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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The ''pelogic family'' tempers out [[135/128|135/128]], the pelogic comma, also known as the major chroma or major limma. The [[5-limit|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.
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-18 12:05:44 UTC</tt>.<br>
: The original revision id was <tt>602440336</tt>.<br>
: The revision comment was: <tt>tel-link removed</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]]
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 pelogic temperament 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|2L 5s)]]
One of the most salient and characteristic features of pelogic temperament 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|2L 5s)]]


Another salient feature of pelogic temperament is the fact that 9 note MOS scales 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| 7L 2s]])
Another salient feature of pelogic temperament is the fact that 9 note MOS scales 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| 7L 2s]])


One of the most common temperaments talked about in the pelogic family is **mavila**, the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.
One of the most common temperaments talked about in the pelogic family is '''mavila''', the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.
 
='''<u>5-limit Parent Temperament</u>'''=
 
=Mavila=
<span style="display: block; text-align: right;">Other languages: [[:de:Mavila Deutsch]]</span>
 
[[Comma|Comma]]s: 135/128
 
[[POTE_tuning|POTE generator]]: 679.806


=**__5-limit Parent Temperament__**=
=Mavila=
&lt;span style="display: block; text-align: right;"&gt;Other languages: [[xenharmonie/Mavila|Deutsch]]
&lt;/span&gt;
[[Comma]]s: 135/128
[[POTE tuning|POTE generator]]: 679.806
Map: [&lt;1 0 7|, &lt;0 1 -3|]
Map: [&lt;1 0 7|, &lt;0 1 -3|]
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23]], [[25edo|25b]], [[30edo|30bc]], [[34edo|34b]], [[41edo|41b]]
EDOs: [[7edo|7]], [[9edo|9]], [[16edo|16]], [[23edo|23]], [[25edo|25b]], [[30edo|30bc]], [[34edo|34b]], [[41edo|41b]]


----
-----
----
 
=__**7-limit children**__=  
-----
=Septimal Mavila=  
 
[[Comma]]s: 135/128, 126/125
=<u>'''7-limit children'''</u>=
[[POTE tuning|POTE generator]]: 677.912
 
=Septimal Mavila=
[[Comma|Comma]]s: 135/128, 126/125
 
[[POTE_tuning|POTE generator]]: 677.912
 
Map: [&lt;1 0 7 20|, &lt;0 1 -3 -11|]
Map: [&lt;1 0 7 20|, &lt;0 1 -3 -11|]
EDOs: [[7edo|7]], [[16edo|16]], [[23edo|23d]]
EDOs: [[7edo|7]], [[16edo|16]], [[23edo|23d]]
Badness: 0.0890
Badness: 0.0890


----
-----
=Pelogic=  
 
[[Comma]]s: 135/128, 21/20
=Pelogic=
[[POTE tuning|POTE generator]]: 672.853
[[Comma|Comma]]s: 135/128, 21/20
 
[[POTE_tuning|POTE generator]]: 672.853
 
Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]
Map: [&lt;1 0 7 9|, &lt;0 1 -3 -4|]
[[Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||
 
[[wedgie|Wedgie]]: &lt;&lt;1 -3 -4 -7 -9 -1||
 
EDOs: [[9edo|9]], [[16edo|16d]]
EDOs: [[9edo|9]], [[16edo|16d]]
Badness: 0.0387
Badness: 0.0387


==11-limit==  
==11-limit==
Commas: 21/20, 33/32, 45/44
Commas: 21/20, 33/32, 45/44
POTE generator: ~3/2 = 672.644
POTE generator: ~3/2 = 672.644
Map: [&lt;1 0 7 9 5|, &lt;0 1 -3 -4 -1|]
Map: [&lt;1 0 7 9 5|, &lt;0 1 -3 -4 -1|]
EDOs: [[9edo|9]], [[16edo|16d]]
EDOs: [[9edo|9]], [[16edo|16d]]
Badness: 0.0228
Badness: 0.0228
----
 
=Armodue=  
-----
[[Comma]]s: 135/128, 36/35
 
[[POTE tuning|POTE generator]]: 673.997
=Armodue=
[[Comma|Comma]]s: 135/128, 36/35
 
[[POTE_tuning|POTE generator]]: 673.997
 
Map: [&lt;1 0 7 -5|, &lt;0 1 -3 5|]
Map: [&lt;1 0 7 -5|, &lt;0 1 -3 5|]
[[Wedgie]]: &lt;&lt;1 -3 5 -7 5 20||
 
[[wedgie|Wedgie]]: &lt;&lt;1 -3 5 -7 5 20||
 
EDOs: [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]]
EDOs: [[9edo|9]], [[16edo|16]], [[23edo|23p]], [[25edo|25b]]
Badness: 0.0490
Badness: 0.0490


==11-limit Armodue==  
==11-limit Armodue==
Commas: 33/32, 36/35, 45/44
Commas: 33/32, 36/35, 45/44
POTE generator: ~3/2 = 673.807
POTE generator: ~3/2 = 673.807
Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]
Map: [&lt;1 0 7 -5 5|, &lt;0 1 -3 5 -1|]
EDOs: [[9edo|9]], [[16edo|16]], [[23edo|23e]], [[25edo|25b]]
EDOs: [[9edo|9]], [[16edo|16]], [[23edo|23e]], [[25edo|25b]]
Badness: 0.0272
Badness: 0.0272


==13-limit Armodue==  
==13-limit Armodue==
Commas: 27/26, 33/32, 36/35, 45/44
Commas: 27/26, 33/32, 36/35, 45/44
POTE generator: ~3/2 = 673.763
POTE generator: ~3/2 = 673.763
Map: [&lt;1 0 7 -5 5 -1|, &lt;0 1 -3 5 -1 3|]
Map: [&lt;1 0 7 -5 5 -1|, &lt;0 1 -3 5 -1 3|]
EDOs: 7, 9, 16, 41bef, 57bef
EDOs: 7, 9, 16, 41bef, 57bef
Badness: 0.0194
Badness: 0.0194
----
 
=Hornbostel=  
-----
[[Comma]]s: 135/128, 875/864
 
[[POTE tuning|POTE generator]]: 678.947
=Hornbostel=
[[Comma|Comma]]s: 135/128, 875/864
 
[[POTE_tuning|POTE generator]]: 678.947
 
Map: [&lt;1 0 7 -16|, &lt;0 1 -3 12|]
Map: [&lt;1 0 7 -16|, &lt;0 1 -3 12|]
[[Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||
 
[[wedgie|Wedgie]]: &lt;&lt;1 -3 12 -7 16 36||
 
EDOs: [[7edo|7]], [[16edo|16d]], [[23edo|23d]]
EDOs: [[7edo|7]], [[16edo|16d]], [[23edo|23d]]
Badness: 0.1213
Badness: 0.1213
----
 
=Superpelog=  
-----
[[Comma]]s: 135/128, 49/48
 
[[POTE tuning|POTE generator]]: 259.952
=Superpelog=
[[Comma|Comma]]s: 135/128, 49/48
 
[[POTE_tuning|POTE generator]]: 259.952
 
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
Map: [&lt;1 0 7 2|, &lt;0 2 -6 1|]
[[Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||
 
[[wedgie|Wedgie]]: &lt;&lt;2 -6 1 -14 -4 19||
 
EDOs: [[9edo|9]], [[14edo|14c]], [[23edo|23d]], [[37edo|37bcd]], [[60edo|60bcd]]
EDOs: [[9edo|9]], [[14edo|14c]], [[23edo|23d]], [[37edo|37bcd]], [[60edo|60bcd]]
Badness: 0.0582
Badness: 0.0582


==11-limit==  
==11-limit==
Commas: 33/32, 45/44, 49/48
Commas: 33/32, 45/44, 49/48
POTE generator: ~8/7 = 259.959
POTE generator: ~8/7 = 259.959
Map: [&lt;1 0 7 2 5|, &lt;0 2 -6 1 -2|]
Map: [&lt;1 0 7 2 5|, &lt;0 2 -6 1 -2|]
EDOs: 9, 14c, 23de, 37bcde
EDOs: 9, 14c, 23de, 37bcde
Badness: 0.0285
Badness: 0.0285


//[[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3|Mindaugas Rex Lithuaniae]]// by [[http://chrisvaisvil.com/?p=2267|Chris Vaisvil]] (in 5\23 tuning)
''[http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3 Mindaugas Rex Lithuaniae]'' by [http://chrisvaisvil.com/?p=2267 Chris Vaisvil] (in 5\23 tuning)
----
 
=Bipelog=  
-----
[[Comma]]s: 135/128, 50/49
 
[[POTE tuning|POTE generator]]: ~3/2 = 681.195
=Bipelog=
[[Comma|Comma]]s: 135/128, 50/49
 
[[POTE_tuning|POTE generator]]: ~3/2 = 681.195
 
Map: [&lt;2 0 14 15|, &lt;0 1 -3 -3|]
Map: [&lt;2 0 14 15|, &lt;0 1 -3 -3|]
[[Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||
 
[[wedgie|Wedgie]]: &lt;&lt;2 -6 -6 -14 -15 3||
 
EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]
EDOs: [[14edo|14c]], [[16edo|16]], [[23edo|23d]], [[37edo|37bcd]]
Badness: 0.0747
Badness: 0.0747


==11-limit==  
==11-limit==
Commas: 33/32 45/44 50/49
Commas: 33/32 45/44 50/49
POTE generator: ~3/2 = 681.280
POTE generator: ~3/2 = 681.280
Map: [&lt;2 0 14 15 10|, &lt;0 1 -3 -3 -1|]
Map: [&lt;2 0 14 15 10|, &lt;0 1 -3 -3 -1|]
EDOs: 14c, 16, 44bcde
EDOs: 14c, 16, 44bcde
Badness: 0.0357
Badness: 0.0357
----
 
=Mohavila=  
-----
 
=Mohavila=
Commas: 135/128, 1323/1250
Commas: 135/128, 1323/1250
POTE generator: ~25/21 = 337.658
POTE generator: ~25/21 = 337.658
Map: [&lt;1 1 4 7|, &lt;0 2 -6 -15|]
Map: [&lt;1 1 4 7|, &lt;0 2 -6 -15|]
Wedgie: &lt;&lt;2 -6 -15 -14 -29 -18||
Wedgie: &lt;&lt;2 -6 -15 -14 -29 -18||
EDOs: 32bd, 36
EDOs: 32bd, 36
Badness: 0.2224
Badness: 0.2224


==11-limit==  
==11-limit==
Commas: 33/32, 45/44, 1323/1250
Commas: 33/32, 45/44, 1323/1250
POTE generator: ~25/21 = 337.633
POTE generator: ~25/21 = 337.633
Map: [&lt;1 1 4 7 4|, &lt;0 2 -6 -15 -2|]
Map: [&lt;1 1 4 7 4|, &lt;0 2 -6 -15 -2|]
EDOs: 32bde
EDOs: 32bde
Badness: 0.0921
Badness: 0.0921


=Mavila Listening examples=  
=Mavila Listening examples=
**[[Gene Ward Smith]]**
'''[[Gene_Ward_Smith|Gene Ward Smith]]'''
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg|Mysterious Mush (spectrally mapped)]]
 
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg|Mysterious Mush (unmapped)]]
[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mushc.ogg Mysterious Mush (spectrally mapped)]
//[[http://micro.soonlabel.com/gene_ward_smith/transformers/hopper.mp3|Hopper]]// by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila
 
[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/mush.ogg Mysterious Mush (unmapped)]
 
''[http://micro.soonlabel.com/gene_ward_smith/transformers/hopper.mp3 Hopper]'' by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila
 
'''[[Mike_Battaglia|Mike Battaglia]]'''
 
[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo The Mavila Experiments - 9-EDO Version]
 
[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo The Mavila Experiments - 16-EDO Version]
 
[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments The Mavila Experiments - 23-EDO Version]
 
[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo The Mavila Experiments - 25-EDO Version]


**[[Mike Battaglia]]**
'''[[John_Moriarty|John Moriarty]]'''
[[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo|The Mavila Experiments - 9-EDO Version]]
[[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo|The Mavila Experiments - 16-EDO Version]]
[[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments|The Mavila Experiments - 23-EDO Version]]
[[https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo|The Mavila Experiments - 25-EDO Version]]


**[[John Moriarty]]**
''[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3 Mavila]''      [[Category:family]]
//[[http://clones.soonlabel.com/public/micro/j_l_moriat/Mavila.mp3|Mavila]]//</pre></div>
[[Category:list]]
<h4>Original HTML content:</h4>
[[Category:listen]]
<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:34:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#x5-limit Parent Temperament"&gt;5-limit Parent Temperament&lt;/a&gt;&lt;/div&gt;
[[Category:overview]]
&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mavila"&gt;Mavila&lt;/a&gt;&lt;/div&gt;
[[Category:pelogic]]
&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#x7-limit children"&gt;7-limit children&lt;/a&gt;&lt;/div&gt;
[[Category:theory]]
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Septimal Mavila"&gt;Septimal Mavila&lt;/a&gt;&lt;/div&gt;
[[Category:todo:add_ipa]]
&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Pelogic"&gt;Pelogic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Pelogic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Armodue"&gt;Armodue&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Armodue-11-limit Armodue"&gt;11-limit Armodue&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Armodue-13-limit Armodue"&gt;13-limit Armodue&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hornbostel"&gt;Hornbostel&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Superpelog"&gt;Superpelog&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Superpelog-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bipelog"&gt;Bipelog&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bipelog-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mohavila"&gt;Mohavila&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Mohavila-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Mavila Listening examples"&gt;Mavila Listening examples&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:52 --&gt;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;
One of the most salient and characteristic features of pelogic temperament 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 &lt;a class="wiki_link" href="/2L%205s"&gt;2L 5s)&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Another salient feature of pelogic temperament is the fact that 9 note MOS scales 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&lt;a class="wiki_link" href="/7L%202s"&gt; 7L 2s&lt;/a&gt;)&lt;br /&gt;
&lt;br /&gt;
One of the most common temperaments talked about in the pelogic family is &lt;strong&gt;mavila&lt;/strong&gt;, the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.&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="x5-limit Parent Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;strong&gt;&lt;u&gt;5-limit Parent Temperament&lt;/u&gt;&lt;/strong&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Mavila"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Mavila&lt;/h1&gt;
&lt;span style="display: block; text-align: right;"&gt;Other languages: &lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Mavila"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 135/128&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 679.806&lt;br /&gt;
Map: [&amp;lt;1 0 7|, &amp;lt;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="/25edo"&gt;25b&lt;/a&gt;, &lt;a class="wiki_link" href="/30edo"&gt;30bc&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34b&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41b&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x7-limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;&lt;strong&gt;7-limit children&lt;/strong&gt;&lt;/u&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Septimal Mavila"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&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;
&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;
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &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;
Badness: 0.0890&lt;br /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Pelogic&lt;/h1&gt;
&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;
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;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16d&lt;/a&gt;&lt;br /&gt;
Badness: 0.0387&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="Pelogic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
Commas: 21/20, 33/32, 45/44&lt;br /&gt;
POTE generator: ~3/2 = 672.644&lt;br /&gt;
Map: [&amp;lt;1 0 7 9 5|, &amp;lt;0 1 -3 -4 -1|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16d&lt;/a&gt;&lt;br /&gt;
Badness: 0.0228&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&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;
&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;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 -3 5 -7 5 20||&lt;br /&gt;
EDOs: &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;br /&gt;
Badness: 0.0490&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="Armodue-11-limit Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit Armodue&lt;/h2&gt;
Commas: 33/32, 36/35, 45/44&lt;br /&gt;
POTE generator: ~3/2 = 673.807&lt;br /&gt;
Map: [&amp;lt;1 0 7 -5 5|, &amp;lt;0 1 -3 5 -1|]&lt;br /&gt;
EDOs: &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;23e&lt;/a&gt;, &lt;a class="wiki_link" href="/25edo"&gt;25b&lt;/a&gt;&lt;br /&gt;
Badness: 0.0272&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Armodue-13-limit Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit Armodue&lt;/h2&gt;
Commas: 27/26, 33/32, 36/35, 45/44&lt;br /&gt;
POTE generator: ~3/2 = 673.763&lt;br /&gt;
Map: [&amp;lt;1 0 7 -5 5 -1|, &amp;lt;0 1 -3 5 -1 3|]&lt;br /&gt;
EDOs: 7, 9, 16, 41bef, 57bef&lt;br /&gt;
Badness: 0.0194&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Hornbostel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Hornbostel&lt;/h1&gt;
&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;
Map: [&amp;lt;1 0 7 -16|, &amp;lt;0 1 -3 12|]&lt;br /&gt;
&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;
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16d&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;&lt;br /&gt;
Badness: 0.1213&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Superpelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&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;
&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;
&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;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23d&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37bcd&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60bcd&lt;/a&gt;&lt;br /&gt;
Badness: 0.0582&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Superpelog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
Commas: 33/32, 45/44, 49/48&lt;br /&gt;
POTE generator: ~8/7 = 259.959&lt;br /&gt;
Map: [&amp;lt;1 0 7 2 5|, &amp;lt;0 2 -6 1 -2|]&lt;br /&gt;
EDOs: 9, 14c, 23de, 37bcde&lt;br /&gt;
Badness: 0.0285&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/MOS/20120418-9mos-mindaugas.mp3" rel="nofollow"&gt;Mindaugas Rex Lithuaniae&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2267" rel="nofollow"&gt;Chris Vaisvil&lt;/a&gt; (in 5\23 tuning)&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Bipelog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&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;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 681.195&lt;br /&gt;
Map: [&amp;lt;2 0 14 15|, &amp;lt;0 1 -3 -3|]&lt;br /&gt;
&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;
EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &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;a class="wiki_link" href="/37edo"&gt;37bcd&lt;/a&gt;&lt;br /&gt;
Badness: 0.0747&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Bipelog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
Commas: 33/32 45/44 50/49&lt;br /&gt;
POTE generator: ~3/2 = 681.280&lt;br /&gt;
Map: [&amp;lt;2 0 14 15 10|, &amp;lt;0 1 -3 -3 -1|]&lt;br /&gt;
EDOs: 14c, 16, 44bcde&lt;br /&gt;
Badness: 0.0357&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Mohavila"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Mohavila&lt;/h1&gt;
Commas: 135/128, 1323/1250&lt;br /&gt;
POTE generator: ~25/21 = 337.658&lt;br /&gt;
Map: [&amp;lt;1 1 4 7|, &amp;lt;0 2 -6 -15|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 -6 -15 -14 -29 -18||&lt;br /&gt;
EDOs: 32bd, 36&lt;br /&gt;
Badness: 0.2224&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Mohavila-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
Commas: 33/32, 45/44, 1323/1250&lt;br /&gt;
POTE generator: ~25/21 = 337.633&lt;br /&gt;
Map: [&amp;lt;1 1 4 7 4|, &amp;lt;0 2 -6 -15 -2|]&lt;br /&gt;
EDOs: 32bde&lt;br /&gt;
Badness: 0.0921&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Mavila Listening examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Mavila Listening examples&lt;/h1&gt;
&lt;strong&gt;&lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;/strong&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;
&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;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/transformers/hopper.mp3" rel="nofollow"&gt;Hopper&lt;/a&gt;&lt;/em&gt; by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;&lt;a class="wiki_link" href="/Mike%20Battaglia"&gt;Mike Battaglia&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo" rel="nofollow"&gt;The Mavila Experiments - 9-EDO Version&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo" rel="nofollow"&gt;The Mavila Experiments - 16-EDO Version&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments" rel="nofollow"&gt;The Mavila Experiments - 23-EDO Version&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo" rel="nofollow"&gt;The Mavila Experiments - 25-EDO Version&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;&lt;a class="wiki_link" href="/John%20Moriarty"&gt;John Moriarty&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;em&gt;&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;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The pelogic family tempers out 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 pelogic temperament 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)

Another salient feature of pelogic temperament is the fact that 9 note MOS scales 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)

One of the most common temperaments talked about in the pelogic family is mavila, the 5-limit temperament eliminating 135/128, from which higher-limit extensions are derived.

5-limit Parent Temperament

Mavila

Other languages: de:Mavila Deutsch

Commas: 135/128

POTE generator: 679.806

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

EDOs: 7, 9, 16, 23, 25b, 30bc, 34b, 41b

7-limit children

Septimal Mavila

Commas: 135/128, 126/125

POTE generator: 677.912

Map: [<1 0 7 20|, <0 1 -3 -11|]

EDOs: 7, 16, 23d

Badness: 0.0890

Pelogic

Commas: 135/128, 21/20

POTE generator: 672.853

Map: [<1 0 7 9|, <0 1 -3 -4|]

Wedgie: <<1 -3 -4 -7 -9 -1||

EDOs: 9, 16d

Badness: 0.0387

11-limit

Commas: 21/20, 33/32, 45/44

POTE generator: ~3/2 = 672.644

Map: [<1 0 7 9 5|, <0 1 -3 -4 -1|]

EDOs: 9, 16d

Badness: 0.0228

Armodue

Commas: 135/128, 36/35

POTE generator: 673.997

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

Wedgie: <<1 -3 5 -7 5 20||

EDOs: 9, 16, 23p, 25b

Badness: 0.0490

11-limit Armodue

Commas: 33/32, 36/35, 45/44

POTE generator: ~3/2 = 673.807

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

EDOs: 9, 16, 23e, 25b

Badness: 0.0272

13-limit Armodue

Commas: 27/26, 33/32, 36/35, 45/44

POTE generator: ~3/2 = 673.763

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

EDOs: 7, 9, 16, 41bef, 57bef

Badness: 0.0194

Hornbostel

Commas: 135/128, 875/864

POTE generator: 678.947

Map: [<1 0 7 -16|, <0 1 -3 12|]

Wedgie: <<1 -3 12 -7 16 36||

EDOs: 7, 16d, 23d

Badness: 0.1213

Superpelog

Commas: 135/128, 49/48

POTE generator: 259.952

Map: [<1 0 7 2|, <0 2 -6 1|]

Wedgie: <<2 -6 1 -14 -4 19||

EDOs: 9, 14c, 23d, 37bcd, 60bcd

Badness: 0.0582

11-limit

Commas: 33/32, 45/44, 49/48

POTE generator: ~8/7 = 259.959

Map: [<1 0 7 2 5|, <0 2 -6 1 -2|]

EDOs: 9, 14c, 23de, 37bcde

Badness: 0.0285

Mindaugas Rex Lithuaniae by Chris Vaisvil (in 5\23 tuning)

Bipelog

Commas: 135/128, 50/49

POTE generator: ~3/2 = 681.195

Map: [<2 0 14 15|, <0 1 -3 -3|]

Wedgie: <<2 -6 -6 -14 -15 3||

EDOs: 14c, 16, 23d, 37bcd

Badness: 0.0747

11-limit

Commas: 33/32 45/44 50/49

POTE generator: ~3/2 = 681.280

Map: [<2 0 14 15 10|, <0 1 -3 -3 -1|]

EDOs: 14c, 16, 44bcde

Badness: 0.0357

Mohavila

Commas: 135/128, 1323/1250

POTE generator: ~25/21 = 337.658

Map: [<1 1 4 7|, <0 2 -6 -15|]

Wedgie: <<2 -6 -15 -14 -29 -18||

EDOs: 32bd, 36

Badness: 0.2224

11-limit

Commas: 33/32, 45/44, 1323/1250

POTE generator: ~25/21 = 337.633

Map: [<1 1 4 7 4|, <0 2 -6 -15 -2|]

EDOs: 32bde

Badness: 0.0921

Mavila Listening examples

Gene Ward Smith

Mysterious Mush (spectrally mapped)

Mysterious Mush (unmapped)

Hopper by Singer-Medora-White-Smith; in f^4-10f+10=0 equal-beating mavila

Mike Battaglia

The Mavila Experiments - 9-EDO Version

The Mavila Experiments - 16-EDO Version

The Mavila Experiments - 23-EDO Version

The Mavila Experiments - 25-EDO Version

John Moriarty

Mavila

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