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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 '''mavila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] [[135/128]], the mavila comma, also known as the major chroma or major limma. The [[5-limit]] temperament is [[mavila]], so named after the Chopi village where it was discovered, and is the base from which higher limit temperaments are derived. The generator for all of these is a very flat fifth, lying on the spectrum between [[7edo]] and [[9edo]].
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-21 11:10:55 UTC</tt>.<br>
: The original revision id was <tt>247383261</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]]


The //pelogic family// tempers out [[135_128|135/128]], the pelogic comma, also known as the major chroma or major limma. The [[5-limit]] temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.
One of the most salient and characteristic features of mavila temperaments is that when you stack 4 of the tempered fifths you get to a minor third instead of the usual major third that you would get if the fifths were pure. This also means that the arrangement of small and large steps in a 7-note mavila scale is the inverse of a diatonic scale of 2 small steps and 5 large steps; mavila has 2 large steps and 5 small steps (see [[2L 5s]]).  


=Mavila=
Another salient feature of mavila temperaments is the fact that 9-note [[mos scale]]s may be produced, thus giving us three different mos scales to choose from that are not decidedly chromatic in nature (5-, 7-, and 9-note scales). This is reflected in the design of the 9 + 7 layout of the Goldsmith keyboard for 16-tone equal temperament (see [[7L 2s]]).
[[Comma]]s: 135/128
[[POTE tuning|POTE generator]]: 679.806
Map: [[1 0 7], [0 1 -3]]
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23]], [[125edo|25b]], [[30edo|30b]]


[[Gene Ward Smith]]
== Mavila ==
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg|Mysterious Mush (spectrally mapped)]]
{{Main| Mavila }}
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg|Mysterious Mush (unmapped)]]


[[Mike Battaglia]]
[[Subgroup]]: 2.3.5
[[http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments|The Mavila Experiments]]


[[John Moriarty]]
[[Comma list]]: 135/128
[[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3|Mavila]]


=Septimal Mavila=
{{Mapping|legend=1| 1 0 7 | 0 1 -3 }}
[[Comma]]s: 135/128, 126/125
: mapping generators: ~2, ~3
[[POTE tuning|POTE generator]]: 677.912
Map: [&lt;1 0 7 20], &lt;0 1 -3 -11|]
EDOs: [[16edo|16]], [[23edo|23d]]


=Pelogic=
[[Optimal tuning]]s:  
[[Comma]]s: 135/128, 21/20
* [[WE]]: ~2 = 1208.287{{c}}, ~3/2 = 684.501{{c}}
[[POTE tuning|POTE generator]]: 672.853
: [[error map]]: {{val| +8.287 -9.167 -6.667 }}
Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.111{{c}}
[[Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||
: error map: {{val| 0.000 -22.844 -23.648 }}
EDOs: [[9edo|9]], [[11edo|11]]


=Armodue=
[[Tuning ranges]]:  
[[Comma]]s: 135/128, 36/35
* [[5-odd-limit]] [[diamond monotone]]: ~3/2 = [600.000, 685.714] (1\2 to 4\7)
[[POTE tuning|POTE generator]]: 673.997
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955] (1/3-comma to Pyth.)
Map: [&lt;1 0 7 -5], &lt;0 1 -3 5|]
[[Wedgie]]: &lt;&lt;11 -3 5 -7 5 20||
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]], [[73edo|73]]


=Hornbostel=
{{Optimal ET sequence|legend=1| 7, 9, 16, 23, 30bc }}
[[Comma]]s: 135/128, 875/864
[[POTE tuning|POTE generator]]: 678.947
Map: [&lt;1 0 7 -16], &lt;0 1 -3 12|]
[[Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||
EDOs: [[7edo|7]], [[23edo|23d]], [[30edo|30bc]]


=Superpelog=
[[Badness]] (Sintel): 0.928
[[Comma]]s: 135/128, 49/48
[[POTE tuning|POTE generator]]: 259.952
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
[[Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||
EDOs: [[5edo|5]], [[9edo|9]], [[14edo|14]], [[23edo|23]], [[37edo|37]], [[60edo|60]]


=Bipelog=
=== Overview to extensions ===
[[Comma]]s: 135/128, 50/49
==== 7-limit extensions ====
[[POTE tuning|POTE generator]]: 681.195
The second comma of the [[normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[36/35]] for armodue, [[126/125]] for mavling, [[21/20]] for pelogic, [[875/864]] for hornbostel, [[49/48]] for superpelog, [[50/49]] for bipelog, and [[1323/1250]] for mohavila.
Map: [&lt;2 0 14 15|, &lt;0 1 -3 -3|]
 
[[Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||
Temperaments discussed elsewhere include
EDOs: [[14edo|14]], [[16edo|16]], [[30edo|30]], [[44edo|44]], [[74edo|74]]
* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa|Very low accuracy temperaments]]
</pre></div>
* ''[[Wallaby]]'' (+28/27) → [[Very low accuracy temperaments #Wallaby|Very low accuracy temperaments]]
<h4>Original HTML content:</h4>
* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog|Semaphoresmic clan]]
<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;Pelogic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&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:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Mavila"&gt;Mavila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Septimal Mavila"&gt;Septimal Mavila&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Pelogic"&gt;Pelogic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Armodue"&gt;Armodue&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Hornbostel"&gt;Hornbostel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Superpelog"&gt;Superpelog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Bipelog"&gt;Bipelog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
* ''[[Clyndro]]'' (+360/343) → [[Gamelismic clan #Clyndro|Gamelismic clan]]
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;br /&gt;
* ''[[Jamesbond]]'' (+25/24) → [[Whitewood family #Jamesbond|Whitewood family]]
The &lt;em&gt;pelogic family&lt;/em&gt; tempers out &lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;, the pelogic comma, also known as the major chroma or major limma. The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; temperament is (5-limit) mavila, so named after the Chopi village where it was discovered. The generator for all of these is a very flat fifth, lying on the spectrum between 7-equal and 9-equal.&lt;br /&gt;
 
&lt;br /&gt;
Considered below are mavling, pelogic, armodue, hornbostel, bipelog, and mohavila.
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Mavila"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mavila&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128&lt;br /&gt;
==== Subgroup extensions ====
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 679.806&lt;br /&gt;
Mavila naturally extends to the 2.3.5.11 subgroup, with the generator standing in for ~16/11 and ~22/15, as is given right below.
Map: [[1 0 7], [0 1 -3]]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;25b&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30b&lt;/a&gt;&lt;br /&gt;
=== 2.3.5.11 subgroup ===
&lt;br /&gt;
Subgroup: 2.3.5.11
&lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg" rel="nofollow"&gt;Mysterious Mush (spectrally mapped)&lt;/a&gt;&lt;br /&gt;
Comma list: 33/32, 45/44
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg" rel="nofollow"&gt;Mysterious Mush (unmapped)&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Subgroup-val mapping: {{mapping| 1 0 7 5 | 0 1 -3 -1 }}
&lt;a class="wiki_link" href="/Mike%20Battaglia"&gt;Mike Battaglia&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments" rel="nofollow"&gt;The Mavila Experiments&lt;/a&gt;&lt;br /&gt;
Gencom mapping: {{mapping| 1 0 7 0 5 | 0 1 -3 0 -1 }}
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/John%20Moriarty"&gt;John Moriarty&lt;/a&gt;&lt;br /&gt;
Optimal tunings:  
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3" rel="nofollow"&gt;Mavila&lt;/a&gt;&lt;br /&gt;
* WE: ~2 = 1208.454{{c}}, ~3/2 = 684.577{{c}}
&lt;br /&gt;
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 678.978{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Septimal Mavila"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal Mavila&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 126/125&lt;br /&gt;
{{Optimal ET sequence|legend=0| 7, 16, 23e, 30bce }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 677.912&lt;br /&gt;
 
Map: [&amp;lt;1 0 7 20], &amp;lt;0 1 -3 -11|]&lt;br /&gt;
Badness (Sintel): 0.424
EDOs: &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Armodue ==
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pelogic&lt;/h1&gt;
Armodue, also known as '''hexadecimal''', is the main 7-limit extension of mavila, and also the main temperament of [[Armodue theory]]. It tempers out 36/35, and can be described as the {{nowrap| 7 & 9 }} temperament. 7/4 is mapped to the minor seventh of the antidiatonic scale, where we will find 9/5 in the 5-limit. [[16edo]] shows us an obvious tuning.
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 21/20&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 672.853&lt;br /&gt;
The name ''armodue'' has been established in 2011 thanks to [[Mike Battaglia]]<ref name="mike's cleanup">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101194.html Yahoo! Tuning Group | ''Higher-limit mavila extension spring cleaning'']</ref>. The alternative name ''hexadecimal'' was attested as early as 2004<ref name="big temp list">[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_8809.html Yahoo! Tuning Group | ''114 7-limit temperaments'']</ref><ref name="pelogic & hex">[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9670.html Yahoo! Tuning Group | ''Pelogic and "hexidecimal"'']</ref>.
Map: [&amp;lt;1 0 7 9|, &amp;lt;0 1 -3 -4|]&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 -4 -7 -9 -1||&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 36/35, 135/128
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Armodue&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 36/35&lt;br /&gt;
{{Mapping|legend=1| 1 0 7 -5 | 0 1 -3 5 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 673.997&lt;br /&gt;
 
Map: [&amp;lt;1 0 7 -5], &amp;lt;0 1 -3 5|]&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;11 -3 5 -7 5 20||&lt;br /&gt;
* [[WE]]: ~2 = 1204.996{{c}}, ~3/2 = 676.803{{c}}
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23p&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25b&lt;/a&gt;, &lt;a class="wiki_link" href="/73edo"&gt;73&lt;/a&gt;&lt;br /&gt;
: [[error map]]: {{val| +4.996 -20.157 +3.261 +15.187 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 674.220{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Hornbostel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hornbostel&lt;/h1&gt;
: error map: {{val| 0.000 -27.735 -8.974 +2.275 }}
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 875/864&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 678.947&lt;br /&gt;
[[Tuning ranges]]:
Map: [&amp;lt;1 0 7 -16], &amp;lt;0 1 -3 12|]&lt;br /&gt;
* [[7-odd-limit]] [[diamond monotone]]: ~3/2 = [666.667, 675.000] (5\9 to 9\16)
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 12 -7 16 36||&lt;br /&gt;
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [666.718, 701.955]
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30bc&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 9, 16 }}
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Superpelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Superpelog&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 49/48&lt;br /&gt;
[[Badness]] (Sintel): 1.24
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 259.952&lt;br /&gt;
 
Map: [&amp;lt;1 0 7 2|, &amp;lt;0 2 -6 1|]&lt;br /&gt;
=== 11-limit ===
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 -6 1 -14 -4 19||&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 33/32, 36/35, 45/44
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Bipelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Bipelog&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128, 50/49&lt;br /&gt;
Mapping: {{mapping| 1 0 7 -5 5 | 0 1 -3 5 -1 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 681.195&lt;br /&gt;
 
Map: [&amp;lt;2 0 14 15|, &amp;lt;0 1 -3 -3|]&lt;br /&gt;
Optimal tunings:
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 -6 -6 -14 -15 3||&lt;br /&gt;
* WE: ~2 = 1205.460{{c}}, ~3/2 = 676.873{{c}}
EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44&lt;/a&gt;, &lt;a class="wiki_link" href="/74edo"&gt;74&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.952{{c}}
 
{{Optimal ET sequence|legend=0| 7, 9, 16 }}
 
Badness (Sintel): 0.900
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 33/32, 36/35, 45/44
 
Mapping: {{mapping| 1 0 7 -5 5 -1 | 0 1 -3 5 -1 3 }}
 
Optimal tunings:
* WE: ~2 = 1205.396{{c}}, ~3/2 = 676.792{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.988{{c}}
 
{{Optimal ET sequence|legend=0| 7, 9, 16 }}
 
Badness (Sintel): 0.800
 
==== Armodog ====
Subgroup: 2.3.5.7.11.13.19
 
Comma list: 27/26, 33/32, 36/35, 39/38, 45/44
 
Subgroup-val mapping: {{mapping| 1 0 7 -5 5 -1 -2 | 0 1 -3 5 -1 3 4 }}
 
Optimal tunings:
* WE: ~2 = 1204.838{{c}}, ~3/2 = 675.997{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 673.540{{c}}
 
{{Optimal ET sequence|legend=0| 7, 9, 16, 25bf }}
 
Badness (Sintel): 0.830
 
== Mavling ==
Mavling tempers out 126/125 and may be described as the {{nowrap| 7d & 16 }} temperament. The 7/4 is mapped to the augmented sixth of the antidiatonic scale.
 
This temperament was formerly known as ''septimal mavila'', but decanonicalized in 2025 per community consensus.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 135/128
 
{{Mapping|legend=1| 1 0 7 20 | 0 1 -3 -11 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1208.187{{c}}, ~3/2 = 682.538{{c}}
: [[error map]]: {{val| +8.187 -11.230 -1.178 -3.057 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 677.350{{c}}
: error map: {{val| 0.000 -24.605 -18.363 -19.672 }}
 
[[Tuning ranges]]:
* [[7-odd-limit]] [[diamond monotone]]: ~3/2 = [675.000, 678.261] (9\16 to 13\23)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [671.229, 701.955]
 
{{Optimal ET sequence|legend=1| 7d, 16, 23d }}
 
[[Badness]] (Sintel): 2.25
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 45/44, 126/125
 
Mapping: {{mapping| 1 0 7 20 5 | 0 1 -3 -11 -1 }}
 
Optimal tunings:
* WE: ~2 = 1208.243{{c}}, ~3/2 = 682.582{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 677.434{{c}}
 
{{Optimal ET sequence|legend=0| 7d, 16, 23de }}
 
Badness (Sintel): 1.39
 
== Pelogic ==
''Pelogic'' (from the Indonesian word ''[[pelog]]'') should probably be pronounced /pɛˈlɒgɪk/ ''pell-LOG-ik''. This name dates back to as early as 2004<ref name="big temp list"/><ref name="pelogic & hex"/> and has been approved of by [[Mike Battaglia]] in 2011, reasoning that Pelog is supposed to be flatter than [[16edo|16-]] or [[23edo]], and this temperament, tempering out 21/20 and described as the {{nowrap| 7d & 9 }} temperament, tends towards such a tuning<ref name="mike's cleanup"/>.
 
The 7/4 is mapped to the major sixth of the antidiatonic scale.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 21/20, 135/128
 
{{Mapping|legend=1| 1 0 7 9 | 0 1 -3 -4 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1210.184{{c}}, ~3/2 = 678.563{{c}}
: [[error map]]: {{val| +10.184 -13.208 +18.732 -32.160 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 671.548{{c}}
: error map: {{val| 0.000 -30.407 -0.957 -55.017 }}
 
[[Tuning ranges]]:
* [[7-odd-limit]] [[diamond monotone]]: ~3/2 = 666.667 (5\9)
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [617.488, 701.955]
 
{{Optimal ET sequence|legend=1| 7d, 9, 16d }}
 
[[Badness]] (Sintel): 0.978
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 21/20, 33/32, 45/44
 
Mapping: {{mapping| 1 0 7 9 5 | 0 1 -3 -4 -1 }}
 
Optimal tunings:
* WE: ~2 = 1209.379{{c}}, ~3/2 = 677.901{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 671.507{{c}}
 
{{Optimal ET sequence|legend=0| 7d, 9, 16d }}
 
Badness (Sintel): 0.752
 
== Hornbostel ==
Hornbostel tempers out 729/700 and may be described as the {{nowrap| 7 & 23d }} temperament. The 7/4 is mapped to the diminished seventh of the antidiatonic scale.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 135/128, 729/700
 
{{Mapping|legend=1| 1 0 7 -16 | 0 1 -3 12 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1207.970{{c}}, ~3/2 = 683.457{{c}}
: [[error map]]: {{val| +7.970 -10.529 -4.805 +0.775 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 679.270{{c}}
: error map: {{val| 0.000 -22.685 -24.124 -17.583 }}
 
{{Optimal ET sequence|legend=1| 7, 16d, 23d, 53bbccd }}
 
[[Badness]] (Sintel): 3.07
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 45/44, 729/700
 
Mapping: {{mapping| 1 0 7 -16 5 | 0 1 -3 12 -1 }}
 
Optimal tunings:  
* WE: ~2 = 1208.145{{c}}, ~3/2 = 683.517{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 679.150{{c}}
 
{{Optimal ET sequence|legend=0| 7, 16d, 23de, 53bbccdee }}
 
Badness (Sintel): 1.82
 
== Bipelog ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 50/49, 135/128
 
{{Mapping|legend=1| 2 0 14 15 | 0 1 -3 -3 }}
 
: mapping generators: ~7/5, ~3
 
[[Optimal tuning]]s:  
* [[WE]]: ~7/5 = 603.757{{c}}, ~3/2 = 685.461{{c}}
: [[error map]]: {{val| +7.514 -8.980 -12.641 +8.604 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~3/2 = 680.206{{c}}
: error map: {{val| 0.000 -21.749 -26.932 -9.444 }}
 
{{Optimal ET sequence|legend=1| 14c, 30bc, 44bccd }}
 
[[Badness]] (Sintel): 1.89
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 45/44, 50/49
 
Mapping: {{mapping| 2 0 14 15 10 | 0 1 -3 -3 -1 }}
 
Optimal tunings:  
* WE: ~7/5 = 603.958{{c}}, ~3/2 = 685.773{{c}}
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 680.267{{c}}
 
{{Optimal ET sequence|legend=0| 14c, 30bce, 44bccdee }}
 
Badness (Sintel): 1.18
 
== Mohavila ==
Named by Mike Battaglia in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104134.html Yahoo! Tuning Group | ''Mohavila temperament'']</ref>, mohavila splits the mavila fifth in two. Unlike [[mohaha]], this generator is not used as an ~11/9. In fact, the prime 11 is the same as in mavila, so the ~11/9 is the major third, tempered together with ~5/4. The fifth is only split to derive septimal intervals.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 135/128, 1323/1250
 
{{Mapping|legend=1| 1 1 4 7 | 0 2 -6 -15 }}
 
: mapping generators: ~2, ~25/21
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1208.410{{c}}, ~25/21 = 340.025{{c}}
: [[error map]]: {{val| +8.410 -13.496 +7.177 -10.327 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~25/21 = 337.260{{c}}
: error map: {{val| 0.000 -27.435 -9.872 -27.722 }}
 
{{Optimal ET sequence|legend=1| 7d, 25b, 32bd }}
 
[[Badness]] (Sintel): 5.63
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 45/44, 1323/1250
 
Mapping: {{mapping| 1 1 4 7 4 | 0 2 -6 -15 -2 }}
 
Optimal tunings:
* WE: ~2 = 1208.211{{c}}, ~25/21 = 339.943{{c}}
* CWE: ~2 = 1200.000{{c}}, ~25/21 = 337.286{{c}}
 
{{Optimal ET sequence|legend=0| 7d, 25b, 32bde }}
 
Badness (Sintel): 3.04
 
== References ==
 
[[Category:Mavila family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Mavila_family"