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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 '''luna family''' tempers out the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}. It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-06 11:59:44 UTC</tt>.<br>
: The original revision id was <tt>251206686</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">The Luna family tempers out the Luna comma; 274877906944/274658203125, which has a monzo of |38 -2 -15&gt;


=Luna=
Temperaments discussed elsewhere include:
Comma: 274877906944/274658203125
* ''[[Subneutral]]'' (+2401/2400) → [[Breedsmic temperaments #Subneutral|Breedsmic temperaments]]
* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]


POTE generator: ~262144/234375 = 193.201
== Luna ==
{{see also|Luna and hemithirds}}


Map: [&lt;1 4 2|, &lt;0 -15 2|]
[[Hemimean clan #Hemithirds|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.
EDOs: 13, 19, 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559
Badness: 0.0206


=[[Gamelismic clan#Hemithirds|Hemithirds]]=
[[Subgroup]]: 2.3.5
Commas: 1029/1024, 3136/3125


POTE generator: ~28/25 = 193.244
[[Comma list]]: 274877906944/274658203125


Map: [&lt;1 4 2 2|, &lt;0 -15 2 5|]
{{Mapping|legend=1| 1 4 2 | 0 -15 2 }}
Wedgie: &lt;&lt;15 -2 -5 -38 -50 -6||
EDOs: 13, 19, 25, 31, 87, 118
Badness: 0.0443


==11-limit==
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~262144/234375 = 193.201
Commas: 385/384, 441/440, 3136/3125


POTE generator: ~28/25 = 193.227
{{Optimal ET sequence|legend=1| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }}


Map: [&lt;1 4 2 2 7|, &lt;0 -15 2 5 -22|]
[[Badness]]: 0.020576
EDOs: 13, 19, 25, 31, 87, 118
Bad: 0.0190


=Lunatic=
; Music
Commas: 4375/4374, 274877906944/274658203125
* "Moongazing" from ''Lesser Groove'' (2020) [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] | [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, luna[25] in 1000edo by [[Xotla]]


POTE generator: ~262144/234375 = 193.196
== Lunatic ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 4 2 2|, &lt;0 -15 2 -113|]
[[Comma list]]: 4375/4374, 274877906944/274658203125
Wedgie: &lt;&lt;15 -2 113 -38 137 268||
 
EDOs: 13, 19, 25, 31, 87, 118, 323, 441, 1205, 1646
{{Mapping|legend=1| 1 4 2 21 | 0 -15 2 -113 }}
Badness: 0.0380</pre></div>
 
<h4>Original HTML content:</h4>
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~262144/234375 = 193.196
<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;Luna Family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The Luna family tempers out the Luna comma; 274877906944/274658203125, which has a monzo of |38 -2 -15&amp;gt;&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 87d, 118, 323, 441, 1205, 1646 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Luna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Luna&lt;/h1&gt;
 
Comma: 274877906944/274658203125&lt;br /&gt;
[[Badness]]: 0.037966
&lt;br /&gt;
 
POTE generator: ~262144/234375 = 193.201&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
Map: [&amp;lt;1 4 2|, &amp;lt;0 -15 2|]&lt;br /&gt;
 
EDOs: 13, 19, 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559&lt;br /&gt;
Comma list: 4375/4374, 12005/11979, 172032/171875
Badness: 0.0206&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 4 2 21 14 | 0 -15 2 -113 -140 }}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Hemithirds"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;a class="wiki_link" href="/Gamelismic%20clan#Hemithirds"&gt;Hemithirds&lt;/a&gt;&lt;/h1&gt;
 
Commas: 1029/1024, 3136/3125&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~352/315 = 193.200
&lt;br /&gt;
 
POTE generator: ~28/25 = 193.244&lt;br /&gt;
{{Optimal ET sequence|legend=1| 118, 323e, 441, 559, 1000e }}
&lt;br /&gt;
 
Map: [&amp;lt;1 4 2 2|, &amp;lt;0 -15 2 5|]&lt;br /&gt;
Badness: 0.058588
Wedgie: &amp;lt;&amp;lt;15 -2 -5 -38 -50 -6||&lt;br /&gt;
 
EDOs: 13, 19, 25, 31, 87, 118&lt;br /&gt;
== Hemiluna ==
Badness: 0.0443&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Hemithirds-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
[[Comma list]]: 48828125/48771072, 67108864/66976875
Commas: 385/384, 441/440, 3136/3125&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 4 2 -5 | 0 -30 4 97 }}
POTE generator: ~28/25 = 193.227&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~2, ~200/189
Map: [&amp;lt;1 4 2 2 7|, &amp;lt;0 -15 2 5 -22|]&lt;br /&gt;
 
EDOs: 13, 19, 25, 31, 87, 118&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 96.591
Bad: 0.0190&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }}
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Lunatic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Lunatic&lt;/h1&gt;
 
Commas: 4375/4374, 274877906944/274658203125&lt;br /&gt;
[[Badness]]: 0.179304
&lt;br /&gt;
 
POTE generator: ~262144/234375 = 193.196&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
Map: [&amp;lt;1 4 2 2|, &amp;lt;0 -15 2 -113|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;15 -2 113 -38 137 268||&lt;br /&gt;
Comma list: 5632/5625, 14641/14580, 131072/130977
EDOs: 13, 19, 25, 31, 87, 118, 323, 441, 1205, 1646&lt;br /&gt;
 
Badness: 0.0380&lt;/body&gt;&lt;/html&gt;</pre></div>
Mapping: {{mapping| 1 4 2 -5 7 | 0 -30 4 97 -44 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 96.587
 
{{Optimal ET sequence|legend=1| 87, 236, 323, 410 }}
 
Badness: 0.100077
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580
 
Mapping: {{mapping| 1 4 2 -5 7 7 | 0 -30 4 97 -44 -41 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~143/135 = 96.586
 
{{Optimal ET sequence|legend=1| 87, 236, 323, 410 }}
 
Badness: 0.046151
 
== Semiluna ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 4802000/4782969, 95703125/95551488
 
{{Mapping|legend=1| 2 8 4 23 | 0 -15 2 -54 }}
 
: mapping generators: ~10125/7168, ~2187/1960
 
[[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~2187/1960 = 193.1725
 
{{Optimal ET sequence|legend=1| 56d, 118, 292, 410 }}
 
[[Badness]]: 0.192167
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 5632/5625, 9801/9800, 14641/14580
 
Mapping: {{mapping| 2 8 4 23 14 | 0 -15 2 -54 -22 }}
 
Optimal tuning (POTE): ~99/70 = 1\2, ~121/108 = 193.1732
 
{{Optimal ET sequence|legend=1| 56d, 118, 292, 410 }}
 
Badness: 0.067783
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Luna family| ]] <!-- main article -->
[[Category:Luna| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Luna_family"