Swetismic temperaments: Difference between revisions

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**Imported revision 264609342 - Original comment: **
Move indra here as we're dissolving the mirkwai family
 
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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]] ([[ratio]]: 540/539, {{monzo|legend=1| 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>2011-10-13 20:48:05 UTC</tt>.<br>
: The original revision id was <tt>264609342</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">These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.


Comma: 540/539
Temperaments discussed elsewhere are:  
* ''[[Terpsichore]]'' (+81/80) → [[Didymus rank-3 family #Terpsichore|Didymus rank-3 family]]
* ''[[Big brother]]'' (+99/98 or 121/120) → [[Biyatismic clan #Big brother|Biyatismic clan]]
* ''[[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]]
* ''[[Claudius]]'' (+2048/2025) → [[Diaschismic rank-3 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]]


Map: [&lt;1 0 0 0 2|, &lt;0 1 0 0 3|, &lt;0 0 0 1 -2|]
Considered below are indra, hades, minos, persephone and hypnos, in the order of increasing [[badness]].
Generators: 2, 3, 5, 7
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578


=Hades=
== Indra ==
Commas: 540/539, 4000/3993
: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Canopic]].''


Map: [&lt;2 1 0 2 3|, &lt;0 3 0 5 -1|, &lt;0 0 1 0 1|]
[[Subgroup]]: 2.3.5.7.11
Generators: 99/70, 9/7, 5
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578
Badness: 0.000361


==13-limit==
[[Comma list]]: 540/539, 1375/1372
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|]
{{Mapping|legend=1| 1 0 -5 -4 5 | 0 1 3 3 0 | 0 0 5 4 -3 }}
Generators: 99/70, 9/7, 5
: Mapping generators: ~2, ~3, ~10/7
EDOs: 36, 58, 72, 130, 224, 354, 578
 
Badness: 0.000535
[[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]
</pre></div>
 
<h4>Original HTML content:</h4>
Lattice basis:
<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;These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.&lt;br /&gt;
: 15/14 length = 0.6184, 55/36 length = 0.7585
&lt;br /&gt;
: Angle (15/14, 55/36) = 68.1048 deg
Comma: 540/539&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
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;
* [[WE]]: ~2 = 1199.9693{{c}}, ~3/2 = 701.7444{{c}}, ~10/7 = 616.1152{{c}}
Generators: 2, 3, 5, 7&lt;br /&gt;
: [[error map]]: {{val| -0.031 -0.241 -0.443 +0.899 +0.183 }}
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7342{{c}}, ~10/7 = 616.1422{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 -0.221 -0.400 +0.946 +0.256 }}
&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;
[[Minimax tuning]]:
&lt;br /&gt;
* [[11-odd-limit]]
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;
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10 10 -3 0 -5 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 6 6 -1 0 -3 }}, {{monzo| 20 18 -6 0 -9 }}]
Generators: 99/70, 9/7, 5&lt;br /&gt;
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.11/9
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578&lt;br /&gt;
 
Badness: 0.000361&lt;br /&gt;
{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}
&lt;br /&gt;
 
&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;
[[Badness]] (Sintel): 0.320
Commas: 540/539, 729/728, 1575/1573&lt;br /&gt;
 
&lt;br /&gt;
[[Projection pair]]s: <code>5 84375/16807 7 16875/2401 11 1372/125</code> to 2.3.7/5
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;
Scales: [[indra31]]
EDOs: 36, 58, 72, 130, 224, 354, 578&lt;br /&gt;
 
Badness: 0.000535&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Shibi ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 729/728, 1375/1372
 
Mapping: {{mapping| 1 0 -5 -4 5 1 | 0 1 3 3 0 3 | 0 0 5 4 -3 -4 }}
 
Optimal tunings:
* WE: ~2 = 1199.9762{{c}}, ~3/2 = 701.7232{{c}}, ~10/7 = 616.1317{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7261{{c}}, ~10/7 = 616.1467{{c}}
 
{{Optimal ET sequence|legend=0| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}
 
Badness (Sintel): 0.674
 
=== Yajna ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 625/624, 1375/1372
 
Mapping: {{mapping| 1 0 -5 -4 5 -24 | 0 1 3 3 0 11 | 0 0 5 4 -3 20 }}
 
Optimal tunings:
* WE: ~2 = 1200.0073{{c}}, ~3/2 = 701.7067{{c}}, ~10/7 = 616.1052{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7089{{c}}, ~10/7 = 616.0986{{c}}
 
Minimax tuning:  
* 13-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo| 8/5 2/5 -8/5 0 0 7/5 }}]
: eigenmonzo (unchanged-interval) basis: 2.9/5.13/5
* 15-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo| 1 1 0 -1/4 0 1/4 }}, {{monzo| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo| 1 1 0 -5/4 0 5/4 }}]
: eigenmonzo (unchanged-interval) basis: 2.3.13/7
 
{{Optimal ET sequence|legend=0| 31, 49f, 72, 103, 121, 152f, 193, 224 }}
 
Badness (Sintel): 0.655
 
=== Vibhu ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 1375/1372
 
Mapping: {{mapping| 1 0 -5 -4 5 -13 | 0 1 3 3 0 6 | 0 0 5 4 -3 14 }}
 
Optimal tunings:  
* WE: ~2 = 1200.1587{{c}}, ~3/2 = 701.2394{{c}}, ~10/7 = 616.6507{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2689{{c}}, ~10/7 = 616.5306{{c}}
 
{{Optimal ET sequence|legend=0| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}
 
Badness (Sintel): 0.772
 
=== Vish ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 364/363, 540/539
 
Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 3 3 0 -2 | 0 0 5 4 -3 -10 }}
 
Optimal tunings:
* WE: ~2 = 1199.9463{{c}}, ~3/2 = 702.3912{{c}}, ~10/7 = 615.5733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3742{{c}}, ~10/7 = 615.6198{{c}}
 
{{Optimal ET sequence|legend=0| 31f, 41, 72, 121, 193 }}
 
Badness (Sintel): 0.870
 
== Hades ==
: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Stearnsmic]].''
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 4000/3993
 
{{Mapping|legend=1| 2 1 0 2 3 | 0 3 0 5 -1 | 0 0 1 0 1 }}
: mapping generators: ~99/70, ~9/7, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 599.9486{{c}}, ~9/7 = 433.9084{{c}}, ~5/4 = 386.2290{{c}}
: [[error map]]: {{val| -0.103 -0.281 -0.290 +0.613 +0.643 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~9/7 = 433.9204{{c}}, ~5/4 = 386.1272{{c}}
: error map: {{val| 0.000 -0.194 -0.187 +0.776 +0.889 }}
 
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee }}
 
[[Badness]] (Sintel): 0.434
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 540/539, 729/728, 1575/1573
 
Mapping: {{mapping| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}
 
Optimal tunings:
* WE: ~99/70 = 599.9598{{c}}, ~9/7 = 433.8891{{c}}, ~5/4 = 386.1680{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~9/7 = 433.9059{{c}}, ~5/4 = 386.1014{{c}}
 
{{Optimal ET sequence|legend=0| 22f, 36ce, 58, 72, 130, 224, 354, 578 }}
 
Badness (Sintel): 0.501
 
=== Cerberus ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 364/363, 540/539
 
Mapping: {{mapping| 2 1 0 2 3 1 | 0 3 0 5 -1 -4 | 0 0 1 0 1 2 }}
 
Optimal tunings:
* WE: ~55/39 = 599.9565{{c}}, ~9/7 = 433.8372{{c}}, ~5/4 = 387.1905{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~9/7 = 433.8475{{c}}, ~5/4 = 387.1030{{c}}
 
{{Optimal ET sequence|legend=0| 8d, 14cf, 22, 36f, 44ceff, 50, 58, 72, 130 }}
 
Badness (Sintel): 0.716
 
== Minos ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 12005/11979
 
{{Mapping|legend=1| 1 0 -3 0 -1 | 0 2 4 3 4 | 0 0 5 1 3 }}
: mapping generators: ~2, ~121/70, ~66/49
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.8923{{c}}, ~121/70 = 950.8327{{c}}, ~66/49 = 516.4492{{c}}
: [[error map]]: {{val| -0.108 -0.290 -0.414 +0.121 +1.468 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~121/70 = 950.8712{{c}}, ~66/49 = 516.5067{{c}}
: error map: {{val| 0.000 -0.213 -0.295 +0.294 +1.687 }}
 
{{Optimal ET sequence|legend=1| 9, …, 49, 58, 72, 130, 193, 202, 323e, 395e, 525e }} *
 
<nowiki>*</nowiki> [[optimal patent val]]: [[467edo|467]]
 
[[Badness]] (Sintel): 1.06
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 364/363, 540/539, 676/675
 
Mapping: {{mapping| 1 0 -3 0 -1 -4 | 0 2 4 3 4 7 | 0 0 5 1 3 5 }}
 
Optimal tunings:
* WE: ~2 = 1199.7669{{c}}, ~26/15 = 950.9360{{c}}, ~66/49 = 516.3652{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.0324{{c}}, ~66/49 = 516.4883{{c}}
 
{{Optimal ET sequence|legend=0| 9, …, 49f, 58, 72, 121, 130, 193, 251e, 323e }}
 
Badness (Sintel): 0.677
 
== Persephone ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 88209/87500
 
{{Mapping|legend=1| 1 0 -6 4 -12 | 0 1 4 0 7 | 0 0 5 -3 11 }}
: mapping generators: ~2, ~3, ~33/25
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0185{{c}}, ~3/2 = 700.9179{{c}}, ~33/25 = 476.7538{{c}}
: [[error map]]: {{val| +0.019 -1.019 +1.090 +0.987 -0.694 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.9220{{c}}, ~33/25 = 476.7393{{c}}
: error map: {{val| 0.000 -1.033 +1.071 +0.956 -0.732 }}
 
{{Optimal ET sequence|legend=1| 8d, …, 45e, 50, 53, 58, 103, 161, 214, 272, 375 }}
 
[[Badness]] (Sintel): 2.42
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 847/845
 
Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 1 4 0 7 5 | 0 0 5 -3 11 7 }}
 
Optimal tunings:
* WE: ~2 = 1199.9553{{c}}, ~3/2 = 700.9477{{c}}, ~33/25 = 476.6709{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9378{{c}}, ~33/25 = 476.7054{{c}}
 
{{Optimal ET sequence|legend=0| 8d, …, 45ef, 50, 53, 58, 103, 111, 161, 214, 375 }}
 
Badness (Sintel): 0.933
 
== 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 tuning]]s:
* [[WE]]: ~2 = 1200.3393{{c}}, ~81/56 = 633.6837{{c}}, ~5/4 = 385.6892{{c}}
: [[error map]]: {{val| +0.339 -0.904 +0.054 +0.677 -0.124 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~81/56 = 633.5228{{c}}, ~5/4 = 385.9359{{c}}
: error map: {{val| 0.000 -1.387 -0.378 -0.075 -1.178 }}
 
{{Optimal ET sequence|legend=1| 17c, 19, …, 36, 53, 72, 161, 214, 233, 286, 358, 591be }}
 
[[Badness]] (Sintel): 1.96
 
=== 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 tunings:
* WE: ~2 = 1200.6306{{c}}, ~81/56 = 633.8505{{c}}, ~5/4 = 385.0539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~81/56 = 633.5546{{c}}, ~5/4 = 385.4668{{c}}
 
{{Optimal ET sequence|legend=0| 17c, 19, 36ce, 53, 72, 125f, 197ef }}
 
Badness (Sintel): 1.35
 
[[Category:Temperament collections]]
[[Category:Swetismic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]

Latest revision as of 12:06, 6 June 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-3 temperaments tempering out the swetisma (ratio: 540/539, monzo: [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 indra, hades, minos, persephone and hypnos, in the order of increasing badness.

Indra

For the 7-limit version, see Miscellaneous 7-limit temperaments #Canopic.

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372

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

Mapping generators: ~2, ~3, ~10/7

Mapping to lattice: [⟨0 2 1 2 3], ⟨0 -1 2 1 -3]]

Lattice basis:

15/14 length = 0.6184, 55/36 length = 0.7585
Angle (15/14, 55/36) = 68.1048 deg

Optimal tunings:

  • WE: ~2 = 1199.9693 ¢, ~3/2 = 701.7444 ¢, ~10/7 = 616.1152 ¢
error map: ⟨-0.031 -0.241 -0.443 +0.899 +0.183]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7342 ¢, ~10/7 = 616.1422 ¢
error map: ⟨0.000 -0.221 -0.400 +0.946 +0.256]

Minimax tuning:

[[1 0 0 0 0⟩, [10 10 -3 0 -5⟩, [0 0 1 0 0⟩, [6 6 -1 0 -3⟩, [20 18 -6 0 -9⟩]
eigenmonzo (unchanged-interval) basis: 2.5.11/9

Optimal ET sequence: 31, 41, 72, 152, 224, 631d, 855d

Badness (Sintel): 0.320

Projection pairs: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5

Scales: indra31

Shibi

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1375/1372

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

Optimal tunings:

  • WE: ~2 = 1199.9762 ¢, ~3/2 = 701.7232 ¢, ~10/7 = 616.1317 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7261 ¢, ~10/7 = 616.1467 ¢

Optimal ET sequence: 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d

Badness (Sintel): 0.674

Yajna

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624, 1375/1372

Mapping: [⟨1 0 -5 -4 5 -24], ⟨0 1 3 3 0 11], ⟨0 0 5 4 -3 20]]

Optimal tunings:

  • WE: ~2 = 1200.0073 ¢, ~3/2 = 701.7067 ¢, ~10/7 = 616.1052 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.7089 ¢, ~10/7 = 616.0986 ¢

Minimax tuning:

  • 13-odd-limit
[[1 0 0 0 0 0⟩, [4/5 6/5 -4/5 0 0 1/5⟩, [8/5 2/5 -3/5 0 0 2/5⟩, [44/25 26/25 -24/25 0 0 11/25⟩, [62/25 48/25 -27/25 0 0 3/25⟩, [8/5 2/5 -8/5 0 0 7/5⟩]
eigenmonzo (unchanged-interval) basis: 2.9/5.13/5
  • 15-odd-limit
[[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [5/4 1/2 0 -5/16 0 5/16⟩, [1 1 0 -1/4 0 1/4⟩, [5/4 3/2 0 3/16 0 -3/16⟩, [1 1 0 -5/4 0 5/4⟩]
eigenmonzo (unchanged-interval) basis: 2.3.13/7

Optimal ET sequence: 31, 49f, 72, 103, 121, 152f, 193, 224

Badness (Sintel): 0.655

Vibhu

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 1375/1372

Mapping: [⟨1 0 -5 -4 5 -13], ⟨0 1 3 3 0 6], ⟨0 0 5 4 -3 14]]

Optimal tunings:

  • WE: ~2 = 1200.1587 ¢, ~3/2 = 701.2394 ¢, ~10/7 = 616.6507 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.2689 ¢, ~10/7 = 616.5306 ¢

Optimal ET sequence: 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f

Badness (Sintel): 0.772

Vish

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 540/539

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

Optimal tunings:

  • WE: ~2 = 1199.9463 ¢, ~3/2 = 702.3912 ¢, ~10/7 = 615.5733 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.3742 ¢, ~10/7 = 615.6198 ¢

Optimal ET sequence: 31f, 41, 72, 121, 193

Badness (Sintel): 0.870

Hades

For the 7-limit version, see Miscellaneous 7-limit temperaments #Stearnsmic.

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]]

mapping generators: ~99/70, ~9/7, ~5

Optimal tunings:

  • WE: ~99/70 = 599.9486 ¢, ~9/7 = 433.9084 ¢, ~5/4 = 386.2290 ¢
error map: ⟨-0.103 -0.281 -0.290 +0.613 +0.643]
  • CWE: ~99/70 = 600.0000 ¢, ~9/7 = 433.9204 ¢, ~5/4 = 386.1272 ¢
error map: ⟨0.000 -0.194 -0.187 +0.776 +0.889]

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

Badness (Sintel): 0.434

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 tunings:

  • WE: ~99/70 = 599.9598 ¢, ~9/7 = 433.8891 ¢, ~5/4 = 386.1680 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~9/7 = 433.9059 ¢, ~5/4 = 386.1014 ¢

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

Badness (Sintel): 0.501

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 tunings:

  • WE: ~55/39 = 599.9565 ¢, ~9/7 = 433.8372 ¢, ~5/4 = 387.1905 ¢
  • CWE: ~55/39 = 600.0000 ¢, ~9/7 = 433.8475 ¢, ~5/4 = 387.1030 ¢

Optimal ET sequence: 8d, 14cf, 22, 36f, 44ceff, 50, 58, 72, 130

Badness (Sintel): 0.716

Minos

Subgroup: 2.3.5.7.11

Comma list: 540/539, 12005/11979

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

mapping generators: ~2, ~121/70, ~66/49

Optimal tunings:

  • WE: ~2 = 1199.8923 ¢, ~121/70 = 950.8327 ¢, ~66/49 = 516.4492 ¢
error map: ⟨-0.108 -0.290 -0.414 +0.121 +1.468]
  • CWE: ~2 = 1200.0000 ¢, ~121/70 = 950.8712 ¢, ~66/49 = 516.5067 ¢
error map: ⟨0.000 -0.213 -0.295 +0.294 +1.687]

Optimal ET sequence: 9, …, 49, 58, 72, 130, 193, 202, 323e, 395e, 525e *

* optimal patent val: 467

Badness (Sintel): 1.06

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tunings:

  • WE: ~2 = 1199.7669 ¢, ~26/15 = 950.9360 ¢, ~66/49 = 516.3652 ¢
  • CWE: ~2 = 1200.0000 ¢, ~26/15 = 951.0324 ¢, ~66/49 = 516.4883 ¢

Optimal ET sequence: 9, …, 49f, 58, 72, 121, 130, 193, 251e, 323e

Badness (Sintel): 0.677

Persephone

Subgroup: 2.3.5.7.11

Comma list: 540/539, 88209/87500

Mapping: [⟨1 0 -6 4 -12], ⟨0 1 4 0 7], ⟨0 0 5 -3 11]]

mapping generators: ~2, ~3, ~33/25

Optimal tunings:

  • WE: ~2 = 1200.0185 ¢, ~3/2 = 700.9179 ¢, ~33/25 = 476.7538 ¢
error map: ⟨+0.019 -1.019 +1.090 +0.987 -0.694]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.9220 ¢, ~33/25 = 476.7393 ¢
error map: ⟨0.000 -1.033 +1.071 +0.956 -0.732]

Optimal ET sequence: 8d, …, 45e, 50, 53, 58, 103, 161, 214, 272, 375

Badness (Sintel): 2.42

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 0 -6 4 -12 -7], ⟨0 1 4 0 7 5], ⟨0 0 5 -3 11 7]]

Optimal tunings:

  • WE: ~2 = 1199.9553 ¢, ~3/2 = 700.9477 ¢, ~33/25 = 476.6709 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.9378 ¢, ~33/25 = 476.7054 ¢

Optimal ET sequence: 8d, …, 45ef, 50, 53, 58, 103, 111, 161, 214, 375

Badness (Sintel): 0.933

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 tunings:

  • WE: ~2 = 1200.3393 ¢, ~81/56 = 633.6837 ¢, ~5/4 = 385.6892 ¢
error map: ⟨+0.339 -0.904 +0.054 +0.677 -0.124]
  • CWE: ~2 = 1200.0000 ¢, ~81/56 = 633.5228 ¢, ~5/4 = 385.9359 ¢
error map: ⟨0.000 -1.387 -0.378 -0.075 -1.178]

Optimal ET sequence: 17c, 19, …, 36, 53, 72, 161, 214, 233, 286, 358, 591be

Badness (Sintel): 1.96

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 tunings:

  • WE: ~2 = 1200.6306 ¢, ~81/56 = 633.8505 ¢, ~5/4 = 385.0539 ¢
  • CWE: ~2 = 1200.0000 ¢, ~81/56 = 633.5546 ¢, ~5/4 = 385.4668 ¢

Optimal ET sequence: 17c, 19, 36ce, 53, 72, 125f, 197ef

Badness (Sintel): 1.35

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