Gamelismic family: Difference between revisions

Line 1:

~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

__FORCETOC__

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

=Gamelan=

~~: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2014-02-08 20:13:15 UTC</tt>.<br>~~

''Gamelan temperament'' is the rank three [[Harmonic_Limit|7-limit]] [[Regular_Temperaments|temperament]] tempering out 1029/1024.

~~: The original revision id was <tt>488195934</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=

//Gamelan temperament// is the rank three [[~~Harmonic Limit~~|7-limit]] [[~~Regular Temperaments~~|temperament]] tempering out 1029/1024.

[[Comma|Comma]]: c = 1029/1024

~~[[Comma]]~~: ~~c = 1029~~/~~1024~~

7-limit minimax tuning: 3, 5, and 7 1/4c flat

~~7-limit minimax tuning: 3, 5, and 7 1/4c flat~~

9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat

TOP-RMS: <1200.486 1901.833 2786.314 3367.676|

[[Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5)

[[Minkowski_lattice_basis|Minkowski lattice basis]]: 8/7 length 0.5192, 5/4 length = log2(5)

Angle(8/7, 5/4) = 90 degrees

Map to lattice: [<0 3 0 -1|, <0 0 1 0|]

Map: [<1 1 0 3|, <0 3 0 -1|,<0 0 1 0|]

[[~~edo~~|EDOs]]: 5, 10, 15, 26, 31, 41, 72, [[118edo|118]], [[159edo|159]], [[190edo|190]]

[[EDO|EDOs]]: 5, 10, 15, 26, 31, 41, 72, [[118edo|118]], [[159edo|159]], [[190edo|190]]

Badness: 0.000176

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

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

=Portent=

Portent has a [[~~Normal lists~~|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.

Portent has a [[Normal_lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.

[[Comma|Commas]]: c = 1029/1024, e = 385/384

Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat

[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>,

|39/14 4/7 1/2 -2/7 -1/2>,

|20/7 -2/7 0 1/7 0>,

|39/14 4/7 -1/2 -2/7 1/2>]

[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7

[[Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931

[[Minkowski_lattice_basis|Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931

Angle(8/7, 12/11) = 86.657 degrees

Map to lattice: [<0 3 1 -1 3|, <0 0 1 0 -1|]

Map: [<1 1 0 3 5|, <0 3 0 -1 4| <0 0 1 0 -1|]

[[~~Generator~~|Generators]]: 2, 8/7, 5

[[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

==Portending==

Commas: 325/324, 364/363, 441/440

Map: [<1 1 0 3 5 6|, <0 3 0 -1 4 12| <0 0 1 0 -1 -2|]

EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf

Badness: 0.000627

==Portentous==

Commas: 385/384, 441/440, 625/624

Map: [<1 1 0 3 5 -5|, <0 3 0 -1 4 -3| <0 0 1 0 -1 4|]

EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef

Badness: 0.000662

==Ominous==

Commas: 351/350, 385/384, 441/440

Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 -10| <0 0 1 0 -1 2|]

EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef

Badness: 0.000751

===17-limit===

Commas: 273/272, 351/350, 441/440, 561/560

Minimax tuning

[|1 0 0 0 0 0 0>,

|7/4 9/10 0 0 -3/10 -3/20 0>,

Line 81:

Line 94:

|7/2 -1/5 0 0 -3/5 7/10 0>,

|4 2/5 0 0 -4/5 3/5 0>]

Eigenmonzos: 2, 13/11, 11/9

Lattice basis: 8/7 0.3859 6/5 1.1303

Angle(8/7, 6/5) = 98.6015

Map to lattice: [<0 1 1 0 0 -1 0|, <0 -1 -1 0 -1 2 1|]

Map: [<1 1 0 3 5 1 1|, <0 3 0 -1 4 -10 -8|,

<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==

Commas: 196/195, 352/351, 385/384

Map: [<1 1 0 3 5 7|, <0 3 0 -4 1 -5|, <0 0 1 0 -1 -1|]

EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def

Badness: 0.000832

==Foreboding==

Commas: 105/104, 144/143, 275/273

Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 2|, <0 0 1 0 -1 1|]

[[~~edo~~|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]

[[EDO|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]

Badness: 0.000873

=Gamel=

Commas: 1029/1024, 540/539

Map: [<1 1 0 3 -1|, <0 3 0 -1 11|, <0 0 1 0 1|]

EDOs: 10, 31, 41, 72

Badness: 0.000853~~</pre></div>~~

~~<h4>Original HTML content:</h4>~~

Badness: 0.000853

<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"><html><head><title>Gamelismic~~ family</title></head><body><a href="#Gamelan">Gamelan</a> | <a href="#Portent">Portent</a> | <a href="#Gamel">Gamel</a>

[[Category:family]]

<h1 id="toc0"><a name="Gamelan"></a>Gamelan</h1>

[[Category:gamelan]]

<em>Gamelan temperament</em> is the rank three <a class="wiki_link" href="/Harmonic%20Limit">7-limit</a> <a class="wiki_link" href="/Regular%20Temperaments">temperament</a> tempering out 1029/1024.<br />

[[Category:gamelismic]]

~~<br />~~

[[Category:planar]]

~~<br />~~

[[Category:theory]]

~~<a class="wiki_link" href="/Comma">Comma</a>: c = 1029/1024<br />~~

~~<br />~~

~~7-limit minimax tuning: 3, 5, and 7 1/4c flat<br />~~

~~9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat<br />~~

~~TOP-RMS: &lt;1200.486 1901.833 2786.314 3367.676|<br />~~

~~<a class="wiki_link" href="/Minkowski%20lattice%20basis">Minkowski lattice basis</a>: 8/7 length 0.5192, 5/4 length = log2(5)<br />~~

~~Angle(8/7, 5/4) = 90 degrees<br />~~

~~Map to lattice:~~ [~~&lt;0 3 0 -1|, &lt;0 0 1 0|]<br />~~

~~<br />~~

~~Map~~: ~~[&lt;1 1 0 3|, &lt;0 3 0 -1|,&lt;0 0 1 0|~~]~~<br />~~

~~Badness: 0.000176<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 3 1024/343 to 2.5.7<br />~~

~~<br />~~

~~<h1 id="toc1"><a name="Portent"></a>Portent</h1>~~

~~Portent has a <a class="wiki_link" href="/Normal%20lists">normal comma list</a> [1029/1024, 385/384~~] ~~and also tempers out 441/440.<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Comma">Commas</a>: c = 1029/1024, e = 385/384<br />~~

~~<br />~~

~~Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat<br />~~

[~~|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,<br />~~

~~|39/14 4/7 1/2 -2/7 -1/2&gt;,<br />~~

~~|20/7 -2/7 0 1/7 0&gt;,<br />~~

~~|39/14 4/7 -1/2 -2/7 1/2&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/10, 9/7<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Minkowski%20lattice%20basis">Minkowski lattice basis</a>: 8/7 length 0.46467, 12/11 length 1.931<br />~~

~~Angle(8/7, 12/11) = 86.657 degrees<br />~~

~~Map to lattice:~~ [~~&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]<br />~~

~~<br />~~

~~Map~~: ~~[&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|~~]~~<br />~~

~~<a class="wiki_link" href="/Generator">Generators</a>: 2, 8/7, 5<br />~~

~~EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190<br />~~

~~Badness: 0.000234<br />~~

~~<br />~~

~~Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7<br />~~

~~<br />~~

~~<h2 id="toc2"><a name="Portent-Portending"></a>Portending</h2>~~

~~Commas: 325/324, 364/363, 441/440<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 5 6|, &lt;0 3 0 -1 4 12| &lt;0 0 1 0 -1 -2|~~]~~<br />~~

~~EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf<br />~~

~~Badness: 0.000627<br />~~

~~<br />~~

~~<h2 id="toc3"><a name="Portent-Portentous"></a>Portentous</h2>~~

~~Commas: 385/384, 441/440, 625/624<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 0 3 5 -5|, &lt;0 3 0 -1 4 -3| &lt;0 0 1 0 -1 4|]<br />~~

~~EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef<br />~~

~~Badness: 0.000662<br />~~

~~<br />~~

~~<h2 id="toc4"><a name="Portent-Ominous"></a>Ominous</h2>~~

~~Commas: 351/350, 385/384, 441/440<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 -10| &lt;0 0 1 0 -1 2|]<br />~~

~~EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef<br />~~

~~Badness: 0.000751<br />~~

~~<br />~~

~~<h3 id="toc5"><a name="Portent-Ominous-17-limit"></a>17-limit</h3>~~

~~Commas~~: ~~273/272, 351/350, 441/440, 561/560<br />~~

~~<br />~~

~~Minimax tuning<br />~~

~~[|1 0 0 0 0 0 0&gt;,<br />~~

~~|7/4 9/10 0 0 -3/10 -3/20 0&gt;,<br />~~

~~|5/2 7/5 0 0 -4/5 1/10 0&gt;,<br />~~

~~|11/4 -3/10 0 0 1/10 1/20 0&gt;,<br />~~

~~|7/2 -1/5 0 0 2/5 -3/10 0&gt;,<br />~~

~~|7/2 -1/5 0 0 -3/5 7/10 0&gt;,<br />~~

~~|4 2/5 0 0 -4/5 3/5 0&gt;~~]~~<br />~~

~~Eigenmonzos: 2, 13/11, 11/9<br />~~

~~<br />~~

~~Lattice basis: 8/7 0.3859 6/5 1.1303<br />~~

~~Angle(8/7, 6/5) = 98.6015<br />~~

~~Map to lattice: [&lt;0 1 1 0 0 -1 0|, &lt;0 -1 -1 0 -1 2 1|~~]~~<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 0 3 5 1 1|, &lt;0 3 0 -1 4 -10 -8|,<br />~~

~~&lt;0 0 1 0 -1 2 2|]<br />~~

~~Generators: 2, 8/7, 5<br />~~

~~EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef<br />~~

~~Badness: 0.000612<br />~~

~~<br />~~

~~<h2 id="toc6"><a name="Portent-Momentous"></a>Momentous</h2>~~

~~Commas: 196/195, 352/351, 385/384<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 1 0 3 5 7|, &lt;0 3 0 -4 1 -5|, &lt;0 0 1 0 -1 -1|]<br />~~

~~EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def<br />~~

~~Badness: 0.000832<br />~~

~~<br />~~

~~<h2 id="toc7"><a name="Portent-Foreboding"></a>Foreboding</h2>~~

~~Commas: 105/104, 144/143, 275/273<br />~~

~~<br />~~

~~Map~~: ~~[&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 2|, &lt;0 0 1 0 -1 1|~~]~~<br />~~

~~Badness: 0.000873<br />~~

~~<br />~~

~~<h1 id="toc8"><a name="Gamel"></a>Gamel</h1>~~

~~Commas: 1029/1024, 540/539<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 -1|, &lt;0 3 0 -1 11|, &lt;0 0 1 0 1|~~]~~<br />~~

~~EDOs: 10, 31, 41, 72<br />~~

~~Badness: 0.000853</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+__FORCETOC__
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+=Gamelan=
-: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2014-02-08 20:13:15 UTC</tt>.<br>
+''Gamelan temperament'' is the rank three [[Harmonic_Limit|7-limit]] [[Regular_Temperaments|temperament]] tempering out 1029/1024.
-: The original revision id was <tt>488195934</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=
-//Gamelan temperament// is the rank three [[Harmonic Limit|7-limit]] [[Regular Temperaments|temperament]] tempering out 1029/1024.
+[[Comma|Comma]]: c = 1029/1024
-[[Comma]]: c = 1029/1024
+-limit minimax tuning: 3, 5, and 7 1/4c flat
--limit minimax tuning: 3, 5, and 7 1/4c flat
 -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)
+[[Minkowski_lattice_basis|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|]
-[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, 72, [[118edo|118]], [[159edo|159]], [[190edo|190]]
+[[EDO|EDOs]]: 5, 10, 15, 26, 31, 41, 72, [[118edo|118]], [[159edo|159]], [[190edo|190]]
 Badness: 0.000176
-[[Projection pair]]: 3 1024/343 to 2.5.7
+[[Projection_pair|Projection pair]]: 3 1024/343 to 2.5.7
 =Portent=
-Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.
+Portent has a [[Normal_lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.
 [[Comma|Commas]]: c = 1029/1024, e = 385/384
 Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
 [|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,
 |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
+[[Minkowski_lattice_basis|Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931
 Angle(8/7, 12/11) = 86.657 degrees
 Map to lattice: [&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]
 Map: [&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|]
-[[Generator|Generators]]: 2, 8/7, 5
+[[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
 ==Portending==
 Commas: 325/324, 364/363, 441/440
 Map: [&lt;1 1 0 3 5 6|, &lt;0 3 0 -1 4 12| &lt;0 0 1 0 -1 -2|]
 EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf
 Badness: 0.000627
 ==Portentous==
 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|]
 EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef
 Badness: 0.000662
 ==Ominous==
 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|]
 EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef
 Badness: 0.000751
 ===17-limit===
 Commas: 273/272, 351/350, 441/440, 561/560
 Minimax tuning
 [|1 0 0 0 0 0 0&gt;,
 |7/4 9/10 0 0 -3/10 -3/20 0&gt;,
@@ Line 81: / Line 94: @@
 |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
 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|,
 &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==
 Commas: 196/195, 352/351, 385/384
 Map: [&lt;1 1 0 3 5 7|, &lt;0 3 0 -4 1 -5|, &lt;0 0 1 0 -1 -1|]
 EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def
 Badness: 0.000832
 ==Foreboding==
 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|]
-[[edo|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]
+[[EDO|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]
 Badness: 0.000873
 =Gamel=
 Commas: 1029/1024, 540/539
 Map: [&lt;1 1 0 3 -1|, &lt;0 3 0 -1 11|, &lt;0 0 1 0 1|]
 EDOs: 10, 31, 41, 72
-Badness: 0.000853</pre></div>
-<h4>Original HTML content:</h4>
+Badness: 0.000853
-<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:18:&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:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;a href="#Gamelan"&gt;Gamelan&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Portent"&gt;Portent&lt;/a&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;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Gamel"&gt;Gamel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
+[[Category:family]]
-&lt;!-- ws:end:WikiTextTocRule:28 --&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;
+[[Category:gamelan]]
- &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;
+[[Category:gamelismic]]
-&lt;br /&gt;
+[[Category:planar]]
-&lt;br /&gt;
+[[Category:theory]]
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: c = 1029/1024&lt;br /&gt;
-&lt;br /&gt;
--limit minimax tuning: 3, 5, and 7 1/4c flat&lt;br /&gt;
--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, &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;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Gamel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Gamel&lt;/h1&gt;
- Commas: 1029/1024, 540/539&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 -1|, &amp;lt;0 3 0 -1 11|, &amp;lt;0 0 1 0 1|]&lt;br /&gt;
-EDOs: 10, 31, 41, 72&lt;br /&gt;
-Badness: 0.000853&lt;/body&gt;&lt;/html&gt;</pre></div>