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:genewardsmith|genewardsmith]] and made on <tt>2011-02-25 20:52:36 UTC</tt>.<br>
: The original revision id was <tt>205167216</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">These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis.


==Roman==
Tempereaments discussed elsewhere are:
Commas: 525/512, 4000/3969
* ''[[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]]


[[POTE tuning|POTE generator]]:
Considered below is submerged.


Map: [&lt;1 4 3 -1|, &lt;0 -7 -2 11|]
== Submerged ==
Wedgie: &lt;&lt;
{{Main| Submerged }}
===11-limit===


===13-limit===</pre></div>
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.
<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;These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis.&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Roman"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Roman&lt;/h2&gt;
[[Comma list]]: 525/512, 3125/3087
Commas: 525/512, 4000/3969&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 -6 3 9 | 0 11 -1 -9 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: &lt;br /&gt;
: mapping generators: ~2, ~8/5
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3 -1|, &amp;lt;0 -7 -2 11|]&lt;br /&gt;
[[Optimal tuning]]s:  
Wedgie: &amp;lt;&amp;lt;&lt;br /&gt;
* [[WE]]: ~2 = 1203.3342{{c}}, ~8/5 = 829.2070{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Roman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h3&gt;
: [[error map]]: {{val| +3.334 -0.683 -5.518 -1.681 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 826.9483{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Roman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
: error map: {{val| 0.000 -5.523 -13.262 -11.361 }}
&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{Optimal ET sequence|legend=1| 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: {{mapping| 1 -6 3 9 0 | 0 11 -1 -9 5 }}
 
Optimal tunings:
* WE: ~2 = 1203.6231{{c}}, ~8/5 = 829.4195{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9730{{c}}
 
{{Optimal ET sequence|legend=0| 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: {{mapping| 1 -6 3 9 0 3 | 0 11 -1 -9 5 1 }}
 
Optimal tunings:  
* WE: ~2 = 1203.6316{{c}}, ~8/5 = 829.4249{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9677{{c}}
 
{{Optimal ET sequence|legend=0| 16, 29, 45ef, 74cdef, 119bccddeeeff }}
 
Badness (Sintel): 1.35
 
[[Category:Temperament collections]]
[[Category:Avicennmic temperaments| ]] <!-- main article -->
[[Category:Rank 2]]

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

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