Kalismic temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{Technical data page}}
: This revision was by author [[User:guest|guest]] and made on <tt>2011-11-07 23:38:45 UTC</tt>.<br>
This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the kalisma, [[9801/9800]]. These temperaments always split the octave into halves.  
: The original revision id was <tt>272999510</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 9801/9800, but we can began by looking at the rank four temperament.


Comma: 9801/9800
Temperaments discussed elsewhere are:  
* ''[[Jubilismic]]'' (+50/49) → [[Jubilismic family #Undecimal jubilismic|Jubilismic family]]
* ''[[Fantastic]]'' (+225/224) → [[Marvel family #Fantastic|Marvel family]]
* ''[[Bisector]]'' (+121/120 or 245/243) → [[Sensamagic family #Bisector|Sensamagic family]]
* ''[[Varda]]'' (+176/175) → [[Diaschismic rank-3 family #Varda|Diaschismic rank-3 family]]
* ''[[Hagrid]]'' (+243/242) → [[Cataharry family #Hagrid|Cataharry family]]
* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
* ''[[Varuna]]'' (+441/440) → [[Werckismic temperaments #Varuna|Werckismic temperaments]]
* ''[[Hades]]'' (+540/539) → [[Swetismic temperaments #Hades|Swetismic temperaments]]
* ''[[Dimcomp]]'' (+1375/1372) → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]]
* ''[[Baldur]]'' (+2401/2400) → [[Breed family #Baldur|Breed family]]
* ''[[Thor]]'' (+3025/3024 or 4375/4374) → [[Ragismic family #Thor|Ragismic family]]
* ''[[Semiporwell]]'' (+6144/6125) → [[Porwell family #Semiporwell|Porwell family]]
* ''[[Semicanou]]'' (+14641/14580) → [[Canou family #Semicanou|Canou family]]
* ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]]


Map: [&lt;2 0 0 0 3|, &lt;0 1 0 0 -2|, &lt;0 0 1 0 1|, &lt;0 0 0 1 1|]
Considered below are lycoris, van gogh, sif, loki, pessoal, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].
Generators: 99/70, 3, 5, 7
EDOs: 4, 12, 22, 46, 58, 72, 118, 130, 152, 270, 342, 512, 836, 1084, 1236, 1406, 1578, 1848, 2684, 4038, 4190, 4532, 11254


==Odin==  
== Lycoris ==
Commas: 9801/9800, 151263/151250
Lycoris tempers out the [[parimo]] in addition to the kalisma, and splits the [[syntonic comma]] into three equal parts, one for [[121/120]], and two for [[243/242]]. It is therefore [[support]]ed by third-comma equal temperaments. [[342edo]] shows an excellent example of this, but it can be tuned much more accurate.


Map: [&lt;6 0 0 8 17|, &lt;0 1 0 -2 -4|, &lt;0 0 1 2 3|]
It was named by [[Flora Canou]] in 2023 after the flower associated with afterlife in Japanese culture, under the impression that a temperament with such intricacy will never be fully explored in a lifetime.  
Generators: 55/49, 3, 5
EDOs: 12, 42, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464
Badness: 0.000116


==Loki==
[[Subgroup]]: 2.3.5.7.11
Commas: 5632/5625, 9801/9800


Map: [&lt;2 0 0 -21 -18|, &lt;0 1 0 4 2|, &lt;0 0 1 3 4|]
[[Comma list]]: 9801/9800, 1771561/1771470
Generators: 99/70, 3, 5
 
EDOs: 12, 22, 86, 108, 118, 130, 248, 270, 670, 822, 940, 1092
{{Mapping|legend=1| 2 0 -2 1 0 | 0 1 1 3 2 | 0 0 6 -5 1 }}
Badness: 0.000493[[image:http://i122.photobucket.com/albums/o255/sweetchuckzx/Tattoodesigns.jpg link="http://www.90ninetattoodesigns.com"]]</pre></div>
: mapping generators: ~99/70, ~3, ~11/9
<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;Kalismic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These are rank three temperaments tempering out 9801/9800, but we can began by looking at the rank four temperament.&lt;br /&gt;
[[Optimal tuning]]s:
&lt;br /&gt;
* [[WE]]: ~99/70 = 600.0018{{c}}, ~3/2 = 701.9411{{c}}, ~11/9 = 347.3976{{c}}
Comma: 9801/9800&lt;br /&gt;
: [[error map]]: {{val| +0.004 -0.010 +0.013 -0.018 -0.031 }}
&lt;br /&gt;
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9414{{c}}, ~11/9 = 347.3969{{c}}
Map: [&amp;lt;2 0 0 0 3|, &amp;lt;0 1 0 0 -2|, &amp;lt;0 0 1 0 1|, &amp;lt;0 0 0 1 1|]&lt;br /&gt;
: error map: {{val| 0.000 -0.014 +0.009 +0.014 -0.038 }}
Generators: 99/70, 3, 5, 7&lt;br /&gt;
 
EDOs: 4, 12, 22, 46, 58, 72, 118, 130, 152, 270, 342, 512, 836, 1084, 1236, 1406, 1578, 1848, 2684, 4038, 4190, 4532, 11254&lt;br /&gt;
{{Optimal ET sequence|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Odin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Odin&lt;/h2&gt;
[[Badness]] (Sintel): 0.299
Commas: 9801/9800, 151263/151250&lt;br /&gt;
 
&lt;br /&gt;
=== Higanbana ===
Map: [&amp;lt;6 0 0 8 17|, &amp;lt;0 1 0 -2 -4|, &amp;lt;0 0 1 2 3|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Generators: 55/49, 3, 5&lt;br /&gt;
 
EDOs: 12, 42, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464&lt;br /&gt;
Comma list: 9801/9800, 10648/10647, 1399680/1399489
Badness: 0.000116&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Loki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Loki&lt;/h2&gt;
: mapping generators: ~99/70, ~1458/1001, ~81/70
Commas: 5632/5625, 9801/9800&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
Map: [&amp;lt;2 0 0 -21 -18|, &amp;lt;0 1 0 4 2|, &amp;lt;0 0 1 3 4|]&lt;br /&gt;
* WE: ~99/70 = 599.9996{{c}}, ~1458/1001 = 650.9717{{c}}, ~11/9 = 347.3963{{c}}
Generators: 99/70, 3, 5&lt;br /&gt;
* CWE: ~99/70 = 600.0000{{c}}, ~1458/1001 = 650.9718{{c}}, ~11/9 = 347.3964{{c}}
EDOs: 12, 22, 86, 108, 118, 130, 248, 270, 670, 822, 940, 1092&lt;br /&gt;
 
Badness: 0.000493&lt;!-- ws:start:WikiTextRemoteImageRule:5:&amp;lt;a href=&amp;quot;http://www.90ninetattoodesigns.com&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://i122.photobucket.com/albums/o255/sweetchuckzx/Tattoodesigns.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.90ninetattoodesigns.com" rel="nofollow"&gt;&lt;img src="http://i122.photobucket.com/albums/o255/sweetchuckzx/Tattoodesigns.jpg" alt="external image Tattoodesigns.jpg" title="external image Tattoodesigns.jpg" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:5 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Optimal ET sequence|legend=0| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }}
 
Badness (Sintel): 0.389
 
== Van gogh ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 9801/9800, 199297406/199290375
 
{{Mapping|legend=1| 2 0 8 0 11 | 0 1 1 2 1 | 0 0 -9 -1 -10 }}
: mapping generators: ~99/70, ~3, ~11/10
 
[[Optimal tuning]]s:  
* [[WE]]: ~99/70 = 600.0022{{c}}, ~3/2 = 701.9464{{c}}, ~11/9 = 164.9319{{c}}
: [[error map]]: {{val| +0.004 -0.004 +0.022 +0.005 -0.046 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9469{{c}}, ~11/9 = 164.9316{{c}}
: error map: {{val| 0.000 -0.008 +0.018 -0.000 -0.055 }}
 
{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }}
 
[[Badness]] (Sintel): 0.358
 
== Sif ==
Sif tempers out 2097152/2096325, and extends to a strong [[13-limit]] temperament by virtue of the identity 2097152/2096325 = ([[4096/4095]])⋅([[6656/6655]]). It was named by [[Flora Canou]] in 2023 as a sharp-tending counterpart of [[thor]].
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 9801/9800, 2097152/2096325
 
{{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }}
: mapping generators: ~99/70, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 599.9863{{c}}, ~3/2 = 701.9658{{c}}, ~48/35 = 546.5930{{c}}
: [[error map]]: {{val| -0.027 -0.017 +0.045 +0.052 +0.000 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9755{{c}}, ~48/35 = 546.6052{{c}}
: error map: {{val| 0.000 +0.021 +0.107 +0.124 +0.101 }}
 
{{Optimal ET sequence|legend=1| 22, 46, 68, 114, 134, 156, 178, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2742, 3236, 3506, 4742d, 10990ccdde, 15732ccdddee }}
 
[[Badness]] (Sintel): 0.508
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 4096/4095, 6656/6655, 9801/9800
 
Mapping: {{mapping| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }}
 
Optimal tunings:
* WE: ~99/70 = 599.9857{{c}}, ~3/2 = 701.9705{{c}}, ~48/35 = 546.5927{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9877{{c}}, ~48/35 = 546.6058{{c}}
 
{{Optimal ET sequence|legend=0| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }}
 
Badness (Sintel): 0.317
 
== Loki ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 5632/5625, 9801/9800
 
{{Mapping|legend=1| 2 0 0 -21 -18 | 0 1 0 4 2 | 0 0 1 3 4 }}
: mapping generators: ~99/70, ~3, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 599.9481{{c}}, ~3/2 = 702.1195{{c}}, ~5/4 = 386.7636{{c}}
: [[error map]]: {{val| -0.104 +0.061 +0.242 -0.005 -0.128 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1647{{c}}, ~5/4 = 386.7768{{c}}
: error map: {{val| 0.000 +0.210 +0.463 +0.163 +0.119 }}
 
{{Optimal ET sequence|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
 
[[Badness]] (Sintel): 0.592
 
== Pessoal ==
{{See also| Pessoalisma }}
 
Pessoal tempers out the [[olympia]]. It was named by [[Aura]] in 2023, meaning [[Wiktionary: pessoal #Portuguese|"personal"]], for the fact that it is associated with [[abigail]], which is in turn a person's name.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 9801/9800, 131072/130977
 
{{Mapping|legend=1| 2 0 1 10 14 | 0 1 0 -1 -3 | 0 0 3 -1 2 }}
: mapping generators: ~99/70, ~3, ~32/21
 
[[Optimal tuning]]s:  
* [[WE]]: ~99/70 = 599.9711{{c}}, ~3/2 = 702.0265{{c}}, ~32/21 = 728.7942{{c}}
: [[error map]]: {{val| -0.058 +0.014 +0.040 +0.122 -0.040 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0635{{c}}, ~32/21 = 728.8214{{c}}
: error map: {{val| 0.000 +0.109 +0.150 +0.289 +0.134 }}
 
{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
 
[[Badness]] (Sintel): 0.599
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 4096/4095
 
Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}
 
Optimal tunings:
* WE: ~99/70 = 599.9835{{c}}, ~3/2 = 702.0253{{c}}, ~32/21 = 728.7700{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0477{{c}}, ~32/21 = 728.7882{{c}}
 
{{Optimal ET sequence|legend=0| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
 
Badness (Sintel): 0.366
 
== Linus ==
{{Main| Linus }}
: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Linus]].''
 
Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the {{nowrap| 80 & 130 & 270 }} temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 9801/9800, 391314/390625
 
{{Mapping|legend=1| 10 0 0 -11 4 | 0 1 0 1 -1 | 0 0 1 1 2 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~15/14 = 119.9975{{c}}, ~3/2 = 702.0188{{c}}, ~5/4 = 386.6399{{c}}
: [[error map]]: {{val| -0.025 +0.039 +0.276 -0.215 -0.143 }}
* [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 702.0181{{c}}, ~5/4 = 386.6218{{c}}
: error map: {{val| 0.000 +0.063 +0.308 -0.186 -0.092 }}
 
{{Optimal ET sequence|legend=1| 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c }}
 
[[Badness]] (Sintel): 1.34
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1001/1000, 4225/4224, 4459/4455
 
Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }}
 
Optimal tunings:  
* WE: ~15/14 = 120.0054{{c}}, ~3/2 = 701.9625{{c}}, ~5/4 = 386.4910{{c}}
* CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 701.9533{{c}}, ~5/4 = 386.5119{{c}}
 
{{Optimal ET sequence|legend=0| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }}
 
Badness (Sintel): 0.721
 
[[Category:Temperament collections]]
[[Category:Kalismic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]

Latest revision as of 14:29, 20 April 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 that temper out the kalisma, 9801/9800. These temperaments always split the octave into halves.

Temperaments discussed elsewhere are:

Considered below are lycoris, van gogh, sif, loki, pessoal, and linus, in the order of increasing badness. For the rank-4 temperament, see Rank-4 temperament #Kalismic (9801/9800).

Lycoris

Lycoris tempers out the parimo in addition to the kalisma, and splits the syntonic comma into three equal parts, one for 121/120, and two for 243/242. It is therefore supported by third-comma equal temperaments. 342edo shows an excellent example of this, but it can be tuned much more accurate.

It was named by Flora Canou in 2023 after the flower associated with afterlife in Japanese culture, under the impression that a temperament with such intricacy will never be fully explored in a lifetime.

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 1771561/1771470

Mapping: [⟨2 0 -2 1 0], ⟨0 1 1 3 2], ⟨0 0 6 -5 1]]

mapping generators: ~99/70, ~3, ~11/9

Optimal tunings:

  • WE: ~99/70 = 600.0018 ¢, ~3/2 = 701.9411 ¢, ~11/9 = 347.3976 ¢
error map: ⟨+0.004 -0.010 +0.013 -0.018 -0.031]
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9414 ¢, ~11/9 = 347.3969 ¢
error map: ⟨0.000 -0.014 +0.009 +0.014 -0.038]

Optimal ET sequence: 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e

Badness (Sintel): 0.299

Higanbana

Subgroup: 2.3.5.7.11.13

Comma list: 9801/9800, 10648/10647, 1399680/1399489

Mapping: [⟨2 1 -1 2 2 4], ⟨0 2 2 6 4 1], ⟨0 0 6 -5 1 4]]

mapping generators: ~99/70, ~1458/1001, ~81/70

Optimal tunings:

  • WE: ~99/70 = 599.9996 ¢, ~1458/1001 = 650.9717 ¢, ~11/9 = 347.3963 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~1458/1001 = 650.9718 ¢, ~11/9 = 347.3964 ¢

Optimal ET sequence: 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938

Badness (Sintel): 0.389

Van gogh

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 199297406/199290375

Mapping: [⟨2 0 8 0 11], ⟨0 1 1 2 1], ⟨0 0 -9 -1 -10]]

mapping generators: ~99/70, ~3, ~11/10

Optimal tunings:

  • WE: ~99/70 = 600.0022 ¢, ~3/2 = 701.9464 ¢, ~11/9 = 164.9319 ¢
error map: ⟨+0.004 -0.004 +0.022 +0.005 -0.046]
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9469 ¢, ~11/9 = 164.9316 ¢
error map: ⟨0.000 -0.008 +0.018 -0.000 -0.055]

Optimal ET sequence: 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992

Badness (Sintel): 0.358

Sif

Sif tempers out 2097152/2096325, and extends to a strong 13-limit temperament by virtue of the identity 2097152/2096325 = (4096/4095)⋅(6656/6655). It was named by Flora Canou in 2023 as a sharp-tending counterpart of thor.

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 2097152/2096325

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

mapping generators: ~99/70, ~3

Optimal tunings:

  • WE: ~99/70 = 599.9863 ¢, ~3/2 = 701.9658 ¢, ~48/35 = 546.5930 ¢
error map: ⟨-0.027 -0.017 +0.045 +0.052 +0.000]
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9755 ¢, ~48/35 = 546.6052 ¢
error map: ⟨0.000 +0.021 +0.107 +0.124 +0.101]

Optimal ET sequence: 22, 46, 68, 114, 134, 156, 178, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2742, 3236, 3506, 4742d, 10990ccdde, 15732ccdddee

Badness (Sintel): 0.508

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 4096/4095, 6656/6655, 9801/9800

Mapping: [⟨2 0 1 7 11 16], ⟨0 1 0 1 -1 -3], ⟨0 0 4 -5 -1 1]]

Optimal tunings:

  • WE: ~99/70 = 599.9857 ¢, ~3/2 = 701.9705 ¢, ~48/35 = 546.5927 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 701.9877 ¢, ~48/35 = 546.6058 ¢

Optimal ET sequence: 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff

Badness (Sintel): 0.317

Loki

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 9801/9800

Mapping: [⟨2 0 0 -21 -18], ⟨0 1 0 4 2], ⟨0 0 1 3 4]]

mapping generators: ~99/70, ~3, ~5

Optimal tunings:

  • WE: ~99/70 = 599.9481 ¢, ~3/2 = 702.1195 ¢, ~5/4 = 386.7636 ¢
error map: ⟨-0.104 +0.061 +0.242 -0.005 -0.128]
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.1647 ¢, ~5/4 = 386.7768 ¢
error map: ⟨0.000 +0.210 +0.463 +0.163 +0.119]

Optimal ET sequence: 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c

Badness (Sintel): 0.592

Pessoal

See also: Pessoalisma

Pessoal tempers out the olympia. It was named by Aura in 2023, meaning "personal", for the fact that it is associated with abigail, which is in turn a person's name.

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 131072/130977

Mapping: [⟨2 0 1 10 14], ⟨0 1 0 -1 -3], ⟨0 0 3 -1 2]]

mapping generators: ~99/70, ~3, ~32/21

Optimal tunings:

  • WE: ~99/70 = 599.9711 ¢, ~3/2 = 702.0265 ¢, ~32/21 = 728.7942 ¢
error map: ⟨-0.058 +0.014 +0.040 +0.122 -0.040]
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.0635 ¢, ~32/21 = 728.8214 ¢
error map: ⟨0.000 +0.109 +0.150 +0.289 +0.134]

Optimal ET sequence: 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde

Badness (Sintel): 0.599

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 4096/4095

Mapping: [⟨2 0 1 10 14 13], ⟨0 1 0 -1 -3 -1], ⟨0 0 3 -1 2 -2]]

Optimal tunings:

  • WE: ~99/70 = 599.9835 ¢, ~3/2 = 702.0253 ¢, ~32/21 = 728.7700 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~3/2 = 702.0477 ¢, ~32/21 = 728.7882 ¢

Optimal ET sequence: 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d

Badness (Sintel): 0.366

Linus

Main article: Linus
For the 7-limit version, see Miscellaneous 7-limit temperaments #Linus.

Linus tempers out the linus comma, [11 -10 -10 10⟩ in the 7-limit and can be described as the 80 & 130 & 270 temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 391314/390625

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

Optimal tunings:

  • WE: ~15/14 = 119.9975 ¢, ~3/2 = 702.0188 ¢, ~5/4 = 386.6399 ¢
error map: ⟨-0.025 +0.039 +0.276 -0.215 -0.143]
  • CWE: ~15/14 = 120.0000 ¢, ~3/2 = 702.0181 ¢, ~5/4 = 386.6218 ¢
error map: ⟨0.000 +0.063 +0.308 -0.186 -0.092]

Optimal ET sequence: 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c

Badness (Sintel): 1.34

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 4225/4224, 4459/4455

Mapping: [⟨10 0 0 -11 4 37], ⟨0 1 0 1 -1 0], ⟨0 0 1 1 2 0]]

Optimal tunings:

  • WE: ~15/14 = 120.0054 ¢, ~3/2 = 701.9625 ¢, ~5/4 = 386.4910 ¢
  • CWE: ~15/14 = 120.0000 ¢, ~3/2 = 701.9533 ¢, ~5/4 = 386.5119 ¢

Optimal ET sequence: 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def

Badness (Sintel): 0.721

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