Kestrel chords - Revision history

FloraC: Cleanup

2025-03-19T13:53:26Z

Cleanup

← Older revision		Revision as of 13:53, 19 March 2025
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	For triads, there are three pairs of chords in inverse relationship:		For triads, there are three pairs of chords in inverse relationship:
	* ~~1-7~~/~~6-18~~/13 with steps of 7/6-13/11-13/9, and its inverse		* 1–7/6–18/13 with steps of 7/6, 13/11, 13/9, and its inverse
	* ~~1-13~~/~~11-18~~/13 with steps of 13/11-7/6-13/9;		* 1–13/11–18/13 with steps of 13/11, 7/6, 13/9;
	* ~~1-14~~/~~11-18~~/13 with steps of 14/11-13/12-13/9, and its inverse		* 1–14/11–18/13 with steps of 14/11, 13/12, 13/9, and its inverse
	* ~~1-13~~/~~12-18~~/13 with steps of 13/12-14/11-13/9;		* 1–13/12–18/13 with steps of 13/12, 14/11, 13/9;
	* ~~1-13~~/~~11-9~~/7 with steps of 13/11-13/12-14/9, and its inverse		* 1–13/11–9/7 with steps of 13/11, 13/12, 14/9, and its inverse
	* ~~1-13~~/~~12-9~~/7 with steps of 13/12-13/11-14/9.		* 1–13/12–9/7 with steps of 13/12, 13/11, 14/9.

	For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
	* ~~1-13~~/~~11-18~~/~~13-18~~/11 with steps of 13/11-7/6-13/11-11/9;		* 1–13/11–18/13–18/11 with steps of 13/11, 7/6, 13/11, 11/9;
	* ~~1-13~~/~~12-18~~/~~13-3~~/2 with steps of 13/12-14/11-13/12-4/3;		* 1–13/12–18/13–3/2 with steps of 13/12, 14/11, 13/12, 4/3;
	* ~~1-13~~/~~12-13~~/~~11-9~~/7 with steps of 13/12-12/11-13/12-14/9.		* 1–13/12–13/11–9/7 with steps of 13/12, 12/11, 13/12, 14/9.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* ~~1-11~~/~~9-13~~/~~9-11~~/7 with steps of 11/9-13/11-13/12-14/11, and its inverse		* 1–11/9–13/9–11/7 with steps of 11/9, 13/11, 13/12, 14/11, and its inverse
	* ~~1-13~~/~~12-9~~/~~7-11~~/7 with steps of 13/12-13/11-11/9-14/11;		* 1–13/12–9/7–11/7 with steps of 13/12, 13/11, 11/9, 14/11;
	* ~~1-7~~/~~6-18~~/~~13-3~~/2 with steps of 7/6-13/11-13/12-4/3, and its inverse		* 1–7/6–18/13–3/2 with steps of 7/6, 13/11, 13/12, 4/3, and its inverse
	* ~~1-13~~/~~12-9~~/~~7-3~~/2 with steps of 13/12-13/11-7/6-4/3;		* 1–13/12–9/7–3/2 with steps of 13/12, 13/11, 7/6, 4/3;
	* ~~1-13~~/~~11-9~~/~~7-18~~/13 with steps of 13/11-13/12-14/13-13/9, and its inverse		* 1–13/11–9/7–18/13 with steps of 13/11, 13/12, 14/13, 13/9, and its inverse
	* ~~1-14~~/~~13-7~~/~~6-18~~/13 with steps of 14/13-13/12-13/11-13/9;		* 1–14/13–7/6–18/13 with steps of 14/13, 13/12, 13/11, 13/9;
	* ~~1-13~~/~~11-14~~/~~11-18~~/13 with steps of 13/11-14/13-13/12-13/9, and its inverse		* 1–13/11–14/11–18/13 with steps of 13/11, 14/13, 13/12, 13/9, and its inverse
	* ~~1-13~~/~~12-7~~/~~6-18~~/13 with steps of 13/12-14/13-13/11-13/9;		* 1–13/12–7/6–18/13 with steps of 13/12, 14/13, 13/11, 13/9;
	* ~~1-7~~/~~6-14~~/~~11-18~~/13 with steps of 7/6-12/11-13/12-13/9, and its inverse		* 1–7/6–14/11–18/13 with steps of 7/6, 12/11, 13/12, 13/9, and its inverse
	* ~~1-13~~/~~12-13~~/~~11-18~~/13 with steps of 13/12-12/11-7/6-13/9;		* 1–13/12–13/11–18/13 with steps of 13/12, 12/11, 7/6, 13/9;
	* ~~1-13~~/~~12-9~~/~~7-18~~/13 with steps of 13/12-13/11-14/13-13/9, and its inverse		* 1–13/12–9/7–18/13 with steps of 13/12, 13/11, 14/13, 13/9, and its inverse
	* ~~1-14~~/~~13-14~~/~~11-18~~/13 with steps of 14/13-13/11-13/12-13/9.		* 1–14/13–14/11–18/13 with steps of 14/13, 13/11, 13/12, 13/9.

	For pentads, there are three pairs of chords in inverse relationship:		For pentads, there are three pairs of chords in inverse relationship:
	* ~~1-13~~/~~11-9~~/~~7-18~~/~~13-18~~/11 with steps of 13/11-13/12-14/13-13/11-11/9, and its inverse		* 1–13/11–9/7–18/13–18/11 with steps of 13/11, 13/12, 14/13, 13/11, 11/9, and its inverse
	* ~~1-13~~/~~11-14~~/~~11-18~~/~~13-18~~/11 with steps of 13/11-14/13-13/12-13/11-11/9;		* 1–13/11–14/11–18/13–18/11 with steps of 13/11, 14/13, 13/12, 13/11, 11/9;
	* ~~1-13~~/~~12-7~~/~~6-18~~/~~13-3~~/2 with steps of 13/12-14/13-13/11-13/12-4/3, and its inverse		* 1–13/12–7/6–18/13–3/2 with steps of 13/12, 14/13, 13/11, 13/12, 4/3, and its inverse
	* ~~1-13~~/~~12-9~~/~~7-18~~/~~13-3~~/2 with steps of 13/12-13/11-14/13-13/12-4/3;		* 1–13/12–9/7–18/13–3/2 with steps of 13/12, 13/11, 14/13, 13/12, 4/3;
	* ~~1-13~~/~~12-13~~/~~11-9~~/~~7-18~~/13 with steps of 13/12-12/11-13/12-14/13-13/9, and its inverse		* 1–13/12–13/11–9/7–18/13 with steps of 13/12, 12/11, 13/12, 14/13, 13/9, and its inverse
	* ~~1-14~~/~~13-7~~/~~6-14~~/~~11-18~~/13 with steps of 14/13-13/12-12/11-13/12-13/9.		* 1–14/13–7/6–14/11–18/13 with steps of 14/13, 13/12, 12/11, 13/12, 13/9.

	Equal temperaments with kestrel chords include {{Optimal ET sequence\|17, 24, 26, 41, 53, 58, 77, 94, 103, 111, 161, 205, 214 and 255}}, with 255edo giving the [[optimal patent val]].		Equal temperaments with kestrel chords include {{Optimal ET sequence\|17, 24, 26, 41, 53, 58, 77, 94, 103, 111, 161, 205, 214 and 255}}, with 255edo giving the [[optimal patent val]].

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

Xenllium: Update the article

2023-11-03T13:48:01Z

Update the article

@@ Line 1: / Line 1: @@
-The ''[[kestrel]] [[tetrad]]'' is the [[13-limit]], [[Dyadic chord|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a [[temperament]] tempering out the kestrel comma, [[1188/1183]], leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two [[Kestrel triad|kestrel triads]], 1-7/6-18/13 and 1-13/11-18/13.
+'''Kestrel chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the kestrel comma, [[1188/1183]].
-Closely related tetrads require the tempering of both 1188/1183 and [[540/539]], with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. [[EDO|Equal temperaments]] tempering out both 1188/1183 and 540/539 include [[41edo|41]], [[53edo|53]], [[58edo|58]], [[94edo|94]], [[103edo|103]], [[111edo|111]], [[161edo|161]], [[205edo|205]], [[214edo|214]], [[255edo|255]].
+Kestrel chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.11.13 subgroup [[13-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.
-edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].
+For triads, there are three pairs of chords in inverse relationship:
 [[Category:13-odd-limit]]
@@ Line 9: / Line 44: @@
 [[Category:Triads]]
 [[Category:Tetrads]]
 [[Category:Kestrel]]

FloraC: Recategorize

2023-05-23T11:40:52Z

Recategorize

← Older revision		Revision as of 11:40, 23 May 2023
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	255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].		255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].

	[[Category:13-limit]]		[[Category:13-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Kestrel]]		[[Category:Kestrel]]

FloraC: Recategorize

2023-04-28T07:28:08Z

Recategorize

← Older revision		Revision as of 07:28, 28 April 2023
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	255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].		255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].

	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:~~Chords~~]]		[[Category:Essentially tempered chords]]
	[[Category:~~Dyadic~~]]		[[Category:Triad]]
			[[Category:Tetrad]]
	[[Category:Kestrel]]		[[Category:Kestrel]]
	~~[[Category:Swetisma]]~~

BudjarnLambeth at 07:36, 20 April 2023

2023-04-20T07:36:01Z

← Older revision		Revision as of 07:36, 20 April 2023
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	The ''[[kestrel]] [[tetrad]]'' is the [[13-limit]], [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a [[temperament]] tempering out the kestrel comma, [[1188/1183]], leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two [[Kestrel triad\|kestrel triads]], 1-7/6-18/13 and 1-13/11-18/13.		The ''[[kestrel]] [[tetrad]]'' is the [[13-limit]], [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a [[temperament]] tempering out the kestrel comma, [[1188/1183]], leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two [[Kestrel triad\|kestrel triads]], 1-7/6-18/13 and 1-13/11-18/13.

	Closely related tetrads require the tempering of both 1188/1183 and [[540/539]], with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include [[41edo\|41]], [[53edo\|53]], [[58edo\|58]], [[94edo\|94]], [[103edo\|103]], [[111edo\|111]], [[161edo\|161]], [[205edo\|205]], [[214edo\|214]], [[255edo\|255]].		Closely related tetrads require the tempering of both 1188/1183 and [[540/539]], with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. [[EDO\|Equal temperaments]] tempering out both 1188/1183 and 540/539 include [[41edo\|41]], [[53edo\|53]], [[58edo\|58]], [[94edo\|94]], [[103edo\|103]], [[111edo\|111]], [[161edo\|161]], [[205edo\|205]], [[214edo\|214]], [[255edo\|255]].

	255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].		255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].

BudjarnLambeth at 07:22, 20 April 2023

2023-04-20T07:22:34Z

← Older revision		Revision as of 07:22, 20 April 2023
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	[[Category:Kestrel]]		[[Category:Kestrel]]
	[[Category:Swetisma]]		[[Category:Swetisma]]
	~~[[Category:Todo:add links]]~~

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

2023-04-20T07:22:24Z

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

← Older revision		Revision as of 07:22, 20 April 2023
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	The ''kestrel tetrad'' is the 13-limit [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.		The ''[[kestrel]] [[tetrad]]'' is the [[13-limit]], [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a [[temperament]] tempering out the kestrel comma, [[1188/1183]], leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two [[Kestrel triad\|kestrel triads]], 1-7/6-18/13 and 1-13/11-18/13.

			Closely related tetrads require the tempering of both 1188/1183 and [[540/539]], with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include [[41edo\|41]], [[53edo\|53]], [[58edo\|58]], [[94edo\|94]], [[103edo\|103]], [[111edo\|111]], [[161edo\|161]], [[205edo\|205]], [[214edo\|214]], [[255edo\|255]].

			255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 [[just intonation subgroup]].
	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:Chords]]		[[Category:Chords]]

ResonantFrequencies: /* top */re-categorisation (AWB)

2019-06-30T00:38:30Z

top: re-categorisation (AWB)

← Older revision		Revision as of 00:38, 30 June 2019
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	The ''kestrel tetrad'' is the 13-limit [[~~Dyadic_chord~~\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the [[~~Optimal_patent_val\|~~optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.		The ''kestrel tetrad'' is the 13-limit [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.
	[[Category:13-limit]]		[[Category:13-limit]]
	[[Category:~~chord~~]]		[[Category:Chords]]
	[[Category:~~dyadic~~]]		[[Category:Dyadic]]
	[[Category:~~kestrel~~]]		[[Category:Kestrel]]
	[[Category:~~swetisma~~]]		[[Category:Swetisma]]
	[[Category:~~todo~~:~~add_links~~]]		[[Category:Todo:add links]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		The ''kestrel tetrad'' is the 13-limit [[Dyadic_chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the [[Optimal_patent_val\|optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.
	~~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:guest\|guest]] and made on <tt>2013-03-26 10:37:02 UTC</tt>.<br>~~		[[Category:chord]]
	~~: The original revision id was <tt>417968310</tt>.<br>~~		[[Category:dyadic]]
	~~: The revision comment was: <tt></tt><br>~~		[[Category:kestrel]]
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~		[[Category:swetisma]]
	~~<h4>Original Wikitext content:</h4>~~		[[Category:todo:add_links]]
	<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 //kestrel tetrad// is the 13-limit [[~~Dyadic chord~~\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.~~</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>kestrel chords</title></head><body>The <em>kestrel tetrad</em> is the 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered tetrad</a> consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</body></html></pre></div>

Wikispaces>guest: Imported revision 417968310 - Original comment:

2013-03-26T10:37:02Z

**Imported revision 417968310 - Original comment: **

← Older revision		Revision as of 10:37, 26 March 2013
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	<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>2013-01-~~31 15~~:50:07 UTC</tt>.<br>		: This revision was by author [[User:guest\|guest]] and made on <tt>2013-03-26 10:37:02 UTC</tt>.<br>
	: The original revision id was <tt>~~403174402~~</tt>.<br>		: The original revision id was <tt>417968310</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 //kestrel tetrad// is the 13-limit [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, ~~165~~, 205, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</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 //kestrel tetrad// is the 13-limit [[Dyadic chord\|essentially tempered tetrad]] consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the [[optimal patent val]] for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</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>kestrel chords</title></head><body>The <em>kestrel tetrad</em> is the 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered tetrad</a> consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, ~~165~~, 205, 214, 255. 255edo is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</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>kestrel chords</title></head><body>The <em>kestrel tetrad</em> is the 13-limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered tetrad</a> consisting, in close position, of the steps 13/11-7/6-13/11-11/9 in a temperament tempering out the kestrel comma, 1188/1183, leading to the tempering of 1-13/11-18/13-18/11. Contained in the kestrel tetrad are the two kestrel triads, 1-7/6-18/13 and 1-13/11-18/13. Closely related tetrads require the tempering of both 1188/1183 and 540/539, with steps of 7/6-13/11-13/11-11/9, leading to the tempered version of 1-7/6-18/13-18/11, and 11/9-13/11-13/11-7/6, leading to the 1-11/9-13/9-12/7 chord. Equal temperaments tempering out both 1188/1183 and 540/539 include 41, 53, 58, 94, 103, 111, 161, 205, 214, 255. 255edo is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for both {1188/1183, 540/539}-tempering and 1188/1183-tempering, so nothing significant is lost in tuning accuracy by also tempering out 540/539. Kestrel tetrads are essentially tempered tetrads of the 2.7/3.11/9.13/9 just intonation subgroup.</body></html></pre></div>

Kestrel chords - Revision history

FloraC: Cleanup

Xenllium: Update the article

FloraC: Recategorize

FloraC: Recategorize

BudjarnLambeth at 07:36, 20 April 2023

BudjarnLambeth at 07:22, 20 April 2023

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

ResonantFrequencies: /* top */re-categorisation (AWB)

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>guest: **Imported revision 417968310 - Original comment: **

Wikispaces>guest: Imported revision 417968310 - Original comment: