Swetismic temperaments: Difference between revisions

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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-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out]] the [[swetisma]], 540/539 = {{monzo| 2 3 1 -2 -1 }}. For the rank-4 swetismic temperament, see [[Catalog of rank-4 temperaments #Swetismic (540/539)]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-23 17:33:15 UTC</tt>.<br>
: The original revision id was <tt>267683026</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]]


These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.
Temperaments discussed elsewhere are:
* ''[[Terpsichore]]'' (+81/80) → [[Didymus rank three family #Terpsichore|Didymus rank-3 family]]
* ''[[Big brother]]'' (+99/98 or 121/120) → [[Nuwell family #Big brother|Nuwell family]]
* ''[[Octarod]]'' (+100/99 or 245/243) → [[Sensamagic family #Octarod|Sensamagic family]]
* ''[[Aplonis]]'' (+126/125) → [[Starling family #Aplonis|Starling family]]
* ''[[Guanyin]]'' (+176/175) → [[Orwellismic family #Guanyin|Orwellismic family]]
* [[Marvel]] (+225/224 or 385/384) → [[Marvel family #Undecimal marvel|Marvel family]]
* [[Jove]] (+243/242 or 441/440) → [[Breed family #Jove|Breed family]]
* ''[[Uni]]'' (+896/891) → [[Hemimage family #Uni|Hemimage family]]
* ''[[Gamel]]'' (+1029/1024) → [[Gamelismic family #Gamel|Gamelismic family]]
* ''[[Indra]]'' (+1375/1372) → [[Mirkwai family #Indra|Mirkwai family]]
* ''[[Claudius]]'' (+2048/2025) → [[Diaschismic rank three family #Claudius|Diaschismic rank-3 family]]
* ''[[Octasand]]'' (+2200/2187) → [[Octagar family #Octasand|Octagar family]]
* ''[[Gariboh]]'' (+3125/3087) → [[Gariboh family #Undecimal gariboh|Gariboh family]]
* ''[[Siebog]]'' (+3136/3125) → [[Hemimean family #Siebog|Hemimean family]]
* ''[[Laka]]'' (+5120/5103) → [[Hemifamity family #Laka|Hemifamity family]]
* ''[[Jupiter]]'' (+5632/5625) → [[Porwell family #Jupiter|Porwell family]]
* ''[[Albus]]'' (+8019/8000) → [[Cataharry family #Albus|Cataharry family]]


Comma: 540/539
Considered below are hades, minos, persephone and hypnos.


Map: [&lt;1 0 0 0 2|, &lt;0 1 0 0 3|, &lt;0 0 0 1 -2|]
== Hades ==
Generators: 2, 3, 5, 7
=== 7-limit (stearnsmic) ===
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578
[[Subgroup]]: 2.3.5.7


=Hades=
[[Comma list]]: 118098/117649
Commas: 540/539, 4000/3993


Map: [&lt;2 1 0 2 3|, &lt;0 3 0 5 -1|, &lt;0 0 1 0 1|]
{{Mapping|legend=1| 2 1 0 2 | 0 3 0 5 | 0 0 1 0 }}
Generators: 99/70, 9/7, 5
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578
Badness: 0.000361


==13-limit==
: mapping generators: ~343/243, ~9/7, ~5
Commas: 540/539, 729/728, 1575/1573


Map: [&lt;2 1 0 2 3 -2 |, &lt;0 3 0 5 -1 13|, &lt;0 0 1 0 1 0|]
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130, 152, 202, 224, 354 }}
Generators: 99/70, 9/7, 5
EDOs: 36, 58, 72, 130, 224, 354, 578
Badness: 0.000535


=Cerberus=
[[Badness]]: 0.748 × 10<sup>-3</sup>
Commas: 351/350, 364/363, 540/539


Map: [&lt;2 1 0 2 3 1|, &lt;0 3 0 5 -1 -4|, &lt;0 0 1 0 1 2|]
=== 11-limit ===
Generators: 55/39.9/7,5
[[Subgroup]]: 2.3.5.7.11
EDOs: 22, 50, 58, 72, 130
 
Badness: 0.000766</pre></div>
[[Comma list]]: 540/539, 4000/3993
<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;Swetismic 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="#Hades"&gt;Hades&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;a href="#Cerberus"&gt;Cerberus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
{{Mapping|legend=1| 2 1 0 2 3 | 0 3 0 5 -1 | 0 0 1 0 1 }}
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
 
These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.&lt;br /&gt;
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee }}
&lt;br /&gt;
 
Comma: 540/539&lt;br /&gt;
[[Badness]]: 0.361 × 10<sup>-3</sup>
&lt;br /&gt;
 
Map: [&amp;lt;1 0 0 0 2|, &amp;lt;0 1 0 0 3|, &amp;lt;0 0 0 1 -2|]&lt;br /&gt;
=== 13-limit ===
Generators: 2, 3, 5, 7&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 540/539, 729/728, 1575/1573
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Hades"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Hades&lt;/h1&gt;
 
Commas: 540/539, 4000/3993&lt;br /&gt;
Mapping: {{mapping| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 0 2 3|, &amp;lt;0 3 0 5 -1|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 22f, 36, 58, 72, 130, 224, 354, 578 }}
Generators: 99/70, 9/7, 5&lt;br /&gt;
 
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578&lt;br /&gt;
Badness: 0.535 × 10<sup>-3</sup>
Badness: 0.000361&lt;br /&gt;
 
&lt;br /&gt;
=== Cerberus ===
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Hades-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h2&gt;
Subgroup: 2.3.5.7.11.13
Commas: 540/539, 729/728, 1575/1573&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 351/350, 364/363, 540/539
Map: [&amp;lt;2 1 0 2 3 -2 |, &amp;lt;0 3 0 5 -1 13|, &amp;lt;0 0 1 0 1 0|]&lt;br /&gt;
 
Generators: 99/70, 9/7, 5&lt;br /&gt;
Mapping: {{mapping| 2 1 0 2 3 1 | 0 3 0 5 -1 -4 | 0 0 1 0 1 2 }}
EDOs: 36, 58, 72, 130, 224, 354, 578&lt;br /&gt;
 
Badness: 0.000535&lt;br /&gt;
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Cerberus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Cerberus&lt;/h1&gt;
Badness: 0.766 × 10<sup>-3</sup>
Commas: 351/350, 364/363, 540/539&lt;br /&gt;
 
&lt;br /&gt;
== Minos ==
Map: [&amp;lt;2 1 0 2 3 1|, &amp;lt;0 3 0 5 -1 -4|, &amp;lt;0 0 1 0 1 2|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
Generators: 55/39.9/7,5&lt;br /&gt;
 
EDOs: 22, 50, 58, 72, 130&lt;br /&gt;
[[Comma list]]: 540/539, 12005/11979
Badness: 0.000766&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{Mapping|legend=1| 1 0 2 1 2 | 0 2 4 3 4 | 0 0 -5 -1 -3 }}
 
: mapping generators: ~2, ~121/70, ~49/33
 
{{Optimal ET sequence|legend=1| 9, 49, 58, 72, 130, 193, 202, 467 }}
 
[[Badness]]: 0.886 × 10<sup>-3</sup>
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 364/363, 540/539, 676/675
 
Mapping: {{mapping| 1 0 2 1 2 1 | 0 2 4 3 4 7 | 0 0 -5 -1 -3 -5 }}
 
{{Optimal ET sequence|legend=1| 9, 54, 58, 72, 121, 130, 193 }}
 
Badness: 0.724 × 10<sup>-3</sup>
 
== Persephone ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 88209/87500
 
{{Mapping|legend=1| 1 0 4 -2 10 | 0 1 4 0 7 | 0 0 -5 3 -11 }}
 
: mapping generators: ~2, ~3, ~100/33
 
{{Optimal ET sequence|legend=1| 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde }}
 
[[Badness]]: 2.015 × 10<sup>-3</sup>
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 847/845
 
Mapping: {{mapping| 1 0 4 -2 10 7 | 0 1 4 0 7 5 | 0 0 -5 3 -11 -7 }}
 
{{Optimal ET sequence|legend=1| 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef }}
 
Badness: 0.997 × 10<sup>-3</sup>
 
== Hypnos ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 72171/71680
 
{{Mapping|legend=1| 1 0 0 -3 8 | 0 3 0 11 -13 | 0 0 1 0 1 }}
 
: mapping generators: ~2, ~81/56, ~5
 
{{Optimal ET sequence|legend=1| 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce }}
 
[[Badness]]: 1.629 × 10<sup>-3</sup>
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 540/539, 729/728
 
Mapping: {{mapping| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}
 
{{Optimal ET sequence|legend=1| 19, 36, 53, 72, 125f, 197ef }}
 
Badness: 1.439 × 10<sup>-3</sup>
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Swetismic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]

Latest revision as of 00:28, 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-3 temperaments tempering out the swetisma, 540/539 = [2 3 1 -2 -1⟩. For the rank-4 swetismic temperament, see Catalog of rank-4 temperaments #Swetismic (540/539).

Temperaments discussed elsewhere are:

Considered below are hades, minos, persephone and hypnos.

Hades

7-limit (stearnsmic)

Subgroup: 2.3.5.7

Comma list: 118098/117649

Mapping: [⟨2 1 0 2], ⟨0 3 0 5], ⟨0 0 1 0]]

mapping generators: ~343/243, ~9/7, ~5

Optimal ET sequence: 22, 50, 58, 72, 130, 152, 202, 224, 354

Badness: 0.748 × 10-3

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993

Mapping: [⟨2 1 0 2 3], ⟨0 3 0 5 -1], ⟨0 0 1 0 1]]

Optimal ET sequence: 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee

Badness: 0.361 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573

Mapping: [⟨2 1 0 2 3 -2], ⟨0 3 0 5 -1 13], ⟨0 0 1 0 1 0]]

Optimal ET sequence: 22f, 36, 58, 72, 130, 224, 354, 578

Badness: 0.535 × 10-3

Cerberus

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 540/539

Mapping: [⟨2 1 0 2 3 1], ⟨0 3 0 5 -1 -4], ⟨0 0 1 0 1 2]]

Optimal ET sequence: 22, 50, 58, 72, 130

Badness: 0.766 × 10-3

Minos

Subgroup: 2.3.5.7.11

Comma list: 540/539, 12005/11979

Mapping: [⟨1 0 2 1 2], ⟨0 2 4 3 4], ⟨0 0 -5 -1 -3]]

mapping generators: ~2, ~121/70, ~49/33

Optimal ET sequence: 9, 49, 58, 72, 130, 193, 202, 467

Badness: 0.886 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 540/539, 676/675

Mapping: [⟨1 0 2 1 2 1], ⟨0 2 4 3 4 7], ⟨0 0 -5 -1 -3 -5]]

Optimal ET sequence: 9, 54, 58, 72, 121, 130, 193

Badness: 0.724 × 10-3

Persephone

Subgroup: 2.3.5.7.11

Comma list: 540/539, 88209/87500

Mapping: [⟨1 0 4 -2 10], ⟨0 1 4 0 7], ⟨0 0 -5 3 -11]]

mapping generators: ~2, ~3, ~100/33

Optimal ET sequence: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde

Badness: 2.015 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 847/845

Mapping: [⟨1 0 4 -2 10 7], ⟨0 1 4 0 7 5], ⟨0 0 -5 3 -11 -7]]

Optimal ET sequence: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef

Badness: 0.997 × 10-3

Hypnos

Subgroup: 2.3.5.7.11

Comma list: 540/539, 72171/71680

Mapping: [⟨1 0 0 -3 8], ⟨0 3 0 11 -13], ⟨0 0 1 0 1]]

mapping generators: ~2, ~81/56, ~5

Optimal ET sequence: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce

Badness: 1.629 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 540/539, 729/728

Mapping: [⟨1 0 0 -3 8 0], ⟨0 3 0 11 -13 7], ⟨0 0 1 0 1 0]]

Optimal ET sequence: 19, 36, 53, 72, 125f, 197ef

Badness: 1.439 × 10-3

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