Nicolic chords - Revision history

FloraC: This is of pattern 1b

2025-03-20T14:29:34Z

This is of pattern 1b

← Older revision		Revision as of 14:29, 20 March 2025
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	'''Nicolic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the nicola, [[1575/1573]].		'''Nicolic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the nicola, [[1575/1573]].

	~~There~~ are ~~three triads, six tetrads and two pentads as~~ [[15-odd-limit]] ~~essentially tempered chords~~.		Nicolic chords are of [[dyadic chord/Pattern of essentially tempered chords\|pattern 1b]] in the [[15-odd-limit]]. There are 3 triads, 6 tetrads and 2 pentads for a total of 11 distinct chord structures.

	The nicolic triads include the following palindromic form,		The nicolic triads include the following palindromic form since it identifies [[13/7]] by a stack of two [[15/11]]'s:
	* 1–[[15/11]]–[[13/7]] with steps of 15/11, 15/11, [[14/13]],		* 1–15/11–13/7 with steps of 15/11, 15/11, [[14/13]].

	~~and~~ a pair in inverse relationship,		And a pair in inverse relationship:
	* 1–15/11–[[11/7]] with steps of 15/11, [[15/13]], [[14/11]], and		* 1–15/11–[[11/7]] with steps of 15/11, [[15/13]], [[14/11]], and its inverse
	* 1–15/11–[[26/15]] with steps of 15/11, 14/11, 15/13.		* 1–15/11–[[26/15]] with steps of 15/11, 14/11, 15/13.

FloraC: Cleanup

2025-03-20T14:21:16Z

Cleanup

← Older revision		Revision as of 14:21, 20 March 2025
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	'''Nicolic chords''' are [[~~Dyadic~~ chord\|essentially tempered chords]] tempered by the nicola, [[1575/1573]].		'''Nicolic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the nicola, [[1575/1573]].

	There are three triads, six tetrads and two pentads as [[15-odd-limit]] essentially tempered chords.		There are three triads, six tetrads and two pentads as [[15-odd-limit]] essentially tempered chords.

	The nicolic triads include the following palindromic form,		The nicolic triads include the following palindromic form,
	* 1-[[15/11]]-[[13/7]] with steps of 15/11-15/11-[[14/13]],		* 1–[[15/11]]–[[13/7]] with steps of 15/11, 15/11, [[14/13]],

	and a pair in inverse relationship,		and a pair in inverse relationship,
	* ~~1-15~~/~~11-~~[[11/7]] with steps of 15/11-[[15/13]]-[[14/11]], and		* 1–15/11–[[11/7]] with steps of 15/11, [[15/13]], [[14/11]], and
	* ~~1-15~~/~~11-~~[[26/15]] with steps of 15/11-14/11-15/13.		* 1–15/11–[[26/15]] with steps of 15/11, 14/11, 15/13.

	For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* ~~1-15~~/~~13-15~~/~~11-11~~/7 with steps of 15/13-[[13/11]]-15/13-14/11;		* 1–15/13–15/11–11/7 with steps of 15/13, [[13/11]], 15/13, 14/11;
	* ~~1-15~~/~~13-~~[[22/15]]~~-11~~/7 with steps of 15/13-14/11-[[15/14]]-14/11.		* 1–15/13–[[22/15]]–11/7 with steps of 15/13, 14/11, [[15/14]], 14/11.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* ~~1-15~~/~~11-11~~/~~7-13~~/7 with steps of 15/11-15/13-13/11-14/13, and its inverse		* 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse
	* ~~1-15~~/~~11-22~~/~~15-26~~/15 with steps of 15/11-14/13-13/11-15/13;		* 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13;
	* ~~1-15~~/~~11-26~~/~~15-13~~/7 with steps of 15/11-14/11-15/14-14/13, and its inverse		* 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse
	* ~~1-15~~/~~11-22~~/~~15-11~~/7 with steps of 15/11-14/13-15/14-14/11.		* 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11.

	They can be extended to pentads:		They can be extended to pentads:
	* ~~1-15~~/~~14-15~~/~~13-15~~/~~11-11~~/7 with steps of 15/14-14/13-13/11-15/13-14/11, and its inverse		* 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse
	* ~~1-15~~/~~13-15~~/~~11-22~~/~~15-11~~/7 with steps of 15/13-13/11-14/13-15/14-14/11.		* 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11.

	[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence\| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}.		[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence\| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}.
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	\|}		\|}

	[[Category:15-odd-limit]]		[[Category:15-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

Xenllium at 23:47, 5 November 2023

2023-11-05T23:47:07Z

← Older revision		Revision as of 23:47, 5 November 2023
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	* 1-15/13-15/11-22/15-11/7 with steps of 15/13-13/11-14/13-15/14-14/11.		* 1-15/13-15/11-22/15-11/7 with steps of 15/13-13/11-14/13-15/14-14/11.

	[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence\| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.		[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence\| 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855 }}.

	Here is a listening sample, tempered to TE tuning of nicolic.		Here is a listening sample, tempered to TE tuning of nicolic.

	{\| class="wikitable center-all~~" style="column-width:10em~~"		{\| class="wikitable center-all"
	! Ratio		! Ratio
	! [[1/1]] \|\| [[15/13]] \|\| [[15/11]] \|\| [[11/7]]		! [[1/1]] \|\| [[15/13]] \|\| [[15/11]] \|\| [[11/7]]

Xenllium: Update the article

2023-11-05T00:04:37Z

Update the article

← Older revision		Revision as of 00:04, 5 November 2023
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	A '''~~nicolic chord~~''' ~~is a [[15-odd-limit]]~~ [[essentially tempered ~~dyadic chord~~]] ~~which is~~ tempered by [[1575/1573]], ~~the nicola~~.		'''Nicolic chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the nicola, [[1575/1573]].

			There are three triads, six tetrads and two pentads as [[15-odd-limit]] essentially tempered chords.

	The nicolic triads include the following palindromic form,		The nicolic triads include the following palindromic form,
	* 1-[[15/11]]-[[13/7]] with steps 15/11-15/11-[[14/13]],		* 1-[[15/11]]-[[13/7]] with steps of 15/11-15/11-[[14/13]],

	and a pair in inverse relationship,		and a pair in inverse relationship,
	* 1-15/11-[[11/7]] with steps 15/11-[[15/13]]-[[14/11]], and		* 1-15/11-[[11/7]] with steps of 15/11-[[15/13]]-[[14/11]], and
	* 1-15/11-[[26/15]] with steps 15/11-14/11-15/13.		* 1-15/11-[[26/15]] with steps of 15/11-14/11-15/13.

			For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
			* 1-15/13-15/11-11/7 with steps of 15/13-[[13/11]]-15/13-14/11;
			* 1-15/13-[[22/15]]-11/7 with steps of 15/13-14/11-[[15/14]]-14/11.

			The inversely related pairs of chords are
			* 1-15/11-11/7-13/7 with steps of 15/11-15/13-13/11-14/13, and its inverse
			* 1-15/11-22/15-26/15 with steps of 15/11-14/13-13/11-15/13;
			* 1-15/11-26/15-13/7 with steps of 15/11-14/11-15/14-14/13, and its inverse
			* 1-15/11-22/15-11/7 with steps of 15/11-14/13-15/14-14/11.

	~~Any~~ of ~~these leads to a tetrad, in close position~~,		They can be extended to pentads:
	* 1-15/13-15/11-11/7, with steps of 15/13-[[13/11]]-15/13-14/11.		* 1-15/14-15/13-15/11-11/7 with steps of 15/14-14/13-13/11-15/13-14/11, and its inverse
			* 1-15/13-15/11-22/15-11/7 with steps of 15/13-13/11-14/13-15/14-14/11.

	[[Equal temperament]]s with nicolic chords include {{~~EDOs~~\| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.		[[Equal temperament]]s with nicolic chords include {{Optimal ET sequence\| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.

	Here is a listening sample, tempered to TE tuning of nicolic.		Here is a listening sample, tempered to TE tuning of nicolic.
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	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
			[[Category:Pentads]]
	[[Category:Nicolic]]		[[Category:Nicolic]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC: Recategorize

2023-05-23T11:43:30Z

Recategorize

← Older revision		Revision as of 11:43, 23 May 2023
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	[[Category:15-odd-limit]]		[[Category:15-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Nicolic]]		[[Category:Nicolic]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC: Update

2022-03-03T20:33:16Z

Update

← Older revision		Revision as of 20:33, 3 March 2022
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	[[Equal temperament]]s with nicolic chords include {{EDOs\| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.		[[Equal temperament]]s with nicolic chords include {{EDOs\| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.

	Here is a listening sample~~. Although it is non-~~tempered~~, it may be regarded as close enough~~.		Here is a listening sample, tempered to TE tuning of nicolic.

	{\| class="wikitable center-all" style="column-width:10em"		{\| class="wikitable center-all" style="column-width:10em"
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	\|-		\|-
	! [[Cent]]s		! [[Cent]]s
	\| 0.00 \|\| 247.74 \|\| 536.95 \|\| ~~782~~.49		\| 0.000 \|\| 247.099 \|\| 536.086 \|\| 783.185
	\|-		\|-
	! Sound <br> <small>[[:File:~~Nocolic~~ tetrad.mp3\|[info]]]</small>		! Sound <br> <small>[[:File:Nicolic tetrad.mp3\|[info]]]</small>
	\| colspan="4" \| [[File:~~Nocolic~~ tetrad.mp3]]		\| colspan="4" \| [[File:Nicolic tetrad.mp3]]
	\|}		\|}

	[[Category:15-odd-limit]]		[[Category:15-odd-limit]]
	[[Category:~~Dyadic~~]]		[[Category:Essentially tempered chords]]
	[[Category:Triad]]		[[Category:Triad]]
	[[Category:Tetrad]]		[[Category:Tetrad]]
	[[Category:Nicolic]]		[[Category:Nicolic]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC: FloraC moved page Nicolic tetrad to Nicolic chords: It has triads as well as tetrads

2022-01-13T13:33:57Z

FloraC moved page Nicolic tetrad to Nicolic chords: It has triads as well as tetrads

← Older revision	Revision as of 13:33, 13 January 2022
(No difference)

FloraC: Expansion on triads and note on the listening sample

2022-01-13T13:33:44Z

Expansion on triads and note on the listening sample

← Older revision		Revision as of 13:33, 13 January 2022
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	~~The~~ '''nicolic ~~tetrad~~''' ~~in close position~~ is a [[~~Unison\|1~~]]-[[15/13]]-[[15/11]]-[[11/7]] ~~in a temperament where the~~ [[~~nicola~~]], ~~1575~~/~~1573, is~~ [[~~tempering out\|tempered out~~]]. ~~It therefore has~~ steps of 15/13-[[13/11]]-15/13-[[14/11~~]], and is a [[15-limit]] chord~~. [[Equal]] ~~divisions~~ with nicolic ~~tetrads~~ include ~~[[58edo]]~~, ~~[[72edo]]~~, ~~[[87edo]]~~, ~~[[103edo]]~~, ~~[[121edo]]~~, ~~[[130edo]]~~, ~~[[190edo]]~~, ~~[[217edo]]~~, ~~[[224edo]]~~, ~~[[311edo]]~~, ~~[[414edo]]~~, ~~[[441edo]]~~, ~~[[665edo]]~~ and ~~[[855edo]]~~.		A '''nicolic chord''' is a [[15-odd-limit]] [[essentially tempered dyadic chord]] which is tempered by [[1575/1573]], the nicola.

			The nicolic triads include the following palindromic form,
			* 1-[[15/11]]-[[13/7]] with steps 15/11-15/11-[[14/13]],

			and a pair in inverse relationship,
			* 1-15/11-[[11/7]] with steps 15/11-[[15/13]]-[[14/11]], and
			* 1-15/11-[[26/15]] with steps 15/11-14/11-15/13.

			Any of these leads to a tetrad, in close position,
			* 1-15/13-15/11-11/7, with steps of 15/13-[[13/11]]-15/13-14/11.

			[[Equal temperament]]s with nicolic chords include {{EDOs\| 58, 72, 87, 103, 121, 130, 190, 217, 224, 311, 414, 441, 665 and 855 }}.

			Here is a listening sample. Although it is non-tempered, it may be regarded as close enough.

	{\| class="wikitable center-all" style="column-width:10em"		{\| class="wikitable center-all" style="column-width:10em"
	! Ratio		! Ratio
	! [[~~Unison\|~~1/1]] \|\| [[15/13]] \|\| [[15/11]] \|\| [[11/7]]		! [[1/1]] \|\| [[15/13]] \|\| [[15/11]] \|\| [[11/7]]
	\|-		\|-
	! [[Cent]]s		! [[Cent]]s
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	\|}		\|}

			[[Category:15-odd-limit]]

	[[Category:15-limit]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:~~Nicola~~]]		[[Category:Triad]]
			[[Category:Tetrad]]
	[[Category:Nicolic]]		[[Category:Nicolic]]
	~~[[Category:Tetrad]]~~
	[[Category:Listen]]		[[Category:Listen]]

Xenwolf: cents with 2 digits

2020-06-13T16:17:00Z

cents with 2 digits

← Older revision		Revision as of 16:17, 13 June 2020
Line 5:		Line 5:
	! [[Unison\|1/1]] \|\| [[15/13]] \|\| [[15/11]] \|\| [[11/7]]		! [[Unison\|1/1]] \|\| [[15/13]] \|\| [[15/11]] \|\| [[11/7]]
	\|-		\|-
	! ~~Cents~~		! [[Cent]]s
	\| 0 \|\| ~~248~~ \|\| ~~537~~ \|\| 782		\| 0.00 \|\| 247.74 \|\| 536.95 \|\| 782.49
	\|-		\|-
	! Sound <br> <small>[[:File:Nocolic tetrad.mp3\|[info]]]</small>		! Sound <br> <small>[[:File:Nocolic tetrad.mp3\|[info]]]</small>
	\| colspan="4" \| [[File:Nocolic tetrad.mp3]]		\| colspan="4" \| [[File:Nocolic tetrad.mp3]]
	\|}		\|}



	[[Category:15-limit]]		[[Category:15-limit]]

Xenwolf: link to sound

2020-06-13T15:49:52Z

link to sound

← Older revision		Revision as of 15:49, 13 June 2020
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	\| 0 \|\| 248 \|\| 537 \|\| 782		\| 0 \|\| 248 \|\| 537 \|\| 782
	\|-		\|-
	! Sound		! Sound <br> <small>[[:File:Nocolic tetrad.mp3\|[info]]]</small>
	\| colspan="4" \| [[File:Nocolic tetrad.mp3]]		\| colspan="4" \| [[File:Nocolic tetrad.mp3]]
	\|}		\|}