Avicennmic temperaments: Difference between revisions

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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>
This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis.
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-09-19 03:01:03 UTC</tt>.<br>
: The original revision id was <tt>592575618</tt>.<br>
: The revision comment was: <tt>added links to edo pages</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]]


These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.
Tempereaments discussed elsewhere are:
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Pelogic|Mavila family]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
* [[Muggles]] (+126/125) → [[Magic family #Muggles|Magic family]]
* ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]]
* ''[[Pycnic]]'' (+245/243) → [[Sensamagic clan #Pycnic|Sensamagic clan]]
* ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]]


=Roman=
Considered below is submerged.
Commas: 525/512, 4000/3969


[[POTE tuning|POTE generator]]: ~63/50 = 414.552
== Submerged ==
{{Main| Submerged }}


Map: [&lt;1 4 3 -1|, &lt;0 -7 -2 11|]
Named by [[Fitzgerald Lee]] in 2025, submerged tempers out 3125/3087, the [[gariboh comma]]. It may be described as the {{nowrap| 16 & 29 }} temperament, generated by a sharply tuned ~8/5, eleven of which minus seven octaves make a perfect fifth; its [[ploidacot]] is therefore zeta-hendecacot. [[45edo]] makes for an excellent tuning.  
Wedgie: &lt;&lt;7 2 -11 -13 -37 -31||
EDOs: [[23edo|23]], [[26edo|26]], [[29edo|29]], [[55edo|55c]]
Badness: 0.1134


==11-limit==
[[Subgroup]]: 2.3.5.7
Commas: 100/99, 245/242, 1375/1344


[[POTE tuning|POTE generator]]: ~14/11 = 414.471
[[Comma list]]: 525/512, 3125/3087


Map: [&lt;1 4 3 -1 0|, &lt;0 -7 -2 11 10|]
{{Mapping|legend=1| 1 -6 3 9 | 0 11 -1 -9 }}
EDOs: 23, 26, 29, 55c
: mapping generators: ~2, ~8/5
Badness: 0.0528


==13-limit==
[[Optimal tuning]]s:
Commas: 65/64, 100/99, 105/104, 245/243
* [[WE]]: ~2 = 1203.3342{{c}}, ~8/5 = 829.2070{{c}}
: [[error map]]: {{val| +3.334 -0.683 -5.518 -1.681 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 826.9483{{c}}
: error map: {{val| 0.000 -5.523 -13.262 -11.361 }}


[[POTE tuning|POTE generator]]: ~14/11 = 414.472
{{Optimal ET sequence|legend=1| 16, 29, 45, 74cd, 119bccdd }}


Map: [&lt;1 4 3 -1 0 3|, &lt;0 -7 -2 11 10 2|]
[[Badness]] (Sintel): 3.98
EDOs: 23, 26, 29, 55
Badness: 0.0300


==17-limit==
=== 11-limit ===
Commas: 35/34, 52/51, 100/99, 169/168, 275/273
Subgroup: 2.3.5.7.11


[[POTE tuning|POTE generator]]: ~14/11 = 414.164
Comma list: 121/120, 441/440, 525/512


Map: [&lt;1 4 3 -1 0 3 1|, &lt;0 -7 -2 11 10 2 9|]
Mapping: {{mapping| 1 -6 3 9 0 | 0 11 -1 -9 5 }}
EDOs: 26, 29, [[84edo|84]], [[113edo|113]]
Badness: 0.0416


==19-limit==
Optimal tunings:
Commas: 35/34, 52/51, 100/99, 121/119, 133/132, 169/168
* WE: ~2 = 1203.6231{{c}}, ~8/5 = 829.4195{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9730{{c}}


[[POTE tuning|POTE generator]]: ~14/11 = 414.130
{{Optimal ET sequence|legend=0| 16, 29, 45e, 74cde, 119bccddeee }}


Map: [&lt;1 4 3 -1 0 3 1 7|, &lt;0 -7 -2 11 10 2 9 -8|]
Badness (Sintel): 1.93
EDOs: 26g, 29
Badness: 0.0337


=Secund=
=== 13-limit ===
Commas: 405/392, 525/512
Subgroup: 2.3.5.7.11.13


POTE generator: ~16/15 = 137.958
Comma list: 65/64, 105/104, 121/120, 441/440


Map: [&lt;1 1 3 2|, &lt;0 5 -6 7|]
Mapping: {{mapping| 1 -6 3 9 0 3 | 0 11 -1 -9 5 1 }}
Wedgie: &lt;&lt;5 -6 7 -21 -3 33||
EDOs: [[9edo|9]], [[17edo|17]], 26, [[61edo|61bc]], [[87edo|87bc]]
Badness: 0.0898


==11-limit==
Optimal tunings:
Commas: 45/44, 99/98, 385/384
* WE: ~2 = 1203.6316{{c}}, ~8/5 = 829.4249{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9677{{c}}


POTE generator: ~12/11 = 137.900
{{Optimal ET sequence|legend=0| 16, 29, 45ef, 74cdef, 119bccddeeeff }}


Map: [&lt;1 1 3 2 3|, &lt;0 5 -6 7 4|]
Badness (Sintel): 1.35
EDOs: 9, 17, 26, 61bc, 87bc
Badness: 0.0426


==13-limit==
[[Category:Temperament collections]]
Commas: 27/26, 45/44, 99/98, 385/384
[[Category:Avicennmic temperaments| ]] <!-- main article -->
 
[[Category:Rank 2]]
POTE generator: ~12/11 = 136.937
 
Map: [&lt;1 1 3 2 3 2|, &lt;0 5 -6 7 4 15|]
EDOs: 9, 26f, [[35edo|35]]
Badness: 0.0497
 
==Secundly==
Commas: 45/44, 78/77, 81/80, 640/637
 
POTE generator: ~12/11 = 137.917
 
Map: [&lt;1 1 3 2 3 3|, &lt;0 5 -6 7 4 6|]
EDOs: 9, 17, 26, 61bcf, 87bcf
Badness: 0.0262
</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Avicennmic temperaments&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="#Roman"&gt;Roman&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&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;a href="#Secund"&gt;Secund&lt;/a&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;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.&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="Roman"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Roman&lt;/h1&gt;
Commas: 525/512, 4000/3969&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~63/50 = 414.552&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 3 -1|, &amp;lt;0 -7 -2 11|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;7 2 -11 -13 -37 -31||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/55edo"&gt;55c&lt;/a&gt;&lt;br /&gt;
Badness: 0.1134&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Roman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
Commas: 100/99, 245/242, 1375/1344&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/11 = 414.471&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 3 -1 0|, &amp;lt;0 -7 -2 11 10|]&lt;br /&gt;
EDOs: 23, 26, 29, 55c&lt;br /&gt;
Badness: 0.0528&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="Roman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
Commas: 65/64, 100/99, 105/104, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/11 = 414.472&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 3 -1 0 3|, &amp;lt;0 -7 -2 11 10 2|]&lt;br /&gt;
EDOs: 23, 26, 29, 55&lt;br /&gt;
Badness: 0.0300&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="Roman-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;17-limit&lt;/h2&gt;
Commas: 35/34, 52/51, 100/99, 169/168, 275/273&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/11 = 414.164&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 3 -1 0 3 1|, &amp;lt;0 -7 -2 11 10 2 9|]&lt;br /&gt;
EDOs: 26, 29, &lt;a class="wiki_link" href="/84edo"&gt;84&lt;/a&gt;, &lt;a class="wiki_link" href="/113edo"&gt;113&lt;/a&gt;&lt;br /&gt;
Badness: 0.0416&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="Roman-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;19-limit&lt;/h2&gt;
Commas: 35/34, 52/51, 100/99, 121/119, 133/132, 169/168&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/11 = 414.130&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 3 -1 0 3 1 7|, &amp;lt;0 -7 -2 11 10 2 9 -8|]&lt;br /&gt;
EDOs: 26g, 29&lt;br /&gt;
Badness: 0.0337&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Secund"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Secund&lt;/h1&gt;
Commas: 405/392, 525/512&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/15 = 137.958&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 2|, &amp;lt;0 5 -6 7|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 -6 7 -21 -3 33||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, 26, &lt;a class="wiki_link" href="/61edo"&gt;61bc&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87bc&lt;/a&gt;&lt;br /&gt;
Badness: 0.0898&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="Secund-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 99/98, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~12/11 = 137.900&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 2 3|, &amp;lt;0 5 -6 7 4|]&lt;br /&gt;
EDOs: 9, 17, 26, 61bc, 87bc&lt;br /&gt;
Badness: 0.0426&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="Secund-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
Commas: 27/26, 45/44, 99/98, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~12/11 = 136.937&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 2 3 2|, &amp;lt;0 5 -6 7 4 15|]&lt;br /&gt;
EDOs: 9, 26f, &lt;a class="wiki_link" href="/35edo"&gt;35&lt;/a&gt;&lt;br /&gt;
Badness: 0.0497&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="Secund-Secundly"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Secundly&lt;/h2&gt;
Commas: 45/44, 78/77, 81/80, 640/637&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~12/11 = 137.917&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 3 2 3 3|, &amp;lt;0 5 -6 7 4 6|]&lt;br /&gt;
EDOs: 9, 17, 26, 61bcf, 87bcf&lt;br /&gt;
Badness: 0.0262&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 18:46, 24 May 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of rank-2 temperaments tempering out the avicennma, 525/512, also known as Avicenna's enharmonic diesis.

Tempereaments discussed elsewhere are:

Considered below is submerged.

Submerged

Main article: Submerged

Named by Fitzgerald Lee in 2025, submerged tempers out 3125/3087, the gariboh comma. It may be described as the 16 & 29 temperament, generated by a sharply tuned ~8/5, eleven of which minus seven octaves make a perfect fifth; its ploidacot is therefore zeta-hendecacot. 45edo makes for an excellent tuning.

Subgroup: 2.3.5.7

Comma list: 525/512, 3125/3087

Mapping: [⟨1 -6 3 9], ⟨0 11 -1 -9]]

mapping generators: ~2, ~8/5

Optimal tunings:

  • WE: ~2 = 1203.3342 ¢, ~8/5 = 829.2070 ¢
error map: ⟨+3.334 -0.683 -5.518 -1.681]
  • CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9483 ¢
error map: ⟨0.000 -5.523 -13.262 -11.361]

Optimal ET sequence: 16, 29, 45, 74cd, 119bccdd

Badness (Sintel): 3.98

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 525/512

Mapping: [⟨1 -6 3 9 0], ⟨0 11 -1 -9 5]]

Optimal tunings:

  • WE: ~2 = 1203.6231 ¢, ~8/5 = 829.4195 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9730 ¢

Optimal ET sequence: 16, 29, 45e, 74cde, 119bccddeee

Badness (Sintel): 1.93

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 65/64, 105/104, 121/120, 441/440

Mapping: [⟨1 -6 3 9 0 3], ⟨0 11 -1 -9 5 1]]

Optimal tunings:

  • WE: ~2 = 1203.6316 ¢, ~8/5 = 829.4249 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9677 ¢

Optimal ET sequence: 16, 29, 45ef, 74cdef, 119bccddeeeff

Badness (Sintel): 1.35

Retrieved from "https://en.xen.wiki/index.php?title=Avicennmic_temperaments&oldid=230845"