Mirkwai family: Difference between revisions

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

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

The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.

~~: This revision was by author~~ [[~~User:genewardsmith|genewardsmith~~]] ~~and made on <tt>2011-08-22 13:35:31 UTC</tt>.<br>~~

~~: The original revision id was <tt>247712219</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~~]]

== Mirkwai ==

[[Subgroup]]: 2.3.5.7

~~The mirkwai family of~~ [[~~planar temperament~~]]~~s tempers out the mirkwai comma,~~ 16875/16807.

[[Comma list]]: 16875/16807 (mirkwai)

~~=Vital statistics=~~

[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 0 0 -5 -4 }}]

[[~~Comma~~]]: ~~mirkwai 16875/16807~~

~~7-limit minimax~~

Mapping generators: ~2, ~3, ~7/5

~~[|1 0 0 0>, |0 4/7 -4/7 5/7>~~,

~~|0 -~~3~~/7 3/7 5/7>~~, ~~|0 0 0 1>]~~

~~[[Eigenmonzo|Eigenmonzos]]: 2, 8/~~7~~, 6~~/5

9-limit ~~minimax~~

[[Minimax tuning]]:

[|1 0 0 0~~>~~, |0 8/11 -4/11 5/11~~>~~,

* [[7-odd-limit]]

|0 -6/11 3/11 10/11~~>~~, |0 0 0 1~~>~~]

: [{{monzo| 1 0 0 0 }}, {{monzo| 0 4/7 -4/7 5/7 }}, {{monzo| 0 -3/7 3/7 5/7 }}, {{monzo| 0 0 0 1 }}]

[[Eigenmonzo~~|Eigenmonzos~~]]: 2, 10/9, 8/7

: [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 6/5

* [[9-odd-limit]]

: [{{monzo| 1 0 0 0 }}, {{monzo| 0 8/11 -4/11 5/11 }}, {{monzo| 0 -6/11 3/11 10/11 }}, {{monzo| 0 0 0 1 }}]

: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7

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

~~[[Generator~~|~~Generators]]: 2~~, 3, ~~7/5~~

~~[[edo|Edos]]: [[72edo|~~72]], ~~[[152edo|~~152]], ~~[[193edo|193]], [[224edo|~~224~~]],~~ [[~~296edo|296]], [[327edo|327~~]]~~, [[775edo|775]]~~

[[Badness]]: 0.342 × 10<sup>-3</sup>

~~Badness~~: 0.~~000342~~

[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5

=Indra=

== Indra ==

[[Comma~~|Commas~~]]: 540/539, 1375/1372

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 540/539, 1375/1372

[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}]

Mapping generators: ~2, ~3, ~7/5

[[~~Minimax tuning~~]]

[[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]

[|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|Eigenmonzos]]: 2, 11/9, 5/4~~

Lattice basis: 15/14 length 0.6184 55/36 length 0.7585

Lattice basis:

Angle(15/14, 55/36) = 68.1048 ~~cents~~

: 15/14 length = 0.6184, 55/36 length = 0.7585

~~Map to lattice: [<0 2 1 2 3|, <0 -1 2 1 -3|]~~

: Angle (15/14, 55/36) = 68.1048 deg

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

[[Minimax tuning]]:

[[~~Generator|Generators~~]]: 2, 3, 7/5

* [[11-odd-limit]]

~~[[edo~~|~~Edos]]:~~ 31, 41, ~~[[72edo|~~72]], ~~[[152edo|~~152]], ~~[[224edo|~~224]], ~~[[296edo|296]]~~, [[~~703edo|703~~]]

: [{{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 }}]

~~Badness~~: 0.~~000266~~

: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4

{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}

[[Badness]]: 0.266 × 10<sup>-3</sup>

[[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5

Line 52:

Line 53:

Scales: [[indra31]]

==Shibi==

=== Shibi ===

~~Commas~~: 540/539, 729/728, 1375/1372

Subgroup: 2.3.5.7.11.13

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

Mapping: [{{val| 1 0 0 0 2 -3 }}, {{val| 0 1 3 3 0 3 }}, {{val| 0 0 -5 -4 4 }}]

{{Optimal ET sequence|legend=1| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}

Badness: 0.721 × 10<sup>-3</sup>

=== Yajna ===

Subgroup: 2.3.5.7.11.13

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

Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 0 0 -5 -4 3 -20 }}]

Mapping generators: ~2, ~3, ~7/5

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]]s (unchanged-intervals): 2, 10/9, 13/10

* 15-odd-limit minimax

: [{{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]]s (unchanged-intervals): 2, 14/13, 4/3

{{Optimal ET sequence|legend=1| 31, 49f, 72, 103, 121, 152f, 193, 224 }}

Badness: 0.700 × 10<sup>-3</sup>

=== Vibhu ===

Subgroup: 2.3.5.7.11.13

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

Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}]

{{Optimal ET sequence|legend=1| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}

~~Map~~: ~~[<1~~ 0 ~~0 0 2 -4 -3|, <0 1 3 3 0 11 3|, <0 0 -5~~ -4 3 ~~4|]~~

Badness: 0.826 × 10<sup>-3</sup>

~~EDOs: 41, 72, 111, 183, 224, 703~~

~~Badness: 0.000721~~

==~~Yajna~~==

=== Vish ===

~~[[Comma|Commas]]~~: ~~540/539, 625/624, 1375/1372~~

Subgroup: 2.3.5.7.11.13

~~13-limit minimax~~

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

~~[|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|Eigenmonzos]]: 2~~, 10/9, 13/10

~~15-limit minimax~~

Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}]

[|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|Eigenmonzos]~~]~~: 2, 14/13, 4/3~~

~~Map: [<1 0 0 0 2 -4~~|~~, <0~~ 1 ~~3 3 0 11|, <0 0 -5 -4 3 -20|]~~

~~[[Generator~~|~~Generators]]: 2, 3~~, ~~7/5~~

~~[[edo|Edos]]: [[31edo|31]]~~, ~~[[72edo|~~72]], ~~[[103edo|103]]~~, ~~[[193edo|~~193~~]], 224, 296, 520, 703~~

~~Badness: 0.000700~~

~~==Vibhu==~~

Badness: 0.930 × 10<sup>-3</sup>

~~[[Comma|Commas]]~~: ~~540~~/~~539, 1375/1372, 351/350~~

~~==Vish==~~

[[Category:Temperament families]]

[[~~Comma|Commas~~]]: ~~540/539, 1375/1372, 325/324~~

[[Category:Pages with mostly numerical content]]

~~</pre></div>~~

[[Category:Mirkwai family]]

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

[[Category:Rank 3]]

<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>Mirkwai family</title></head><body><a href="#Vital statistics">Vital statistics</a> | <a href="#Indra">Indra</a>

~~<br />~~

~~<br />~~

~~The mirkwai family of <a class="wiki_link" href="/planar%20temperament">planar temperament</a>s tempers out the mirkwai comma, 16875/16807.<br />~~

~~<br />~~

~~<h1 id="toc0"><a name="Vital statistics"></a>Vital statistics</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>: mirkwai 16875/16807<br />~~

~~<br />~~

~~7-limit minimax<br />~~

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

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

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7, 6/5<br />~~

~~<br />~~

~~9-limit minimax<br />~~

~~[|1 0 0 0&gt;, |0 8/11 -4/11 5/11&gt;, <br />~~

~~|0 -6/11 3/11 10/11&gt;, |0 0 0 1&gt;~~]~~<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9, 8/7<br />~~

~~<br />~~

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

~~<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br />~~

~~Badness: 0.000342<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 84375/16807 7 16875/2401 to 2.3.7/5<br />~~

~~<br />~~

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

~~<a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />~~

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

~~|6 6 -1 0 -3&gt;, |20 18 -6 0 -9&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>~~: ~~2, 11/9, 5/4<br />~~

~~<br />~~

~~Lattice basis: 15/14 length 0.6184 55/36 length 0.7585<br />~~

~~Angle(15/14, 55/36) = 68.1048 cents<br />~~

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

~~<br />~~

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

~~<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br />~~

~~Badness: 0.000266<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5<br />~~

~~<br />~~

~~Scales: <a class="wiki_link" href="/indra31">indra31</a><br />~~

~~<br />~~

~~<~~!-- ~~ws:start:WikiTextHeadingRule:4:&lt;h2&gt;~~ --~~><h2 id="toc2"><a name="Indra-Shibi"></a>Shibi</h2>~~

~~Commas: 540/539, 729/728, 1375/1372<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]<br />~~

~~EDOs: 41, 72, 111, 183, 224, 703<br />~~

~~Badness: 0.000721<br />~~

~~<br />~~

~~<h2 id="toc3"><a name="Indra-Yajna"></a>Yajna</h2>~~

~~<a class="wiki_link" href="/Comma">Commas</a>: 540/539, 625/624, 1375/1372<br />~~

~~<br />~~

~~13-limit minimax<br />~~

[~~|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;, <br />~~

~~|8/5 2/5 -3/5 0 0 2/5&gt;, <br />~~

~~|44/25 26/25 -24/25 0 0 11/25&gt;, <br />~~

~~|62/25 48/25 -27/25 0 0 3/25&gt;, <br />~~

~~|8/5 2/5 -8/5 0 0 7/5&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>~~: ~~2, 10/9, 13/10<br />~~

~~<br />~~

~~15-limit minimax<br />~~

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

~~|5/4 1/2 0 -5/16 0 5/16&gt;,<br />~~

~~|1 1 0 -1/4 0 1/4&gt;, <br />~~

~~|5/4~~ 3~~/2 0 3/16 0 -3/16&gt;, <br />~~

~~|1 1 0 -5/4 0 5/4&gt;~~]~~<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 14/13, 4/3<br />~~

~~<br />~~

~~Map: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|~~]~~<br />~~

~~<a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 7/5<br />~~

~~Badness: 0.000700<br />~~

~~<br />~~

~~<h2 id="toc4"><a name="Indra-Vibhu"></a>Vibhu</h2>~~

~~<a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372, 351/350<br />~~

~~<br />~~

~~<h2 id="toc5"><a name="Indra-Vish"></a>Vish</h2>~~

~~<a class="wiki_link" href="/Comma">Commas</a>: 540/539, 1375/1372, 325/324</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<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 '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 13:35:31 UTC</tt>.<br>
-: The original revision id was <tt>247712219</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]]
+== Mirkwai ==
+[[Subgroup]]: 2.3.5.7
-The mirkwai family of [[planar temperament]]s tempers out the mirkwai comma, 16875/16807.
+[[Comma list]]: 16875/16807 (mirkwai)
-=Vital statistics=
+[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 0 0 -5 -4 }}]
-[[Comma]]: mirkwai 16875/16807
--limit minimax
+Mapping generators: ~2, ~3, ~7/5
-[|1 0 0 0&gt;, |0 4/7 -4/7 5/7&gt;,
-|0 -3/7 3/7 5/7&gt;, |0 0 0 1&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 6/5
--limit minimax
+[[Minimax tuning]]:
-[|1 0 0 0&gt;, |0 8/11 -4/11 5/11&gt;,
+* [[7-odd-limit]]
-|0 -6/11 3/11 10/11&gt;, |0 0 0 1&gt;]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 0 4/7 -4/7 5/7 }}, {{monzo| 0 -3/7 3/7 5/7 }}, {{monzo| 0 0 0 1 }}]
-[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 8/7
+: [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 6/5
+* [[9-odd-limit]]
+: [{{monzo| 1 0 0 0 }}, {{monzo| 0 8/11 -4/11 5/11 }}, {{monzo| 0 -6/11 3/11 10/11 }}, {{monzo| 0 0 0 1 }}]
+: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7
-Map: [&lt;1 0 0 0|, &lt;0 1 3 3|, &lt;0 0 -5 -4|]
+{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }}
-[[Generator|Generators]]: 2, 3, 7/5
-[[edo|Edos]]: [[72edo|72]], [[152edo|152]], [[193edo|193]], [[224edo|224]], [[296edo|296]], [[327edo|327]], [[775edo|775]]
+[[Badness]]: 0.342 × 10<sup>-3</sup>
-Badness: 0.000342
 [[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5
-=Indra=
+== Indra ==
-[[Comma|Commas]]: 540/539, 1375/1372
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 540/539, 1375/1372
+[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}]
+Mapping generators: ~2, ~3, ~7/5
-[[Minimax tuning]]
+[[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}]
-[|1 0 0 0 0&gt;, |10 10 -3 0 -5&gt;, |0 0 1 0 0&gt;,
-|6 6 -1 0 -3&gt;, |20 18 -6 0 -9&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 5/4
-Lattice basis: 15/14 length 0.6184 55/36 length 0.7585
+Lattice basis:
-Angle(15/14, 55/36) = 68.1048 cents
+: 15/14 length = 0.6184, 55/36 length = 0.7585
-Map to lattice: [&lt;0 2 1 2 3|, &lt;0 -1 2 1 -3|]
+: Angle (15/14, 55/36) = 68.1048 deg
-Map: [&lt;1 0 0 0 2|, &lt;0 1 3 3 0|, &lt;0 0 -5 -4 3|]
+[[Minimax tuning]]:
-[[Generator|Generators]]: 2, 3, 7/5
+* [[11-odd-limit]]
-[[edo|Edos]]: 31, 41, [[72edo|72]], [[152edo|152]], [[224edo|224]], [[296edo|296]], [[703edo|703]]
+: [{{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 }}]
-Badness: 0.000266
+: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4
+{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }}
+[[Badness]]: 0.266 × 10<sup>-3</sup>
 [[Projection pair]]s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
@@ Line 52: / Line 53: @@
 Scales: [[indra31]]
-==Shibi==
+=== Shibi ===
-Commas: 540/539, 729/728, 1375/1372
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 729/728, 1375/1372
+Mapping: [{{val| 1 0 0 0 2 -3 }}, {{val| 0 1 3 3 0 3 }}, {{val| 0 0 -5 -4 4 }}]
+{{Optimal ET sequence|legend=1| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}
+Badness: 0.721 × 10<sup>-3</sup>
+=== Yajna ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 625/624, 1375/1372
+Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 0 0 -5 -4 3 -20 }}]
+Mapping generators: ~2, ~3, ~7/5
+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]]s (unchanged-intervals): 2, 10/9, 13/10
+* 15-odd-limit minimax
+: [{{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]]s (unchanged-intervals): 2, 14/13, 4/3
+{{Optimal ET sequence|legend=1| 31, 49f, 72, 103, 121, 152f, 193, 224 }}
+Badness: 0.700 × 10<sup>-3</sup>
+=== Vibhu ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 351/350, 540/539, 1375/1372
+Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}]
+{{Optimal ET sequence|legend=1| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}
-Map: [&lt;1 0 0 0 2 -4 -3|, &lt;0 1 3 3 0 11 3|, &lt;0 0 -5 -4 3 4|]
+Badness: 0.826 × 10<sup>-3</sup>
-EDOs: 41, 72, 111, 183, 224, 703
-Badness: 0.000721
-==Yajna==
+=== Vish ===
-[[Comma|Commas]]: 540/539, 625/624, 1375/1372
+Subgroup: 2.3.5.7.11.13
--limit minimax
+Comma list: 325/324, 364/363, 540/539
-[|1 0 0 0 0 0&gt;, |4/5 6/5 -4/5 0 0 1/5&gt;,
-|8/5 2/5 -3/5 0 0 2/5&gt;,
-|44/25 26/25 -24/25 0 0 11/25&gt;,
-|62/25 48/25 -27/25 0 0 3/25&gt;,
-|8/5 2/5 -8/5 0 0 7/5&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 13/10
--limit minimax
+Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}]
-[|1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;,
-|5/4 1/2 0 -5/16 0 5/16&gt;,
-|1 1 0 -1/4 0 1/4&gt;,
-|5/4 3/2 0 3/16 0 -3/16&gt;,
-|1 1 0 -5/4 0 5/4&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 14/13, 4/3
-Map: [&lt;1 0 0 0 2 -4|, &lt;0 1 3 3 0 11|, &lt;0 0 -5 -4 3 -20|]
+{{Optimal ET sequence|legend=1| 31f, 41, 72, 121, 193 }}
-[[Generator|Generators]]: 2, 3, 7/5
-[[edo|Edos]]: [[31edo|31]], [[72edo|72]], [[103edo|103]], [[193edo|193]], 224, 296, 520, 703
-Badness: 0.000700
-==Vibhu==
+Badness: 0.930 × 10<sup>-3</sup>
-[[Comma|Commas]]: 540/539, 1375/1372, 351/350
-==Vish==
+[[Category:Temperament families]]
-[[Comma|Commas]]: 540/539, 1375/1372, 325/324
+[[Category:Pages with mostly numerical content]]
-</pre></div>
+[[Category:Mirkwai family]] <!-- main article -->
-<h4>Original HTML content:</h4>
+[[Category:Rank 3]]
-<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;Mirkwai family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Vital statistics"&gt;Vital statistics&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Indra"&gt;Indra&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
-&lt;br /&gt;
-The mirkwai family of &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;s tempers out the mirkwai comma, 16875/16807.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Vital statistics"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vital statistics&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: mirkwai 16875/16807&lt;br /&gt;
-&lt;br /&gt;
--limit minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |0 4/7 -4/7 5/7&amp;gt;, &lt;br /&gt;
-|0 -3/7 3/7 5/7&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 8/7, 6/5&lt;br /&gt;
-&lt;br /&gt;
--limit minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |0 8/11 -4/11 5/11&amp;gt;, &lt;br /&gt;
-|0 -6/11 3/11 10/11&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 0|, &amp;lt;0 1 3 3|, &amp;lt;0 0 -5 -4|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 7/5&lt;br /&gt;
-&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, &lt;a class="wiki_link" href="/224edo"&gt;224&lt;/a&gt;, &lt;a class="wiki_link" href="/296edo"&gt;296&lt;/a&gt;, &lt;a class="wiki_link" href="/327edo"&gt;327&lt;/a&gt;, &lt;a class="wiki_link" href="/775edo"&gt;775&lt;/a&gt;&lt;br /&gt;
-Badness: 0.000342&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 84375/16807 7 16875/2401 to 2.3.7/5&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="Indra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Indra&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 1375/1372&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |10 10 -3 0 -5&amp;gt;, |0 0 1 0 0&amp;gt;, &lt;br /&gt;
-|6 6 -1 0 -3&amp;gt;, |20 18 -6 0 -9&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/9, 5/4&lt;br /&gt;
-&lt;br /&gt;
-Lattice basis: 15/14 length 0.6184 55/36 length 0.7585&lt;br /&gt;
-Angle(15/14, 55/36) = 68.1048 cents&lt;br /&gt;
-Map to lattice: [&amp;lt;0 2 1 2 3|, &amp;lt;0 -1 2 1 -3|]&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 0 2|, &amp;lt;0 1 3 3 0|, &amp;lt;0 0 -5 -4 3|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 7/5&lt;br /&gt;
-&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 31, 41, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/224edo"&gt;224&lt;/a&gt;, &lt;a class="wiki_link" href="/296edo"&gt;296&lt;/a&gt;, &lt;a class="wiki_link" href="/703edo"&gt;703&lt;/a&gt;&lt;br /&gt;
-Badness: 0.000266&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5&lt;br /&gt;
-&lt;br /&gt;
-Scales: &lt;a class="wiki_link" href="/indra31"&gt;indra31&lt;/a&gt;&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="Indra-Shibi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Shibi&lt;/h2&gt;
-Commas: 540/539, 729/728, 1375/1372&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 0 2 -4 -3|, &amp;lt;0 1 3 3 0 11 3|, &amp;lt;0 0 -5 -4 3 4|]&lt;br /&gt;
-EDOs: 41, 72, 111, 183, 224, 703&lt;br /&gt;
-Badness: 0.000721&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="Indra-Yajna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Yajna&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 625/624, 1375/1372&lt;br /&gt;
-&lt;br /&gt;
--limit minimax&lt;br /&gt;
-[|1 0 0 0 0 0&amp;gt;, |4/5 6/5 -4/5 0 0 1/5&amp;gt;, &lt;br /&gt;
-|8/5 2/5 -3/5 0 0 2/5&amp;gt;, &lt;br /&gt;
-|44/25 26/25 -24/25 0 0 11/25&amp;gt;, &lt;br /&gt;
-|62/25 48/25 -27/25 0 0 3/25&amp;gt;, &lt;br /&gt;
-|8/5 2/5 -8/5 0 0 7/5&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 10/9, 13/10&lt;br /&gt;
-&lt;br /&gt;
--limit minimax&lt;br /&gt;
-[|1 0 0 0 0 0&amp;gt;, |0 1 0 0 0 0&amp;gt;, &lt;br /&gt;
-|5/4 1/2 0 -5/16 0 5/16&amp;gt;,&lt;br /&gt;
-|1 1 0 -1/4 0 1/4&amp;gt;, &lt;br /&gt;
-|5/4 3/2 0 3/16 0 -3/16&amp;gt;, &lt;br /&gt;
-|1 1 0 -5/4 0 5/4&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 14/13, 4/3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 0 0 2 -4|, &amp;lt;0 1 3 3 0 11|, &amp;lt;0 0 -5 -4 3 -20|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 7/5&lt;br /&gt;
-&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/103edo"&gt;103&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, 224, 296, 520, 703&lt;br /&gt;
-Badness: 0.000700&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="Indra-Vibhu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Vibhu&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 1375/1372, 351/350&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Indra-Vish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Vish&lt;/h2&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 540/539, 1375/1372, 325/324&lt;/body&gt;&lt;/html&gt;</pre></div>