Petrmic chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Petrmic chords''' are [[essentially tempered dyadic chord]]s tempered by the petrma, [[2200/2197]].  
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-27 17:08:50 UTC</tt>.<br>
The petrmic triad is a palindrome in the 2.5.11.13 [[subgroup]] [[13-odd-limit]], consisting of two [[13/10]] intervals followed by a [[13/11]], closing at the [[octave]]. In other words:
: The original revision id was <tt>243131369</tt>.<br>
* 1–13/10–22/13 with steps 13/10, 13/10, 13/11.  
: 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>
It can be extended to the following palindromic tetrad:  
<h4>Original Wikitext content:</h4>
* 1–11/10–13/10–22/13 with steps 11/10, 13/11, 13/10, 13/11.  
<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 //petrmic triad// is a 13-limit [[Dyadic chord|essentially tempered dyadic chord]] consisting of two 13/10 intervals followed by a 13/11, in other words a 13/10-13/10-13/11 chord, tempered by the petrma, 2200/2197, so that it closes at the octave. Another way to say this is that it is the petrmic tempering of 1-13/10-22/13 or 1-13/11-20/13. Equal temperaments with petrmic triads include 29, 37, 50, 53, 58, 84, 87, 111, 121, 140, 190, 198, 224, 311, 414, 422, and 612. 37, 50 and especially 29 have notably good petrmic triads.</pre></div>
 
<h4>Original HTML content:</h4>
[[Equal temperament]]s with petrmic chords include {{EDOs| 29, 37, 50, 53, 58, 84, 87, 111, 121, 140, 190, 198, 224, 311, 414, 422, and 612 }}. 37, 50 and especially 29 have notably good petrmic triads.
<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;petrmic triad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;petrmic triad&lt;/em&gt; is a 13-limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered dyadic chord&lt;/a&gt; consisting of two 13/10 intervals followed by a 13/11, in other words a 13/10-13/10-13/11 chord, tempered by the petrma, 2200/2197, so that it closes at the octave. Another way to say this is that it is the petrmic tempering of 1-13/10-22/13 or 1-13/11-20/13. Equal temperaments with petrmic triads include 29, 37, 50, 53, 58, 84, 87, 111, 121, 140, 190, 198, 224, 311, 414, 422, and 612. 37, 50 and especially 29 have notably good petrmic triads.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Petrmic]]

Latest revision as of 14:08, 19 March 2025

Petrmic chords are essentially tempered dyadic chords tempered by the petrma, 2200/2197.

The petrmic triad is a palindrome in the 2.5.11.13 subgroup 13-odd-limit, consisting of two 13/10 intervals followed by a 13/11, closing at the octave. In other words:

  • 1–13/10–22/13 with steps 13/10, 13/10, 13/11.

It can be extended to the following palindromic tetrad:

  • 1–11/10–13/10–22/13 with steps 11/10, 13/11, 13/10, 13/11.

Equal temperaments with petrmic chords include 29, 37, 50, 53, 58, 84, 87, 111, 121, 140, 190, 198, 224, 311, 414, 422, and 612. 37, 50 and especially 29 have notably good petrmic triads.