Chords of octacot - Revision history

FloraC: Note 11-odd-limit

2025-09-27T13:49:56Z

Note 11-odd-limit

← Older revision		Revision as of 13:49, 27 September 2025
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	Below are listed the [[dyadic chord]]s of 11-limit [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[540/539]] are [[swetismic chords\|swetismic]], by [[441/440]] [[werckismic chords\|werckismic]], by [[243/242]] [[rastmic chords\|rastmic]], by [[245/243]] [[sensamagic chords\|sensamagic]], by [[245/242]] [[frostmic chords\|frostmic]], and by [[100/99]] [[ptolemismic chords\|ptolemismic]]. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled [[jove chords\|jove]], those requiring any two of 441/440, 245/242 or 100/99 [[nakika chords\|nakika]], those requiring any two of 540/539, 245/243 or 100/99 [[octarod chords\|octarod]]. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.		Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[540/539]] are [[swetismic chords\|swetismic]], by [[441/440]] [[werckismic chords\|werckismic]], by [[243/242]] [[rastmic chords\|rastmic]], by [[245/243]] [[sensamagic chords\|sensamagic]], by [[245/242]] [[frostmic chords\|frostmic]], and by [[100/99]] [[ptolemismic chords\|ptolemismic]]. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled [[jove chords\|jove]], those requiring any two of 441/440, 245/242 or 100/99 [[nakika chords\|nakika]], those requiring any two of 540/539, 245/243 or 100/99 [[octarod chords\|octarod]]. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.

	Octacot has [[mos]] of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.		Octacot has [[mos]] of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.

	== Triads ==		== Triads ==
	{\| class="wikitable"		{\| class="wikitable center-1"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
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	== Tetrads ==		== Tetrads ==
	{\| class="wikitable"		{\| class="wikitable center-1"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
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	== Pentads ==		== Pentads ==
	{\| class="wikitable"		{\| class="wikitable center-1"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
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	== Hexads ==		== Hexads ==
	{\| class="wikitable"		{\| class="wikitable center-1"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal

FloraC: Cassacot -> frostmic. Octagari -> nakika. Note octarod. Fix heading levels. - empty columns.

2025-09-27T13:48:23Z

Cassacot -> frostmic. Octagari -> nakika. Note octarod. Fix heading levels. - empty columns.

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ArrowHead294 at 13:28, 27 September 2025

2025-09-27T13:28:26Z

← Older revision		Revision as of 13:28, 27 September 2025
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	Below are listed the [[dyadic chord]]s of 11-limit [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.		Below are listed the [[dyadic chord]]s of 11-limit [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.

	Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-cent equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of ~~88 cents temperament~~. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.		Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.

	= Triads =		= Triads =

ArrowHead294 at 13:27, 27 September 2025

2025-09-27T13:27:20Z

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BudjarnLambeth: Categorised this uncategorised page

2023-04-25T11:06:00Z

Categorised this uncategorised page

← Older revision		Revision as of 11:06, 25 April 2023
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	\| \| octagari		\| \| octagari
	\|}		\|}
			[[Category:Lists of chords]]
			[[Category:Dyadic chords]]
			[[Category:11-limit]]
			[[Category:Octacot]]
			[[Category:88cet]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

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Wikispaces>genewardsmith: Imported revision 288623986 - Original comment:

2011-12-28T01:49:22Z

**Imported revision 288623986 - Original comment: **

← Older revision		Revision as of 01:49, 28 December 2011
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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>2011-12-28 01:43:46 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2011-12-28 01:49:22 UTC</tt>.<br>
	: The original revision id was <tt>~~288623796~~</tt>.<br>		: The original revision id was <tt>288623986</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>
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	<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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Tetracot family#Octacot\|octacot temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.		<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">Below are listed the [[Dyadic chord\|dyadic chords]] of 11-limit [[Tetracot family#Octacot\|octacot temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.

	Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the [[88cET\|88 ~~cent~~ temperament]] is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 ~~cent~~ temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.		Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the [[88cET\|88 cents temperament]] is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.

	=Triads=		=Triads=
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	<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>Chords of octacot</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Tetracot%20family#Octacot">octacot temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot. <br />		<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>Chords of octacot</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Tetracot%20family#Octacot">octacot temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot. <br />
	<br />		<br />
	Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the <a class="wiki_link" href="/88cET">88 ~~cent~~ temperament</a> is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 ~~cent~~ temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.<br />		Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the <a class="wiki_link" href="/88cET">88 cents temperament</a> is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.<br />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>		<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>

Wikispaces>genewardsmith: Imported revision 288623796 - Original comment:

2011-12-28T01:43:46Z

**Imported revision 288623796 - Original comment: **

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Chords of octacot - Revision history

FloraC: Note 11-odd-limit

FloraC: Cassacot -> frostmic. Octagari -> nakika. Note octarod. Fix heading levels. - empty columns.

ArrowHead294 at 13:28, 27 September 2025

ArrowHead294 at 13:27, 27 September 2025

BudjarnLambeth: Categorised this uncategorised page

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>genewardsmith: **Imported revision 288623986 - Original comment: **

Wikispaces>genewardsmith: **Imported revision 288623796 - Original comment: **

Wikispaces>genewardsmith: Imported revision 288623986 - Original comment:

Wikispaces>genewardsmith: Imported revision 288623796 - Original comment: