Petrmic chords - Revision history

FloraC: Cleanup

2025-03-19T14:08:03Z

Cleanup

← Older revision		Revision as of 14:08, 19 March 2025
Line 2:		Line 2:

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

	It can be extended to the following palindromic tetrad:		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		* 1–11/10–13/10–22/13 with steps 11/10, 13/11, 13/10, 13/11.

	[[~~EDO\|~~Equal ~~temperaments~~]] 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.		[[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.

	[[Category:13-odd-limit]]		[[Category:13-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
	[[Category:Petrmic]]		[[Category:Petrmic]]

FloraC: Recategorize

2023-05-23T11:44:16Z

Recategorize

← Older revision		Revision as of 11:44, 23 May 2023
Line 11:		Line 11:
	[[Category:13-odd-limit]]		[[Category:13-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Petrmic]]		[[Category:Petrmic]]

FloraC: FloraC moved page Petrmic triad to Petrmic chords: More than triads

2023-05-11T11:14:59Z

FloraC moved page Petrmic triad to Petrmic chords: More than triads

← Older revision	Revision as of 11:14, 11 May 2023
(No difference)

FloraC: Expansion

2023-05-11T11:14:42Z

Expansion

@@ Line 1: / Line 1: @@
-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. [[EDO|Equal temperaments]] with petrmic triads include [[29edo|29]], [[37edo|37]], [[50edo|50]], [[53edo|53]], [[58edo|58]], [[84edo|84]], [[87edo|87]], [[111edo|111]], [[121edo|121]], [[140edo|140]], [[190edo|190]], [[198edo|198]], [[224edo|224]], [[311edo|311]], [[414edo|414]], [[422edo|422]], and [[612edo|612]]. 37, 50 and especially 29 have notably good petrmic triads.
+'''Petrmic chords''' are [[essentially tempered dyadic chord]]s tempered by the petrma, [[2200/2197]].
 [[Category:13-limit]]
-[[Category:petrmic]]
+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:
-[[Category:triad]]
+* 1-13/10-22/13 with steps 13/10-13/10-13/11.

BudjarnLambeth: Added links (as requested by the to:do notice)

2023-04-20T07:46:29Z

Added links (as requested by the to:do notice)

← Older revision		Revision as of 07:46, 20 April 2023
Line 1:		Line 1:
	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.		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. [[EDO\|Equal temperaments]] with petrmic triads include [[29edo\|29]], [[37edo\|37]], [[50edo\|50]], [[53edo\|53]], [[58edo\|58]], [[84edo\|84]], [[87edo\|87]], [[111edo\|111]], [[121edo\|121]], [[140edo\|140]], [[190edo\|190]], [[198edo\|198]], [[224edo\|224]], [[311edo\|311]], [[414edo\|414]], [[422edo\|422]], and [[612edo\|612]]. 37, 50 and especially 29 have notably good petrmic triads.
	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:petrmic]]		[[Category:petrmic]]
	~~[[Category:todo:add_links]]~~
	[[Category:triad]]		[[Category:triad]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
Line 1:		Line 1:
	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		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.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~		[[Category:13-limit]]
	~~: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-07-27 17:08:50 UTC</tt>.<br>~~		[[Category:petrmic]]
	~~: The original revision id was <tt>243131369</tt>.<br>~~		[[Category:todo:add_links]]
	~~: The revision comment was: <tt></tt><br>~~		[[Category:triad]]
	~~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 //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>~~
	~~<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"><html><head><title>petrmic~~ triad</title></head><body>The <em>petrmic triad</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> 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.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 243131369 - Original comment:

2011-07-27T17:08:50Z

**Imported revision 243131369 - Original comment: **

← Older revision		Revision as of 17:08, 27 July 2011
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		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 16:33:47 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-07-27 17:08:50 UTC</tt>.<br>
	: The original revision id was <tt>~~243126347~~</tt>.<br>		: The original revision id was <tt>243131369</tt>.<br>
	: The revision comment was: <tt></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>		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>		<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 //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 87 have notably good petrmic triads.</pre></div>		<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>		<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"><html><head><title>petrmic triad</title></head><body>The <em>petrmic triad</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> 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 87 have notably good petrmic triads.</body></html></pre></div>		<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"><html><head><title>petrmic triad</title></head><body>The <em>petrmic triad</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> 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.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 243126347 - Original comment:

2011-07-27T16:33:47Z

**Imported revision 243126347 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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 16:33:47 UTC</tt>.<br>
: The original revision id was <tt>243126347</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 //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 87 have notably good petrmic triads.</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"><html><head><title>petrmic triad</title></head><body>The <em>petrmic triad</em> is a 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered dyadic chord</a> 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 87 have notably good petrmic triads.</body></html></pre></div>