525/512: Difference between revisions

525/512, known as Avicenna's enharmonic diesis or avicennma, is the 7-limit medium comma between 64/63 and 25/24, or between 32/25 and 21/16.

Temperaments

Tempering it out equates 64/63 with 25/24 and leads to the avicennmic temperament.

Avicennmic temperament

Subgroup: 2.3.5.7

Comma list: 525/512

Mapping: [⟨1 0 0 9], ⟨0 1 0 -1], ⟨0 0 1 -2]]

POTE generators: ~3/2 = 695.5265, ~5/4 = 374.1745

Optimal ET sequence: 7, 9, 10, 16, 19, 45, 64cd, 93cdd, 119bccdd, 138bccdd

Badness: 0.4765 × 10^-3

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox Interval
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| Name = Avicenna's enharmonic diesis, avicennma
-: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-17 10:44:19 UTC</tt>.<br>
+| Color name = Lzyy1, lazoyoyo unison
-: The original revision id was <tt>592476470</tt>.<br>
+| Comma = yes
-: 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>
+'''525/512''', known as '''Avicenna's enharmonic diesis''' or '''avicennma''', is the [[7-limit]] [[medium comma]] between [[64/63]] and [[25/24]], or between [[32/25]] and [[21/16]].
-<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">525/512, known as Avicenna's enharmonic diesis or the Avicenna, is the interval between [[64_63|64/63]] and [[25_24|25/24]]. Tempering it out equates the two and leads to [[avicennmic temperaments]].</pre></div>
-<h4>Original HTML content:</h4>
+== Temperaments ==
-<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;525_512&lt;/title&gt;&lt;/head&gt;&lt;body&gt;525/512, known as Avicenna's enharmonic diesis or the Avicenna, is the interval between &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt; and &lt;a class="wiki_link" href="/25_24"&gt;25/24&lt;/a&gt;. Tempering it out equates the two and leads to &lt;a class="wiki_link" href="/avicennmic%20temperaments"&gt;avicennmic temperaments&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
+Tempering it out equates 64/63 with 25/24 and leads to the avicennmic temperament.
+=== Avicennmic temperament ===
+Subgroup: 2.3.5.7
+[[Comma list]]: 525/512
+[[Mapping]]: [{{val| 1 0 0 9 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -2 }}]
+[[POTE generator]]s: ~3/2 = 695.5265, ~5/4 = 374.1745
+{{Optimal ET sequence|legend=1| 7, 9, 10, 16, 19, 45, 64cd, 93cdd, 119bccdd, 138bccdd }}
+[[Badness]]: 0.4765 × 10<sup>-3</sup>
+== See also ==
+* [[Medium comma]]
+* [[Avicennmic temperaments]], a collection of rank-2 temperaments where it is tempered out
+[[Category:Avicennmic]]
+[[Category:Commas named after polymaths]]

525/512: Difference between revisions

Latest revision as of 02:13, 4 November 2024

Temperaments

Avicennmic temperament

See also

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