal buzzard|Buzzardsmic clan]]
* ''[[Sruti]]'' (+2048/2025) → [[Diaschismic family #Sruti|Diaschismic family]]
* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven|Gamelismic clan]]
* ''[[Weasel]]'' (+50/49) → [[Tetracot family #Weasel|Tetracot family]]
* ''[[Unicorn]]'' (+126/125) → [[Unicorn family #Septimal unicorn|Unicorn family]]
* ''[[Hamity]]'' (+2430/2401) → [[Amity family #Hamity|Amity family]]
* ''[[Tuskaloosa]]'' (+110592/109375) → [[Mabila family #Tuskaloosa|Mabila family]]
* ''[[Hemiquintile]]'' (+589824/588245) → [[Quintile family #Hemiquintile|Quintile family]]
* [[Harry]] (+2401/2400) → [[Gravity family #Harry|Gravity family]]
* ''[[Subpental]]'' (+3136/3125) → [[Hemimean clan #Subpental|Hemimean clan]]
* ''[[Mirkat]]'' (+16875/16807) → [[Canopic clan #Mirkat|Canopic clan]]
* ''[[Hours]]'' (+33075/32768) → [[Compton family #Hours|Compton family]]


=Swetneus=
Considered below is swetneus and majvamoid, in the order of increasing [[badness]].  
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
== Swetneus ==
Swetneus tempers out the [[trimyna comma]] and may be described as the {{nowrap| 58 & 91 }} temperament. It takes its name from the fact that the generator is [[~]][[49/45]], a [[neutral second]] that is a [[swetisma]] away from [[12/11]]. Note that in the data that follow, the generator is its [[octave complement]], ~[[90/49]], so that twenty of them reach the [[interval class]] of [[3/1|3]]. In the [[11-limit]], this generator is equated with not [[11/6]] but [[81/44]].


POTE generator: ~49/45 = 144.956
[[Subgroup]]: 2.3.5.7


Map: [|1 4 8 8&gt;, |0 -20 -47 -43&gt;]
[[Comma list]]: 19683/19600, 50421/50000
Wedgie: &lt;&lt;20 47 43 28 12 -32||
EDOs: 58, 91, 149, 505d, 654bd, 803bd
Badness: 0.1332


==11-limit==
{{Mapping|legend=1| 1 -16 -39 -35 | 0 20 47 43 }}
Commas: 441/440, 3388/3375, 19683/19600
: mapping generators: ~2, ~90/49


POTE generator: ~49/45 = 144.941
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.2604{{c}}, ~90/49 = 1055.2729{{c}}
: [[error map]]: {{val| +0.260 -0.663 +1.357 -1.205 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~90/49 = 1055.0513{{c}}
: error map: {{val| 0.000 -0.928 +1.099 -1.618 }}


Map: [|1 4 8 8 13&gt;, |0 -20 -47 -43 -79&gt;]
{{Optimal ET sequence|legend=1| 33cd, 58, 91, 149 }}
EDOs: 58, 149, 207, 356e, 563cde, 919bcde
Badness: 0.0552


==13-limit==
[[Badness]] (Sintel): 3.37
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 -16 -39 -35 -66 | 0 20 47 43 79 }}
</pre></div>
 
<h4>Original HTML content:</h4>
Optimal tunings:
<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;&lt;!-- ws:start:WikiTextTocRule:6:&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:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Swetneus"&gt;Swetneus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
* WE: ~2 = 1200.1548{{c}}, ~81/44 = 1055.0954{{c}}
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~81/44 = 1055.0631{{c}}
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=0| 58, 149, 207, 356e }}
&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 (Sintel): 1.82
&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 -16 -39 -35 -66 -64 | 0 20 47 43 79 77 }}
EDOs: 58, 91, 149, 505d, 654bd, 803bd&lt;br /&gt;
 
Badness: 0.1332&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1200.1473{{c}}, ~81/44 = 1055.1904{{c}}
&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;
* CWE: ~2 = 1200.0000{{c}}, ~81/44 = 1055.0644{{c}}
Commas: 441/440, 3388/3375, 19683/19600&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 58, 149, 207, 356e }}
POTE generator: ~49/45 = 144.941&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.19
Map: [|1 4 8 8 13&amp;gt;, |0 -20 -47 -43 -79&amp;gt;]&lt;br /&gt;
 
EDOs: 58, 149, 207, 356e, 563cde, 919bcde&lt;br /&gt;
== Majvamoid ==
Badness: 0.0552&lt;br /&gt;
Named by [[Xenllium]] in 2021, majvamoid tempers out the [[quasiorwellisma]] and may be described as the {{nowrap| 149 & 183 }} temperament. It is an [[extension]] of the [[majvam]] temperament.
&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;
[[Subgroup]]: 2.3.5.7
Commas: 351/350, 441/440, 676/675, 847/845&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 19683/19600, 29360128/29296875
POTE generator: ~49/45 = 144.939&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 -12 -2 -54 | 0 22 7 92 }}
Map: [|1 4 8 8 13 13&amp;gt;, |0 -20 -47 -43 -79 -77&amp;gt;]&lt;br /&gt;
: mapping generators: ~2, ~192/125
EDOs: 58, 149, 207, 356e, 563cde, 919bcdef&lt;br /&gt;
 
Badness: 0.0289&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0181{{c}}, ~192/125 = 740.9804{{c}}
: [[error map]]: {{val| +0.018 -0.603 +0.513 +0.395 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~192/125 = 740.9695{{c}}
: error map: {{val| 0.000 -0.627 +0.473 +0.365 }}
 
{{Optimal ET sequence|legend=1| 34d, 115d, 149, 183, 332, 515, 847 }}
 
[[Badness]] (Sintel): 5.25
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 5632/5625, 19683/19600
 
Mapping: {{mapping| 1 -12 -2 -54 -41 | 0 22 7 92 72 }}
 
Optimal tunings:
* WE: ~2 = 1200.0467{{c}}, ~135/88 = 741.0021{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~135/88 = 740.9738{{c}}
 
{{Optimal ET sequence|legend=0| 34d, 115de, 149, 183, 332e, 515e }}
 
Badness (Sintel): 2.18
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 676/675, 1573/1568, 4225/4224
 
Mapping: {{mapping| 1 -12 -2 -54 -41 -21 | 0 22 7 92 72 40 }}
 
Optimal tunings:
* WE: ~2 = 1200.1305{{c}}, ~135/88 = 741.0523{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~135/88 = 740.9735{{c}}
 
{{Optimal ET sequence|legend=0| 34d, 115def, 149, 183, 332ef, 515ef }}
 
Badness (Sintel): 1.43
 
=== 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 -12 -2 -54 -41 -21 1 | 0 22 7 92 72 40 5 }}
 
Optimal tunings:
* WE: ~2 = 1200.0995{{c}}, ~135/88 = 741.0345{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~135/88 = 740.9741{{c}}
 
{{Optimal ET sequence|legend=0| 34d, 115def, 149, 183, 332ef, 515ef }}
 
Badness (Sintel): 1.19
 
[[Category:Cataharry temperaments| ]] <!-- main article -->
[[Category:Temperament collections]]
[[Category:Rank 2]]

Latest revision as of 11:32, 20 July 2026

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 cataharry temperaments, which temper out the cataharry comma (monzo: [-4 9 -2 -2⟩, ratio: 19683/19600). For the family of rank-3 temperaments, see Cataharry family.

Discussed elsewhere are:

Considered below is swetneus and majvamoid, in the order of increasing badness.

Swetneus

Swetneus tempers out the trimyna comma and may be described as the 58 & 91 temperament. It takes its name from the fact that the generator is ~49/45, a neutral second that is a swetisma away from 12/11. Note that in the data that follow, the generator is its octave complement, ~90/49, so that twenty of them reach the interval class of 3. In the 11-limit, this generator is equated with not 11/6 but 81/44.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 50421/50000

Mapping: [⟨1 -16 -39 -35], ⟨0 20 47 43]]

mapping generators: ~2, ~90/49

Optimal tunings:

  • WE: ~2 = 1200.2604 ¢, ~90/49 = 1055.2729 ¢
error map: ⟨+0.260 -0.663 +1.357 -1.205]
  • CWE: ~2 = 1200.0000 ¢, ~90/49 = 1055.0513 ¢
error map: ⟨0.000 -0.928 +1.099 -1.618]

Optimal ET sequence: 33cd, 58, 91, 149

Badness (Sintel): 3.37

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -16 -39 -35 -66], ⟨0 20 47 43 79]]

Optimal tunings:

  • WE: ~2 = 1200.1548 ¢, ~81/44 = 1055.0954 ¢
  • CWE: ~2 = 1200.0000 ¢, ~81/44 = 1055.0631 ¢

Optimal ET sequence: 58, 149, 207, 356e

Badness (Sintel): 1.82

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -16 -39 -35 -66 -64], ⟨0 20 47 43 79 77]]

Optimal tunings:

  • WE: ~2 = 1200.1473 ¢, ~81/44 = 1055.1904 ¢
  • CWE: ~2 = 1200.0000 ¢, ~81/44 = 1055.0644 ¢

Optimal ET sequence: 58, 149, 207, 356e

Badness (Sintel): 1.19

Majvamoid

Named by Xenllium in 2021, majvamoid tempers out the quasiorwellisma and may be described as the 149 & 183 temperament. It is an extension of the majvam temperament.

Subgroup: 2.3.5.7

Comma list: 19683/19600, 29360128/29296875

Mapping: [⟨1 -12 -2 -54], ⟨0 22 7 92]]

mapping generators: ~2, ~192/125

Optimal tunings:

  • WE: ~2 = 1200.0181 ¢, ~192/125 = 740.9804 ¢
error map: ⟨+0.018 -0.603 +0.513 +0.395]
  • CWE: ~2 = 1200.0000 ¢, ~192/125 = 740.9695 ¢
error map: ⟨0.000 -0.627 +0.473 +0.365]

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

Badness (Sintel): 5.25

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -12 -2 -54 -41], ⟨0 22 7 92 72]]

Optimal tunings:

  • WE: ~2 = 1200.0467 ¢, ~135/88 = 741.0021 ¢
  • CWE: ~2 = 1200.0000 ¢, ~135/88 = 740.9738 ¢

Optimal ET sequence: 34d, 115de, 149, 183, 332e, 515e

Badness (Sintel): 2.18

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -12 -2 -54 -41 -21], ⟨0 22 7 92 72 40]]

Optimal tunings:

  • WE: ~2 = 1200.1305 ¢, ~135/88 = 741.0523 ¢
  • CWE: ~2 = 1200.0000 ¢, ~135/88 = 740.9735 ¢

Optimal ET sequence: 34d, 115def, 149, 183, 332ef, 515ef

Badness (Sintel): 1.43

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 -12 -2 -54 -41 -21 1], ⟨0 22 7 92 72 40 5]]

Optimal tunings:

  • WE: ~2 = 1200.0995 ¢, ~135/88 = 741.0345 ¢
  • CWE: ~2 = 1200.0000 ¢, ~135/88 = 740.9741 ¢

Optimal ET sequence: 34d, 115def, 149, 183, 332ef, 515ef

Badness (Sintel): 1.19

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