Cimbrismic chords - Revision history

FloraC at 09:15, 6 December 2025

2025-12-06T09:15:08Z

← Older revision		Revision as of 09:15, 6 December 2025
Line 40:		Line 40:
	Equal temperaments with cimbrismic chords include {{Optimal ET sequence\| 31, 41, 50, 53, 58, 60, 68, 72, 111, 121, 130, 140, 171, 183, 243, 311, 354, 364 and 494 }}.		Equal temperaments with cimbrismic chords include {{Optimal ET sequence\| 31, 41, 50, 53, 58, 60, 68, 72, 111, 121, 130, 140, 171, 183, 243, 311, 354, 364 and 494 }}.

	[[Category:17-odd-limit]]		[[Category:17-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

FloraC: Cleanup

2025-12-06T09:14:55Z

Cleanup

← Older revision		Revision as of 09:14, 6 December 2025
Line 1:		Line 1:
	'''Cimbrismic chords''' are [[~~Dyadic~~ chord\|essentially tempered chords]] tempered by the cimbrisma, [[1275/1274]].		'''Cimbrismic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the cimbrisma, [[1275/1274]].

	Cimbrismic chords are of [[~~Dyadic~~ chord/Pattern of essentially tempered chords\|pattern 2]] in the 2.3.5.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.		Cimbrismic chords are of [[dyadic chord/Pattern of essentially tempered chords\|pattern 2]] in the 2.3.5.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

	For triads, there are three pairs of chords in inverse relationship:		For triads, there are three pairs of chords in inverse relationship:
	* ~~1-17~~/~~13-7~~/5 with steps of 17/13-15/14-10/7, and its inverse		* 1–17/13–7/5 with steps of 17/13, 15/14, 10/7, and its inverse
	* ~~1-15~~/~~14-7~~/5 with steps of 15/14-17/13-10/7;		* 1–15/14–7/5 with steps of 15/14, 17/13, 10/7;
	* ~~1-17~~/~~14-7~~/5 with steps of 17/14-15/13-10/7, and its inverse		* 1–17/14–7/5 with steps of 17/14, 15/13, 10/7, and its inverse
	* ~~1-15~~/~~13-7~~/5 with steps of 15/13-17/14-10/7;		* 1–15/13–7/5 with steps of 15/13, 17/14, 10/7;
	* ~~1-17~~/~~14-13~~/10 with steps of 17/14-15/14-20/13, and its inverse		* 1–17/14–13/10 with steps of 17/14, 15/14, 20/13, and its inverse
	* ~~1-15~~/~~14-13~~/10 with steps of 15/14-17/14-20/13.		* 1–15/14–13/10 with steps of 15/14, 17/14, 20/13.

	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
	* ~~1-20~~/~~17-10~~/~~7-28~~/17 with steps of 20/17-17/14-15/13-17/14;		* 1–20/17–10/7–28/17 with steps of 20/17, 17/14, 15/13, 17/14;
	* ~~1-15~~/~~14-7~~/~~5-3~~/2 with steps of 15/14-17/13-15/14-4/3;		* 1–15/14–7/5–3/2 with steps of 15/14, 17/13, 15/14, 4/3;
	* ~~1-15~~/~~14-17~~/~~14-13~~/10 with steps of 15/14-17/15-15/14-20/13.		* 1–15/14–17/14–13/10 with steps of 15/14, 17/15, 15/14, 20/13.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* ~~1-20~~/~~17-10~~/~~7-26~~/17 with steps of 20/17-17/14-15/14-17/13, and its inverse		* 1–20/17–10/7–26/17 with steps of 20/17, 17/14, 15/14, 17/13, and its inverse
	* ~~1-15~~/~~14-13~~/~~10-26~~/17 with steps of 15/14-17/14-20/17-17/13;		* 1–15/14–13/10–26/17 with steps of 15/14, 17/14, 20/17, 17/13;
	* ~~1-15~~/~~13-7~~/~~5-3~~/2 with steps of 15/13-17/14-15/14-4/3, and its inverse		* 1–15/13–7/5–3/2 with steps of 15/13, 17/14, 15/14, 4/3, and its inverse
	* ~~1-15~~/~~14-13~~/~~10-3~~/2 with steps of 15/14-17/14-15/13-4/3;		* 1–15/14–13/10–3/2 with steps of 15/14, 17/14, 15/13, 4/3;
	* ~~1-17~~/~~14-17~~/~~13-7~~/5 with steps of 17/14-14/13-15/14-10/7, and its inverse		* 1–17/14–17/13–7/5 with steps of 17/14, 14/13, 15/14, 10/7, and its inverse
	* ~~1-15~~/~~14-15~~/~~13-7~~/5 with steps of 15/14-14/13-17/14-10/7;		* 1–15/14–15/13–7/5 with steps of 15/14, 14/13, 17/14, 10/7;
	* ~~1-17~~/~~14-13~~/~~10-7~~/5 with steps of 17/14-15/14-14/13-10/7, and its inverse		* 1–17/14–13/10–7/5 with steps of 17/14, 15/14, 14/13, 10/7, and its inverse
	* ~~1-14~~/~~13-15~~/~~13-7~~/5 with steps of 14/13-15/14-17/14-10/7;		* 1–14/13–15/13–7/5 with steps of 14/13, 15/14, 17/14, 10/7;
	* ~~1-15~~/~~13-17~~/~~13-7~~/5 with steps of 15/13-17/15-15/14-10/7, and its inverse		* 1–15/13–17/13–7/5 with steps of 15/13, 17/15, 15/14, 10/7, and its inverse
	* ~~1-15~~/~~14-17~~/~~14-7~~/5 with steps of 15/14-17/15-15/13-10/7;		* 1–15/14–17/14–7/5 with steps of 15/14, 17/15, 15/13, 10/7;
	* ~~1-14~~/~~13-17~~/~~13-7~~/5 with steps of 14/13-17/14-15/14-10/7, and its inverse		* 1–14/13–17/13–7/5 with steps of 14/13, 17/14, 15/14, 10/7, and its inverse
	* ~~1-15~~/~~14-13~~/~~10-7~~/5 with steps of 15/14-17/14-14/13-10/7.		* 1–15/14–13/10–7/5 with steps of 15/14, 17/14, 14/13, 10/7.

	For pentads, there are three pairs of chords in inverse relationship:		For pentads, there are three pairs of chords in inverse relationship:
	* ~~1-20~~/~~17-10~~/~~7-26~~/~~17-28~~/17 with steps of 20/17-17/14-15/14-14/13-17/14, and its inverse		* 1–20/17–10/7–26/17–28/17 with steps of 20/17, 17/14, 15/14, 14/13, 17/14, and its inverse
	* ~~1-14~~/~~13-15~~/~~13-7~~/~~5-28~~/17 with steps of 14/13-15/14-17/14-20/17-17/14;		* 1–14/13–15/13–7/5–28/17 with steps of 14/13, 15/14, 17/14, 20/17, 17/14;
	* ~~1-15~~/~~14-13~~/~~10-7~~/~~5-3~~/2 with steps of 15/14-17/14-14/13-15/14-4/3, and its inverse		* 1–15/14–13/10–7/5–3/2 with steps of 15/14, 17/14, 14/13, 15/14, 4/3, and its inverse
	* ~~1-15~~/~~14-15~~/~~13-7~~/~~5-3~~/2 with steps of 15/14-14/13-17/14-15/14-4/3;		* 1–15/14–15/13–7/5–3/2 with steps of 15/14, 14/13, 17/14, 15/14, 4/3;
	* ~~1-14~~/~~13-15~~/~~13-17~~/~~13-7~~/5 with steps of 14/13-15/14-17/15-15/14-10/7, and its inverse		* 1–14/13–15/13–17/13–7/5 with steps of 14/13, 15/14, 17/15, 15/14, 10/7, and its inverse
	* ~~1-15~~/~~14-17~~/~~14-13~~/~~10-7~~/5 with steps of 15/14-17/15-15/14-14/13-10/7.		* 1–15/14–17/14–13/10–7/5 with steps of 15/14, 17/15, 15/14, 14/13, 10/7.

	Equal temperaments with cimbrismic chords include {{Optimal ET sequence\|31, 41, 50, 53, 58, 60, 68, 72, 111, 121, 130, 140, 171, 183, 243, 311, 354, 364 and 494 }}.		Equal temperaments with cimbrismic chords include {{Optimal ET sequence\| 31, 41, 50, 53, 58, 60, 68, 72, 111, 121, 130, 140, 171, 183, 243, 311, 354, 364 and 494 }}.

	[[Category:17-odd-limit]]		[[Category:17-odd-limit]]

Xenllium at 11:20, 8 December 2023

2023-12-08T11:20:44Z

← Older revision		Revision as of 11:20, 8 December 2023
Line 1:		Line 1:
	'''Cimbrismic chords''' are [[Dyadic chord\|essentially tempered ~~dyadic~~ chords]] tempered by the cimbrisma, [[1275/1274]].		'''Cimbrismic chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the cimbrisma, [[1275/1274]].

	Cimbrismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 2]] in the 2.3.5.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.		Cimbrismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 2]] in the 2.3.5.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.
Line 12:		Line 12:

	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
	* 1-17/14-7/5-17~~/10~~ with steps of 17/14-15/13-17/14~~-20/17~~;		* 1-20/17-10/7-28/17 with steps of 20/17-17/14-15/13-17/14;
	* 1-15/14-7/5-3/2 with steps of 15/14-17/13-15/14-4/3;		* 1-15/14-7/5-3/2 with steps of 15/14-17/13-15/14-4/3;
	* 1-15/14-17/14-13/10 with steps of 15/14-17/15-15/14-20/13.		* 1-15/14-17/14-13/10 with steps of 15/14-17/15-15/14-20/13.

Xenllium: Created page with "'''Cimbrismic chords''' are essentially tempered dyadic chords tempered by the cimbrisma, 1275/1274. Cimbrismic chords are of Dyadic chord/Pattern of e..."

2023-11-26T04:17:49Z

Created page with "'''Cimbrismic chords''' are essentially tempered dyadic chords tempered by the cimbrisma, 1275/1274. Cimbrismic chords are of Dyadic chord/Pattern of e..."

New page

'''Cimbrismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the cimbrisma, [[1275/1274]].

Cimbrismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

For triads, there are three pairs of chords in inverse relationship:
* 1-17/13-7/5 with steps of 17/13-15/14-10/7, and its inverse
* 1-15/14-7/5 with steps of 15/14-17/13-10/7;
* 1-17/14-7/5 with steps of 17/14-15/13-10/7, and its inverse
* 1-15/13-7/5 with steps of 15/13-17/14-10/7;
* 1-17/14-13/10 with steps of 17/14-15/14-20/13, and its inverse
* 1-15/14-13/10 with steps of 15/14-17/14-20/13.

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
* 1-17/14-7/5-17/10 with steps of 17/14-15/13-17/14-20/17;
* 1-15/14-7/5-3/2 with steps of 15/14-17/13-15/14-4/3;
* 1-15/14-17/14-13/10 with steps of 15/14-17/15-15/14-20/13.

The inversely related pairs of chords are
* 1-20/17-10/7-26/17 with steps of 20/17-17/14-15/14-17/13, and its inverse
* 1-15/14-13/10-26/17 with steps of 15/14-17/14-20/17-17/13;
* 1-15/13-7/5-3/2 with steps of 15/13-17/14-15/14-4/3, and its inverse
* 1-15/14-13/10-3/2 with steps of 15/14-17/14-15/13-4/3;
* 1-17/14-17/13-7/5 with steps of 17/14-14/13-15/14-10/7, and its inverse
* 1-15/14-15/13-7/5 with steps of 15/14-14/13-17/14-10/7;
* 1-17/14-13/10-7/5 with steps of 17/14-15/14-14/13-10/7, and its inverse
* 1-14/13-15/13-7/5 with steps of 14/13-15/14-17/14-10/7;
* 1-15/13-17/13-7/5 with steps of 15/13-17/15-15/14-10/7, and its inverse
* 1-15/14-17/14-7/5 with steps of 15/14-17/15-15/13-10/7;
* 1-14/13-17/13-7/5 with steps of 14/13-17/14-15/14-10/7, and its inverse
* 1-15/14-13/10-7/5 with steps of 15/14-17/14-14/13-10/7.

For pentads, there are three pairs of chords in inverse relationship:
* 1-20/17-10/7-26/17-28/17 with steps of 20/17-17/14-15/14-14/13-17/14, and its inverse
* 1-14/13-15/13-7/5-28/17 with steps of 14/13-15/14-17/14-20/17-17/14;
* 1-15/14-13/10-7/5-3/2 with steps of 15/14-17/14-14/13-15/14-4/3, and its inverse
* 1-15/14-15/13-7/5-3/2 with steps of 15/14-14/13-17/14-15/14-4/3;
* 1-14/13-15/13-17/13-7/5 with steps of 14/13-15/14-17/15-15/14-10/7, and its inverse
* 1-15/14-17/14-13/10-7/5 with steps of 15/14-17/15-15/14-14/13-10/7.

Equal temperaments with cimbrismic chords include {{Optimal ET sequence|31, 41, 50, 53, 58, 60, 68, 72, 111, 121, 130, 140, 171, 183, 243, 311, 354, 364 and 494 }}.

[[Category:17-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Cimbrismic]]