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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>
The '''gamelismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[gamelisma]], 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same [[2.3.7 subgroup|2.3.7-subgroup]] structure as [[slendric]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-11 23:21:37 UTC</tt>.<br>
: The original revision id was <tt>274561190</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]]


=Gamelan=
See [[Gamelismic clan]] for the rank-2 temperament without the last generator of gamelismic, and its various extensions.  
//Gamelan temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024.  


== Gamelismic ==
{{Main| Gamelismic and portent }}


[[Comma]]: c = 1029/1024
[[Subgroup]]: 2.3.5.7


7-limit minimax tuning: 3, 5, and 7 1/4c flat
[[Comma list]]: 1029/1024
9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat
TOP-RMS: &lt;1200.486 1901.833 2786.314 3367.676|
[[Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5)
Angle(8/7, 5/4) = 90 degrees
Map to lattice: [&lt;0 3 0 -1|, &lt;0 0 1 0|]


Map: [&lt;1 1 0 3|, &lt;0 3 0 -1|,&lt;0 0 1 0|]
{{Mapping|legend=1| 1 1 0 3 | 0 3 0 -1 | 0 0 1 0 }}
[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, 72, 118, [[118edo|118]], [[159edo|159]], [[190edo|190]]
: mapping generators: ~2, ~8/7, ~5
Badness: 0.000176
 
[[Mapping to lattice]]: [{{val| 0 3 0 -1 }}, {{val| 0 0 1 0 }}]
 
[[Minkowski lattice basis]]:  
: 8/7 length = 0.5192, 5/4 length = log<sub>2</sub>5
: Angle (8/7, 5/4) = 90 degrees
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4859{{c}}, ~8/7 = 233.7822{{c}}, ~5/4 = 385.3412{{c}}
: [[error map]]: {{val| +0.486 -0.123 -0.001 -1.151 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7474{{c}}, ~5/4 = 385.5205{{c}}
: error map: {{val| 0.000 -0.713 -0.793 -2.573 }}
 
[[Minimax tuning]]: ''c'' = 1029/1024
* [[7-odd-limit]]: 3, 5, and 7 (1/4)''c'' flat
: {{Monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 5/2 -1/4 1 -3/4 | 5/2 -1/4 0 1/4 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3.5/3
* [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat
: {{Monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 10/7 -1/7 1 -3/7 | 20/7 -2/7 0 1/7 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7
 
{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 190 }}
 
[[Badness]] (Sintel): 0.777


[[Projection pair]]: 3 1024/343 to 2.5.7
[[Projection pair]]: 3 1024/343 to 2.5.7


=Portent=
Scales: [[portent26]]
Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.  
 
== Portent ==
{{Main| Gamelismic and portent }}
 
Portent tempers out [[385/384]] and [[441/440]] and is the main extension of gamelismic. Notice the identity 1029/1024 = (385/384)⋅(441/440).
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 385/384, 441/440
 
{{Mapping|legend=1| 1 1 0 3 5 | 0 3 0 -1 4 | 0 0 1 0 -1 }}
 
[[Mapping to lattice]]: [{{val| 0 3 1 -1 3 }}, {{val| 0 0 1 0 -1 }}]
 
Minkowski lattice basis:
: 8/7 length = 0.46467, 12/11 length = 1.931
: Angle (8/7, 12/11) = 86.657 degrees
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4902{{c}}, ~8/7 = 233.7839{{c}}, ~5/4 = 385.3191{{c}}
: [[error map]]: {{val| +0.490 -0.113 -0.014 -1.139 -0.031 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7616{{c}}, ~5/4 = 385.3149{{c}}
: error map: {{val| 0.000 -0.670 -0.999 -2.587 -1.586 }}
 
[[Minimax tuning]]: ''c''<sub>1</sub> = 1029/1024, ''c''<sub>2</sub> = 385/384
* [[11-odd-limit]]: 3 (1/7)''c''<sub>1</sub> flat, 5 and 7 (2/7)''c''<sub>1</sub> flat, 11 (''c''<sub>2</sub> - (3/7)''c''<sub>1</sub>) flat
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 39/14 4/7 -1/2 -2/7 1/2 }}]
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/5
 
{{Optimal ET sequence|legend=1| 15, 26, 31, 41, 72, 118, 159, 190 }}
 
[[Badness]] (Sintel): 0.281
 
[[Projection pair]]s: 3 1024/343 11 131072/12005 to 2.5.7
 
Scales: [[portent26]]
 
=== Portending ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 364/363, 385/384
 
Mapping: {{mapping| 1 1 0 3 5 6 | 0 3 0 -1 4 12 | 0 0 1 0 -1 -2 }}
 
Optimal tunings:
* WE: ~2 = 1200.4540{{c}}, ~8/7 = 234.0013{{c}}, ~5/4 = 384.8733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9748{{c}}, ~5/4 = 384.8812{{c}}
 
{{Optimal ET sequence|legend=0| 15, 26, 31f, 41, 46, 72, 87, 159 }}
 
Badness (Sintel): 0.587
 
Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13
 
=== Portentous ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 385/384, 441/440, 625/624
 
Mapping: {{mapping| 1 1 0 3 5 -5 | 0 3 0 -1 4 -3 | 0 0 1 0 -1 4 }}
 
Optimal tunings:
* WE: ~2 = 1200.4888{{c}}, ~8/7 = 233.7795{{c}}, ~5/4 = 385.1398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7575{{c}}, ~5/4 = 385.1447{{c}}
 
{{Optimal ET sequence|legend=0| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 452cdef, 611cddef }}
 
Badness (Sintel): 0.618
 
=== Ominous ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 385/384, 441/440
 
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 -10 | 0 0 1 0 -1 2 }}
 
Optimal tunings:
* WE: ~2 = 1200.7019{{c}}, ~8/7 = 233.5453{{c}}, ~5/4 = 385.6079{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4510{{c}}, ~5/4 = 385.6739{{c}}
 
{{Optimal ET sequence|legend=0| 15f, 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}
 
Badness (Sintel): 0.702
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 351/350, 385/384, 441/440
 
Mapping: {{mapping| 1 1 0 3 5 1 1 | 0 3 0 -1 4 -10 -8 | 0 0 1 0 -1 2 2 }}
 
Mapping to lattice: [{{val| 0 1 1 0 0 -1 0 }}, {{val| 0 -1 -1 0 -1 2 1 }}]
 
Lattice basis:
: 8/7 length = 0.3859, 6/5 length = 1.1303
: Angle (8/7, 6/5) = 98.6015
 
Optimal tunings:
* WE: ~2 = 1200.6745{{c}}, ~8/7 = 233.5625{{c}}, ~5/4 = 385.5056{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4679{{c}}, ~5/4 = 385.5892{{c}}
 
Minimax tuning:
* 17-odd-limit
: [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 7/4 9/10 0 0 -3/10 -3/20 0 }}, {{monzo| 5/2 7/5 0 0 -4/5 1/10 0 }}, {{monzo| 11/4 -3/10 0 0 1/10 1/20 0 }}, {{monzo| 7/2 -1/5 0 0 2/5 -3/10 0 }}, {{monzo| 7/2 -1/5 0 0 -3/5 7/10 0 }}, {{monzo| 4 2/5 0 0 -4/5 3/5 0 }}]
: unchanged-interval (eigenmonzo) basis: 2.11/9.13/9
 
{{Optimal ET sequence|legend=0| 15f, 20c, 26, 31, 46, 72, 103, 149, 221ef }}
 
Badness (Sintel): 0.582
 
=== Momentous ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 385/384
 
Mapping: {{mapping| 1 1 0 3 5 7 | 0 3 0 -4 1 -5 | 0 0 1 0 -1 -1 }}
 
Optimal tunings:
* WE: ~2 = 1200.0652{{c}}, ~8/7 = 234.1856{{c}}, ~5/4 = 386.6199{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.1748{{c}}, ~5/4 = 386.5951{{c}}
 
{{Optimal ET sequence|legend=0| 15f, 21e, 31, 41, 46, 72f, 77, 87, 118, 164, 205d }}
 
Badness (Sintel): 0.778
 
=== Foreboding ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 275/273
 
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 2 | 0 0 1 0 -1 1 }}
 
Optimal tunings:
* WE: ~2 = 1200.2251{{c}}, ~8/7 = 233.4102{{c}}, ~5/4 = 382.4142{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4017{{c}}, ~5/4 = 382.4261{{c}}
 
{{Optimal ET sequence|legend=0| 5, 10, 15, 25e, 26, 31, 41, 72f }}
 
Badness (Sintel): 0.816
 
=== Portannic ===
Subgroup: 2.3.5.7.11.13


[[Comma|Commas]]: c = 1029/1024, e = 385/384
Comma list: 385/384, 441/440, 10985/10976


Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11  e-3/7c flat
Mapping: {{mapping| 1 1 2 3 3 4 | 0 3 0 -1 4 -1 | 0 0 3 0 -3 -1 }}
[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,
: mapping generators: ~2, ~8/7, ~14/13
|39/14 4/7 1/2 -2/7 -1/2&gt;,
|20/7 -2/7 0 1/7 0&gt;,
|39/14 4/7 -1/2 -2/7 1/2&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7


[[Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931
Optimal tunings:  
Angle(8/7, 12/11) = 86.657 degrees
* WE: ~2 = 1200.5451{{c}}, ~8/7 = 233.7495{{c}}, ~14/13 = 128.4023{{c}}
Map to lattice: [&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6930{{c}}, ~14/13 = 128.3684{{c}}


Map: [&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|]
{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}
[[Generator|Generators]]: 2, 8/7, 5
Edos: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190
Badness: 0.000234


Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7
Badness (Sintel): 1.67


==Portending==
==== 17-limit ====
Commas: 325/324, 364/363, 441/440
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 1 0 3 5 6|, &lt;0 3 0 -1 4 12| &lt;0 0 1 0 -1 -2|]
Comma list: 273/272, 385/384, 441/440, 8624/8619
EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf
Badness: 0.000627


==Portentous==
Mapping: {{mapping| 1 1 2 3 3 4 4 | 0 3 0 -1 4 -1 1 | 0 0 3 0 -3 -1 -1 }}
Commas: 385/384, 441/440, 625/624


Map: [&lt;1 1 0 3 5 -5|, &lt;0 3 0 -1 4 -3| &lt;0 0 1 0 -1 4|]
Optimal tunings:  
EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef
* WE: ~2 = 1200.4416{{c}}, ~8/7 = 233.7663{{c}}, ~14/13 = 128.4622{{c}}
Badness: 0.000662
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7173{{c}}, ~14/13 = 128.4269{{c}}


==Ominous==
{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}
Commas: 351/350, 385/384, 441/440


Map: [&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 -10| &lt;0 0 1 0 -1 2|]
Badness (Sintel): 1.24
EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef
Badness: 0.000751


===17-limit===
== Gamel ==
Commas: 273/272, 351/350, 441/440, 561/560
This esoteric alternative extension tempers out [[540/539]], and sometimes comes up in temperament searches. In practice however, it is almost always desirable to further temper it to [[miracle]], in which case is is identical to portent anyway. This enables many more [[essentially tempered chord]]s while introducing virtually no additional error.


Minimax tuning
[[Subgroup]]: 2.3.5.7.11
[|1 0 0 0 0 0 0&gt;,
|7/4 9/10 0 0 -3/10 -3/20 0&gt;,
|5/2 7/5 0 0 -4/5 1/10 0&gt;,
|11/4 -3/10 0 0 1/10 1/20 0&gt;,
|7/2 -1/5 0 0 2/5 -3/10 0&gt;,
|7/2 -1/5 0 0 -3/5 7/10 0&gt;,
|4 2/5 0 0 -4/5 3/5 0&gt;]
Eigenmonzos: 2, 13/11, 11/9


Lattice basis: 8/7 0.3859 6/5 1.1303
[[Comma list]]: 540/539, 1029/1024
Angle(8/7, 6/5) = 98.6015
Map to lattice: [&lt;0 1 1 0 0 -1 0|, &lt;0 -1 -1 0 -1 2 1|]


Map: [&lt;1 1 0 3 5 1 1|, &lt;0 3 0 -1 4 -10 -8|,
{{Mapping|legend=1| 1 1 0 3 -1 | 0 3 0 -1 11 | 0 0 1 0 1 }}
&lt;0 0 1 0 -1 2 2|]
Generators: 2, 8/7, 5
EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef
Badness: 0.000612


==Momentous==
[[Optimal tuning]]s:
Commas: 196/195, 352/351, 385/384
* [[WE]]: ~2 = 1200.6462{{c}}, ~8/7 = 233.4166{{c}}, ~5/4 = 384.4189{{c}}
: [[error map]]: {{val| +0.646 -1.059 -0.602 -0.304 +1.329 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.3289{{c}}, ~5/4 = 384.5627{{c}}
: error map: {{val| 0.000 -1.968 -1.751 -2.155 -0.137 }}


Map: [&lt;1 1 0 3 5 7|, &lt;0 3 0 -4 1 -5|, &lt;0 0 1 0 -1 -1|]
{{Optimal ET sequence|legend=1| 5e, 10, 21e, 26e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}
EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def
Badness: 0.000832


==Foreboding==
[[Badness]] (Sintel): 1.02
Commas: 105/104, 144/143, 275/273


Map: [&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 2|, &lt;0 0 1 0 -1 1|]
[[Category:Gamelismic family| ]] <!-- main article -->
[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]
[[Category:Temperament families]]
Badness: 0.000873</pre></div>
[[Category:Catalogs of rank-3 temperaments]]
<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;Gamelismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:16:&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:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;a href="#Gamelan"&gt;Gamelan&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Portent"&gt;Portent&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Gamelan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Gamelan&lt;/h1&gt;
&lt;em&gt;Gamelan temperament&lt;/em&gt; is the rank three &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt; tempering out 1029/1024. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: c = 1029/1024&lt;br /&gt;
&lt;br /&gt;
7-limit minimax tuning: 3, 5, and 7 1/4c flat&lt;br /&gt;
9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat&lt;br /&gt;
TOP-RMS: &amp;lt;1200.486 1901.833 2786.314 3367.676|&lt;br /&gt;
&lt;a class="wiki_link" href="/Minkowski%20lattice%20basis"&gt;Minkowski lattice basis&lt;/a&gt;: 8/7 length 0.5192, 5/4 length = log2(5)&lt;br /&gt;
Angle(8/7, 5/4) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 3 0 -1|, &amp;lt;0 0 1 0|] &lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3|, &amp;lt;0 3 0 -1|,&amp;lt;0 0 1 0|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: 5, 10, 15, 26, 31, 41, 72, 118, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/190edo"&gt;190&lt;/a&gt;&lt;br /&gt;
Badness: 0.000176&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 3 1024/343 to 2.5.7&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Portent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Portent&lt;/h1&gt;
Portent has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; [1029/1024, 385/384] and also tempers out 441/440. &lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: c = 1029/1024, e = 385/384&lt;br /&gt;
&lt;br /&gt;
Minimax:  3 1/7c flat, 5 and 7 2/7c flat, 11  e-3/7c flat&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |10/7 6/7 0 -3/7 0&amp;gt;, &lt;br /&gt;
|39/14 4/7 1/2 -2/7 -1/2&amp;gt;,&lt;br /&gt;
|20/7 -2/7 0 1/7 0&amp;gt;, &lt;br /&gt;
|39/14 4/7 -1/2 -2/7 1/2&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 9/7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Minkowski%20lattice%20basis"&gt;Minkowski lattice basis&lt;/a&gt;: 8/7 length 0.46467, 12/11 length 1.931&lt;br /&gt;
Angle(8/7, 12/11) = 86.657 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 3 1 -1 3|, &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5|, &amp;lt;0 3 0 -1 4| &amp;lt;0 0 1 0 -1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 8/7, 5&lt;br /&gt;
Edos: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190&lt;br /&gt;
Badness: 0.000234&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Portent-Portending"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Portending&lt;/h2&gt;
Commas: 325/324, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 6|, &amp;lt;0 3 0 -1 4 12| &amp;lt;0 0 1 0 -1 -2|]&lt;br /&gt;
EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf&lt;br /&gt;
Badness: 0.000627&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Portent-Portentous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Portentous&lt;/h2&gt;
Commas: 385/384, 441/440, 625/624&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 -5|, &amp;lt;0 3 0 -1 4 -3| &amp;lt;0 0 1 0 -1 4|]&lt;br /&gt;
EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef&lt;br /&gt;
Badness: 0.000662&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Portent-Ominous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Ominous&lt;/h2&gt;
Commas: 351/350, 385/384, 441/440&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 0 -1 4 -10| &amp;lt;0 0 1 0 -1 2|]&lt;br /&gt;
EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef&lt;br /&gt;
Badness: 0.000751&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Portent-Ominous-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;17-limit&lt;/h3&gt;
Commas: 273/272, 351/350, 441/440, 561/560&lt;br /&gt;
&lt;br /&gt;
Minimax tuning&lt;br /&gt;
[|1 0 0 0 0 0 0&amp;gt;, &lt;br /&gt;
|7/4 9/10 0 0 -3/10 -3/20 0&amp;gt;, &lt;br /&gt;
|5/2 7/5 0 0 -4/5 1/10 0&amp;gt;, &lt;br /&gt;
|11/4 -3/10 0 0 1/10 1/20 0&amp;gt;, &lt;br /&gt;
|7/2 -1/5 0 0 2/5 -3/10 0&amp;gt;, &lt;br /&gt;
|7/2 -1/5 0 0 -3/5 7/10 0&amp;gt;, &lt;br /&gt;
|4 2/5 0 0 -4/5 3/5 0&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 13/11, 11/9&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 8/7 0.3859 6/5 1.1303&lt;br /&gt;
Angle(8/7, 6/5) = 98.6015&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 1 0 0 -1 0|, &amp;lt;0 -1 -1 0 -1 2 1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1 1|, &amp;lt;0 3 0 -1 4 -10 -8|, &lt;br /&gt;
&amp;lt;0 0 1 0 -1 2 2|]&lt;br /&gt;
Generators: 2, 8/7, 5&lt;br /&gt;
EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef&lt;br /&gt;
Badness: 0.000612&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Portent-Momentous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Momentous&lt;/h2&gt;
Commas: 196/195, 352/351, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 7|, &amp;lt;0 3 0 -4 1 -5|, &amp;lt;0 0 1 0 -1 -1|]&lt;br /&gt;
EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def&lt;br /&gt;
Badness: 0.000832&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Portent-Foreboding"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Foreboding&lt;/h2&gt;
Commas: 105/104, 144/143, 275/273&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 0 -1 4 2|, &amp;lt;0 0 1 0 -1 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: 5, 10, 15, 26, 31, 41, &lt;a class="wiki_link" href="/72edo"&gt;72f&lt;/a&gt;, &lt;a class="wiki_link" href="/185edo"&gt;185cf&lt;/a&gt;&lt;br /&gt;
Badness: 0.000873&lt;/body&gt;&lt;/html&gt;</pre></div>
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