Aureusmic chords - Revision history

FloraC: +pattern of chords

2023-07-26T15:42:09Z

+pattern of chords

FloraC: Readability

2023-07-21T06:35:09Z

Readability

← Older revision		Revision as of 06:35, 21 July 2023
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	There is an inversely related pair which is even more squeezed:		There is an inversely related pair which is even more squeezed:
	* 1-17/16-19/17 with steps 17/16-20/19-34/19 and its inverse 1-20/19-19/17 with steps 20/19-17/16-34/19.		* 1-17/16-19/17 with steps 17/16-20/19-34/19, and its inverse
			* 1-20/19-19/17 with steps 20/19-17/16-34/19.

	They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are		They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
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	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5 and its inverse 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;		* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
	* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5 and its inverse 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.		* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
			* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
			* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

	Then there are two inversely related pentads:		Then there are two inversely related pentads:
	* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.		* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,
			* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.

	Equal temperaments with aureusmic chords include {{Optimal ET sequence\|12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286}}.		Equal temperaments with aureusmic chords include {{Optimal ET sequence\| 12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286 }}.

	[[Category:19-odd-limit]]		[[Category:19-odd-limit]]

Xenllium at 23:56, 20 July 2023

2023-07-20T23:56:55Z

← Older revision		Revision as of 23:56, 20 July 2023
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	The most typical aureusmic triad is a palindrome in the 2.5.17.19 [[subgroup]] [[19-odd-limit]] since it identifies 5/4 by a stack of two 19/17's:		The most typical aureusmic triad is a palindrome in the 2.5.17.19 [[subgroup]] [[19-odd-limit]] since it identifies 5/4 by a stack of two 19/17's:
	* 1-19/17-5/4 with steps 19/17-19/17-8/5.		* 1-19/17-5/4 chord with steps 19/17-19/17-8/5.

	There is an inversely related pair which is even more squeezed:		There is an inversely related pair which is even more squeezed:
	* 1-17/16-19/17 with steps 17/16-20/19-8/5, and its inverse		* 1-17/16-19/17 with steps 17/16-20/19-34/19 and its inverse 1-20/19-19/17 with steps 20/19-17/16-34/19.
	* 1-20/19-19/17 with steps 20/19-17/16-8/5.

	They can be extended to the following ~~inversely related~~ tetrads, ~~all~~ of ~~which seem to be based largely on a sort~~ of ~~secundal harmony:~~		They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse		* 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19;
	* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;		* 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10.
	* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
	* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.		The inversely related pairs of chords are
			* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5 and its inverse 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
			* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5 and its inverse 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

	Then there are two inversely related pentads:		Then there are two inversely related pentads:
	* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5, and its inverse		* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.
	* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.
			Equal temperaments with aureusmic chords include {{Optimal ET sequence\|12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286}}.

	[[Category:19-odd-limit]]		[[Category:19-odd-limit]]

FloraC: Recategorize

2023-05-23T11:34:53Z

Recategorize

← Older revision		Revision as of 11:34, 23 May 2023
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	[[Category:19-odd-limit]]		[[Category:19-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:~~Pentad~~]]		[[Category:Pentads]]
	[[Category:Aureusmic]]		[[Category:Aureusmic]]

FloraC: I found more

2023-05-11T11:36:14Z

I found more

← Older revision		Revision as of 11:36, 11 May 2023
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	'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].		'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].

	The aureusmic triad is a palindrome in the 2.5.17.19 [[subgroup]] [[19-odd-limit]] since it identifies 5/4 by a stack of two 19/17's:		The most typical aureusmic triad is a palindrome in the 2.5.17.19 [[subgroup]] [[19-odd-limit]] since it identifies 5/4 by a stack of two 19/17's:
	* 1-19/17-5/4 with steps 19/17-19/17-8/5.		* 1-19/17-5/4 with steps 19/17-19/17-8/5.

	It can be extended to the following inversely related tetrads, all of which seem to be based largely on a sort of secundal harmony:		There is an inversely related pair which is even more squeezed:
			* 1-17/16-19/17 with steps 17/16-20/19-8/5, and its inverse
			* 1-20/19-19/17 with steps 20/19-17/16-8/5.

			They can be extended to the following inversely related tetrads, all of which seem to be based largely on a sort of secundal harmony:
	* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse		* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
	* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5.		* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
	* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse		* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
	* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.		* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

FloraC at 11:11, 11 May 2023

2023-05-11T11:11:00Z

← Older revision		Revision as of 11:11, 11 May 2023
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	'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].		'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].

	The aureusmic triad in the 2.5.17.19 subgroup 19-odd-limit ~~is a palindrome~~ since it identifies 5/4 by a stack of two 19/17's:		The aureusmic triad is a palindrome in the 2.5.17.19 [[subgroup]] [[19-odd-limit]] since it identifies 5/4 by a stack of two 19/17's:
	* 1-19/17-5/4 with steps 19/17-19/17-8/5.		* 1-19/17-5/4 with steps 19/17-19/17-8/5.

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	* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.		* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.

			[[Category:19-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triad]]		[[Category:Triad]]

FloraC: Created page with "'''Aureusmic chords''' are essentially tempered dyadic chords tempered by the aureusma, 1445/1444. The aureusmic triad in the 2.5.17.19 subgroup 19-odd-limit is a pa..."

2023-05-11T09:12:55Z

Created page with "'''Aureusmic chords''' are essentially tempered dyadic chords tempered by the aureusma, 1445/1444. The aureusmic triad in the 2.5.17.19 subgroup 19-odd-limit is a pa..."

New page

'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].

The aureusmic triad in the 2.5.17.19 subgroup 19-odd-limit is a palindrome since it identifies 5/4 by a stack of two 19/17's:
* 1-19/17-5/4 with steps 19/17-19/17-8/5.

It can be extended to the following inversely related tetrads, all of which seem to be based largely on a sort of secundal harmony:
* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5.
* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

Then there are two inversely related pentads:
* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5, and its inverse
* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.

[[Category:Essentially tempered chords]]
[[Category:Triad]]
[[Category:Tetrad]]
[[Category:Pentad]]
[[Category:Aureusmic]]

← Older revision		Revision as of 15:42, 26 July 2023
Line 1:		Line 1:
	'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].		'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]].

	~~The most typical aureusmic triad is a palindrome~~ in the 2.5.17.19 [[subgroup]] [[19-odd-limit]] since it identifies 5/4 by a stack of two 19/17's:		Aureusmic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 1a]] in the 2.5.17.19 [[subgroup]] [[19-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

			The most typical aureusmic triad is a palindrome since it identifies 5/4 by a stack of two 19/17's:
	* 1-19/17-5/4 chord with steps 19/17-19/17-8/5.		* 1-19/17-5/4 chord with steps 19/17-19/17-8/5.

Line 8:		Line 10:
	* 1-20/19-19/17 with steps 20/19-17/16-34/19.		* 1-20/19-19/17 with steps 20/19-17/16-34/19.

	They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic ~~chords~~ are		They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are
	* 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19;		* 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19;
	* 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10.		* 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10.

	The inversely related pairs of ~~chords~~ are		The inversely related pairs of tetrads are
	* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse		* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
	* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;		* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
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	* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.		* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

	Then there ~~are two~~ inversely related pentads:		Then there is an inversely related pair of pentads:
	* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,		* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,
	* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.		* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.