Ragismic chords - Revision history

Xenllium at 03:12, 24 November 2023

2023-11-24T03:12:54Z

← Older revision		Revision as of 03:12, 24 November 2023
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	For pentads, there are two palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are		For pentads, there are two palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are
	* 1-27/25-7/6-3/2-14/9 with steps of 27/25-27/25-9/7-28/27-9/7;		* 1-27/25-7/6-3/2-14/9 with steps of 27/25-27/25-9/7-28/27-9/7;
	* 1-25/24-27/25~~-9/8~~-3/2 with steps of 25/24-28/27-25/24~~-4/3~~-4/3.		* 1-4/3-25/18-36/25-3/2 with steps of 4/3-25/24-28/27-25/24-4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
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	* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27, and its inverse		* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27, and its inverse
	* 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;		* 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;
	* 1-25/21-9/7-4/3-25~~/18~~ with steps of 25~~/21~~-27/25-28/27-25~~/24~~-36/25, and its inverse		* 1-36/25-3/2-14/9-42/25 with steps of 36/25-25/24-28/27-27/25-25/21, and its inverse
	* 1-25/24-27/25-7/6-25/18 with steps of 25/24-~~28/27-27~~/25-25/21-36/25;		* 1-25/24-3/2-25/14-27/14 with steps of 25/24-36/25-25/21-27/25-28/27;
	* 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7, and its inverse		* 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7, and its inverse
	* 1-28/27-27/25-28/25-7/6 with steps of 28/27-25/24-28/27-25/24-12/7.		* 1-28/27-27/25-28/25-7/6 with steps of 28/27-25/24-28/27-25/24-12/7.

Xenllium at 02:31, 24 November 2023

2023-11-24T02:31:56Z

Show changes

Xenllium: Update: adding 1-25/24-27/14 chord and its derivation

2023-07-17T07:28:11Z

Update: adding 1-25/24-27/14 chord and its derivation

← Older revision		Revision as of 07:28, 17 July 2023
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	'''Ragismic chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the ragisma, [[4375/4374]].		'''Ragismic chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the ragisma, [[4375/4374]].

	~~The~~ [[~~Ragismic microtemperaments~~\|~~ragismic temperament~~]] ~~has 4~~ triads, 11 tetrads, 9 pentads and 2 hexads as essentially tempered chords.		Since the temperament is complex, even the simplest ragismic chords are [[27-odd-limit]], although they contain only [[7-limit\|7-prime-limit]] intervals. There are 6 triads, 21 tetrads, 22 pentads and 7 hexads as essentially tempered chords.

	For triads, there are two palindromic chords and ~~a pair~~ of chords in inverse relationship. The palindromic chords are		For triads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;		* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
	* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.		* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.

	The inversely related ~~pair~~ of chords is		The inversely related pairs of chords are
	* 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25.		* 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25;
			* 1-25/24-27/25 with steps of 25/24-28/27-50/27 and its inverse 1-25/24-27/14 with steps of 25/24-50/27-28/27.

	For tetrads, there are ~~three~~ palindromic chords and ~~four~~ pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are five palindromic chords and eight pairs of chords in inverse relationship. The palindromic chords are
			* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
	* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;		* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
	* 1-27/25-25/18~~-14/9~~ chord with steps of 27/25-9/7-28/25-9/7;		* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25;
	* 1-27/25-9/~~7-25/18~~ chord with steps of 27/25-25/21-27/25-36/25.		* 1-25/24-27/25-9/8 chord with steps of 25/24-28/27-25/24-16/9;
			* 1-25/24-27/25-27/14 chord with steps of 25/24-28/27-25/14-28/27.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3~~-9/7~~ and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7~~-4/3~~;		* 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3 and its inverse 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7;
	* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;		* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
	* 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27 and its inverse 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7;		* 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7 and its inverse 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27;
	* 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27 and its inverse 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27.		* 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27 and its inverse 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27;
			* 1-25/24-27/25-3/2 with steps of 25/24-28/27-25/18-4/3 and its inverse 1-25/24-25/18-27/14 with steps of 25/24-4/3-25/18-28/27;
			* 1-25/24-27/25-25/18 with steps of 25/24-28/27-9/7-36/25 and its inverse 1-25/24-3/2-27/14 with steps of 25/24-36/25-9/7-28/27;
			* 1-27/25-9/8-7/6 with steps of 27/25-25/24-28/27-12/7 and its inverse 1-25/24-9/8-27/14 with steps of 25/24-27/25-12/7-28/27;
			* 1-25/24-27/25-7/6 with steps of 25/24-28/27-27/25-12/7 and its inverse 1-25/24-25/14-27/14 with steps of 25/24-12/7-27/25-28/27.

	For pentads, there are ~~one~~ palindromic ~~chord~~ and ~~four~~ pairs of chords in inverse relationship. The palindromic ~~chord is~~		For pentads, there are two palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are
	* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7.		* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7;
			* 1-25/24-27/25-9/8-3/2 chord with steps of 25/24-28/27-25/24-4/3-4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-27/25-25/18-3/~~2-27/14~~ with steps of 27/25-9/7-27/25-9/7~~-28/27~~ and its inverse 1-9/7~~-25~~/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27;		* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
	* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;		* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
	* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2~~-42/25~~ with steps of 27/25-27/25-9/7-28/25-25/21;		* 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27 and its inverse 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27;
	* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21.		* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;
			* 1-27/25-9/8-7/6-3/2 with steps of 27/25-25/24-28/27-9/7-4/3 and its inverse 1-9/7-4/3-25/18-3/2 with steps of 9/7-28/27-25/24-27/25-4/3;
			* 1-25/24-27/25-7/6-3/2 with steps of 25/24-28/27-27/25-9/7-4/3 and its inverse 1-9/7-25/18-36/25-3/2 with steps of 9/7-27/25-28/27-25/24-4/3;
			* 1-25/24-27/25-25/18-3/2 with steps of 25/24-28/27-9/7-27/25-4/3 and its inverse 1-27/25-25/18-36/25-3/2 with steps of 27/25-9/7-28/27-25/24-4/3;
			* 1-25/24-27/25-7/6-25/18 with steps of 25/24-28/27-27/25-25/21-36/25 and its inverse 1-25/21-9/7-4/3-25/18 with steps of 25/21-27/25-28/27-25/24-36/25.
			* 1-25/24-27/25-25/18-27/14 with steps of 25/24-28/27-9/7-25/18-28/27 and its inverse 1-25/24-27/25-3/2-27/14 with steps of 25/24-28/27-25/18-9/7-28/27.
			* 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7 and its inverse 1-25/24-27/25-9/8-27/14 with steps of 25/24-28/27-25/24-12/7-28/27.

			For hexads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
			* 1-25/24-27/25-25/18-3/2-27/14 chord with steps of 25/24-28/27-9/7-27/25-9/7-28/27.

	~~They can be extended to hexads as~~		The inversely related pairs of chords are
	* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21.		* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21;
			* 1-25/24-27/25-7/6-25/18-3/2 with steps of 25/24-28/27-27/25-25/21-27/25-4/3 and its inverse 1-27/25-9/7-25/18-36/25-3/2 with steps of 27/25-25/21-27/25-28/27-25/24-4/3;
			* 1-25/24-27/25-9/8-7/6-3/2 with steps of 25/24-28/27-25/24-28/27-9/7-4/3 and its inverse 1-25/24-27/25-9/8-3/2-27/14 with steps of 25/24-28/27-25/24-4/3-9/7-28/27.

	Equal temperaments with ragismic chords include {{Optimal ET sequence\|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.		Equal temperaments with ragismic chords include {{Optimal ET sequence\|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.

Xenllium at 03:50, 14 July 2023

2023-07-14T03:50:18Z

← Older revision		Revision as of 03:50, 14 July 2023
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	For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are		For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
	* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;		* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
	* 1-25/18-36/25 chord with steps of 25/18-28/27~~-25/18~~.		* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.

	The inversely related pair of chords is		The inversely related pair of chords is
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	For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
	* 1-27/25-36/25-14/9 chord with steps of 27/25-4/3-27/25-9/7;		* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
	* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;		* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
	* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.		* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.
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	* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;		* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
	* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;		* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
	* 1-27/25-25/18-36/25 with steps of 27/25-9/7-28/27~~-25/18~~ and its inverse 1-25~~/18~~-36/25-50/27 with steps of 25/18-28/27-9/7-27/25;		* 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27 and its inverse 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7;
	* 1-25/18-36/~~25-~~14/9 with steps of 25/18-28/27~~-27/25-9/7~~ and its inverse 1-9/7-25/18-36/25 with steps of 9/7-27/25-28/27~~-25/18~~.		* 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27 and its inverse 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27.

	For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is		For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is
	* 1-27/25-25/18-36/25-50/27 chord with steps of 27/25-9/7-28/27-9/7~~-27/25~~.		* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-27/25-25/18-36/25-14/9 with steps of 27/25-9/7~~-28/27~~-27/25-9/7 and its inverse 1-9/7-25/18-36/25-50/27 with steps of 9/7-27/25~~-28/27~~-9/7-27/25;		* 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27 and its inverse 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27;
	* 1-27/25-9/7-25/18-50/27 with steps of 27/25-25/21-27/25-4/3~~-27/25~~ and its inverse 1-27/25-36/25-14/9-50/27 with steps of 27/25-4/3-27/25-25/21~~-27/25~~;		* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
	* 1-27/25-9/7-36/25-50/27 with steps of 27/25-25/21-28/25-9/7~~-27/25~~ and its inverse 1-27/25-25/18-14/9-50/27 with steps of 27/25-9/7-28/25-25/21~~-27/25~~;		* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
	* 1-27/25-9/7-25/18-36/25 with steps of 27/25-25/21-27/25-28/27~~-25/18~~ and its inverse 1-25~~/18~~-36/25-14/9-50/27 with steps of 25/18-28/27-27/25-25/21~~-27/25~~.		* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21.

	They can be extended to hexads as		They can be extended to hexads as
	* 1-27/25-9/7-25/18-36/25-50/27 with steps of 27/25-25/21-27/25-28/27-9/7~~-27/25~~ and its inverse 1-27/25-25/18-36/25-14/9-50/27 with steps of 27/25-9/7-28/27-27/25-25/21~~-27/25~~.		* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21.

	Equal temperaments with ragismic chords include {{Optimal ET sequence\|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.		Equal temperaments with ragismic chords include {{Optimal ET sequence\|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.

Xenllium: Created page with "'''Ragismic chords''' are essentially tempered chords tempered by the ragisma, 4375/4374. The ragismic temperament has 4 t..."

2023-07-01T06:30:29Z

Created page with "'''Ragismic chords''' are essentially tempered chords tempered by the ragisma, 4375/4374. The ragismic temperament has 4 t..."

New page

'''Ragismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the ragisma, [[4375/4374]].

The [[Ragismic microtemperaments|ragismic temperament]] has 4 triads, 11 tetrads, 9 pentads and 2 hexads as essentially tempered chords.

For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
* 1-25/18-36/25 chord with steps of 25/18-28/27-25/18.

The inversely related pair of chords is
* 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25.

For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
* 1-27/25-36/25-14/9 chord with steps of 27/25-4/3-27/25-9/7;
* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.

The inversely related pairs of chords are
* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
* 1-27/25-25/18-36/25 with steps of 27/25-9/7-28/27-25/18 and its inverse 1-25/18-36/25-50/27 with steps of 25/18-28/27-9/7-27/25;
* 1-25/18-36/25-14/9 with steps of 25/18-28/27-27/25-9/7 and its inverse 1-9/7-25/18-36/25 with steps of 9/7-27/25-28/27-25/18.

For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is
* 1-27/25-25/18-36/25-50/27 chord with steps of 27/25-9/7-28/27-9/7-27/25.

The inversely related pairs of chords are
* 1-27/25-25/18-36/25-14/9 with steps of 27/25-9/7-28/27-27/25-9/7 and its inverse 1-9/7-25/18-36/25-50/27 with steps of 9/7-27/25-28/27-9/7-27/25;
* 1-27/25-9/7-25/18-50/27 with steps of 27/25-25/21-27/25-4/3-27/25 and its inverse 1-27/25-36/25-14/9-50/27 with steps of 27/25-4/3-27/25-25/21-27/25;
* 1-27/25-9/7-36/25-50/27 with steps of 27/25-25/21-28/25-9/7-27/25 and its inverse 1-27/25-25/18-14/9-50/27 with steps of 27/25-9/7-28/25-25/21-27/25;
* 1-27/25-9/7-25/18-36/25 with steps of 27/25-25/21-27/25-28/27-25/18 and its inverse 1-25/18-36/25-14/9-50/27 with steps of 25/18-28/27-27/25-25/21-27/25.

They can be extended to hexads as
* 1-27/25-9/7-25/18-36/25-50/27 with steps of 27/25-25/21-27/25-28/27-9/7-27/25 and its inverse 1-27/25-25/18-36/25-14/9-50/27 with steps of 27/25-9/7-28/27-27/25-25/21-27/25.

Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.

[[Category:27-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Ragismic]]