Ramanujanismic chords - Revision history

Xenllium at 08:12, 26 November 2023

2023-11-26T08:12:01Z

← Older revision		Revision as of 08:12, 26 November 2023
Line 1:		Line 1:
	'''Ramanujanismic chords''' are [[essentially tempered ~~dyadic chord~~]]s tempered by the ramanujanisma, [[1729/1728]].		'''Ramanujanismic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the ramanujanisma, [[1729/1728]].

	Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:		Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:
Line 158:		Line 158:
	* 1-7/6-4/3-3/2-19/12-24/13 with steps 7/6-8/7-9/8-19/18-7/6-13/12.		* 1-7/6-4/3-3/2-19/12-24/13 with steps 7/6-8/7-9/8-19/18-7/6-13/12.

	[[Category:21-odd-limit]]		Equal temperaments with ramanujanismic chords include {{Optimal ET sequence\|17, 27, 36, 41, 53, 77, 94, 104, 113, 130, 140, 166, 207, 234, 243, 270, 347, 400 and 477}}.

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

FloraC: Expansion +2

2023-05-31T12:46:53Z

Expansion +2

@@ Line 116: / Line 116: @@
 * 1-19/16-3/2-7/4-24/13 with steps 19/16-24/19-7/6-19/18-13/12.
-For hexads, the known ones are
+These chords put two otonal 19's against a utonal 7 or 13, or the other way around:
 * 1-9/8-19/16-9/7-18/13-3/2 with steps 9/8-19/18-13/12-14/13-13/12-4/3, and its inverse
-* 1-13/12-7/6-24/19-4/3-3/2 with steps 13/12-14/13-13/12-19/18-9/8-4/3;
+* 1-13/12-7/6-24/19-4/3-3/2 with steps 13/12-14/13-13/12-19/18-9/8-4/3.
-* 1-19/16-9/7-3/2-13/8-12/7 with steps 19/16-13/12-7/6-13/12-19/18-7/6, and its inverse
-* 1-7/6-24/19-3/2-7/4-24/13 with steps 7/6-13/12-19/16-7/6-19/18-13/12;
+These chords put otonal 9 and 7 against utonal 13 and 19, or the other way around:
 [[Category:21-odd-limit]]

FloraC: Expansion +1

2023-05-31T10:10:34Z

Expansion +1

Show changes

FloraC: Expansion and sorting

2023-05-31T09:29:09Z

Expansion and sorting

← Older revision		Revision as of 09:29, 31 May 2023
Line 3:		Line 3:
	Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:		Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:
	* 1-7/6-24/19 with steps 7/6-13/12-19/12, and its inverse		* 1-7/6-24/19 with steps 7/6-13/12-19/12, and its inverse
	* 1-7/6-24/13 with steps 7/6-19/12-13/12;		* 1-7/6-24/13 with steps 7/6-19/12-13/12.

	~~Other ramanujanismic triads are~~		These chords feature the 19th harmonic:
	* 1-19/16-9/7 with steps 19/16-13/12-14/9, and its inverse		* 1-19/16-9/7 with steps 19/16-13/12-14/9, and its inverse
	* 1-19/16-24/13 with steps 19/16-14/9-13/12;		* 1-19/16-24/13 with steps 19/16-14/9-13/12;
	* 1-19/16-18/13 with steps 19/16-7/6-13/9, and its inverse		* 1-19/16-18/13 with steps 19/16-7/6-13/9, and its inverse
	* 1-19/16-12/7 with steps 19/16-13/9-7/6.		* 1-19/16-12/7 with steps 19/16-13/9-7/6.

			These chords feature the 7th harmonic:
	* 1-7/4-36/19 with steps 7/4-13/12-19/18, and its inverse		* 1-7/4-36/19 with steps 7/4-13/12-19/18, and its inverse
	* 1-7/4-24/13 with steps 7/4-19/18-13/12;		* 1-7/4-24/13 with steps 7/4-19/18-13/12;
			* 1-18/13-7/4 with steps 18/13-24/19-8/7, and its inverse
			* 1-24/19-7/4 with steps 24/19-18/13-8/7.

			These chords feature the 13th harmonic:
	* 1-13/8-36/19 with steps 13/8-7/6-19/18, and its inverse		* 1-13/8-36/19 with steps 13/8-7/6-19/18, and its inverse
	* 1-13/8-12/7 with steps 13/8-19/18-7/6;		* 1-13/8-12/7 with steps 13/8-19/18-7/6;
	* 1-18/13-7/4 with steps 18/13-24/19-8/7, and its inverse
	* 1-24/19-7/4 with steps 24/19-18/13-8/7;
	* 1-9/7-13/8 with steps 9/7-24/19-16/13, and its inverse		* 1-9/7-13/8 with steps 9/7-24/19-16/13, and its inverse
	* 1-24/19-13/8 with steps 24/19-9/7-16/13;		* 1-24/19-13/8 with steps 24/19-9/7-16/13.

	If we allow the [[21-odd-limit]], we have these additional triads:		If we allow the [[21-odd-limit]], we have these additional triads:
Line 66:		Line 70:
	* 1-9/8-21/16-36/19 with steps 9/8-7/6-13/9-19/18, and its inverse		* 1-9/8-21/16-36/19 with steps 9/8-7/6-13/9-19/18, and its inverse
	* 1-9/8-19/16-12/7 with steps 9/8-19/18-13/9-7/6.		* 1-9/8-19/16-12/7 with steps 9/8-19/18-13/9-7/6.

			For pentads, the following chords put an otonal 19 against utonal 7 and 13:
			* 1-19/16-9/7-18/13-3/2 with steps 19/16-13/12-14/13-13/12-4/3, and its inverse
			* 1-13/12-7/6-24/19-3/2 with steps 13/12-14/13-13/12-19/16-4/3;
			* 1-3/2-13/8-7/4-36/19 with steps 3/2-13/12-14/13-13/12-19/18, and its inverse
			* 1-3/2-19/12-12/7-24/13 with steps 3/2-19/18-13/12-14/13-13/12.

			These chords put an otonal 7 against utonal 13 and 19:
			* 1-18/13-3/2-7/4-36/19 with steps 18/13-13/12-7/6-13/12-19/18, and its inverse
			* 1-13/12-3/2-19/12-12/7 with steps 13/12-18/13-19/18-13/12-7/6;
			* 1-24/19-3/2-7/4-24/13 with steps 24/19-19/16-7/6-19/18-13/12, and its inverse
			* 1-19/16-3/2-13/8-12/7 with steps 19/16-24/19-13/12-19/18-7/6.

			These chords put an otonal 13 against utonal 7 and 19:
			* 1-9/7-3/2-13/8-36/19 with steps 9/7-7/6-13/12-7/6-19/18, and its inverse
			* 1-7/6-3/2-19/12-24/13 with steps 7/6-9/7-19/18-7/6-13/12;
			* 1-24/19-3/2-13/8-12/7 with steps 24/19-19/16-13/12-19/18-7/6, and its inverse
			* 1-19/16-3/2-7/4-24/13 with steps 19/16-24/19-7/6-19/18-13/12.

			For hexads, the known ones are
			* 1-9/8-19/16-9/7-18/13-3/2 with steps 9/8-19/18-13/12-14/13-13/12-4/3, and its inverse
			* 1-13/12-7/6-24/19-4/3-3/2 with steps 13/12-14/13-13/12-19/18-9/8-4/3;
			* 1-19/16-9/7-3/2-13/8-12/7 with steps 19/16-13/12-7/6-13/12-19/18-7/6, and its inverse
			* 1-7/6-24/19-3/2-7/4-24/13 with steps 7/6-13/12-19/16-7/6-19/18-13/12;

	[[Category:21-odd-limit]]		[[Category:21-odd-limit]]
Line 71:		Line 99:
	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
			[[Category:Pentads]]
			[[Category:Hexads]]
	[[Category:Ramanujanismic]]		[[Category:Ramanujanismic]]

FloraC: Recategorize

2023-05-23T11:44:47Z

Recategorize

← Older revision		Revision as of 11:44, 23 May 2023
Line 69:		Line 69:
	[[Category:21-odd-limit]]		[[Category:21-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Ramanujanismic]]		[[Category:Ramanujanismic]]

FloraC: Created page with "'''Ramanujanismic chords''' are essentially tempered dyadic chords tempered by the ramanujanisma, 1729/1728. Ramanujanismic chords are numerous. A basic ramanujanism..."

2023-05-21T14:15:43Z

Created page with "'''Ramanujanismic chords''' are essentially tempered dyadic chords tempered by the ramanujanisma, 1729/1728. Ramanujanismic chords are numerous. A basic ramanujanism..."

New page

'''Ramanujanismic chords''' are [[essentially tempered dyadic chord]]s tempered by the ramanujanisma, [[1729/1728]].

Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:
* 1-7/6-24/19 with steps 7/6-13/12-19/12, and its inverse
* 1-7/6-24/13 with steps 7/6-19/12-13/12;

Other ramanujanismic triads are
* 1-19/16-9/7 with steps 19/16-13/12-14/9, and its inverse
* 1-19/16-24/13 with steps 19/16-14/9-13/12;
* 1-19/16-18/13 with steps 19/16-7/6-13/9, and its inverse
* 1-19/16-12/7 with steps 19/16-13/9-7/6.
* 1-7/4-36/19 with steps 7/4-13/12-19/18, and its inverse
* 1-7/4-24/13 with steps 7/4-19/18-13/12;
* 1-13/8-36/19 with steps 13/8-7/6-19/18, and its inverse
* 1-13/8-12/7 with steps 13/8-19/18-7/6;
* 1-18/13-7/4 with steps 18/13-24/19-8/7, and its inverse
* 1-24/19-7/4 with steps 24/19-18/13-8/7;
* 1-9/7-13/8 with steps 9/7-24/19-16/13, and its inverse
* 1-24/19-13/8 with steps 24/19-9/7-16/13;

If we allow the [[21-odd-limit]], we have these additional triads:
* 1-21/16-36/19 with steps 21/16-13/9-19/18, and its inverse
* 1-21/16-18/13 with steps 21/16-19/18-13/9.

All the triads listed above work well with a perfect fifth, so we have the following tetrads:
* 1-19/16-9/7-3/2 with steps 19/16-13/12-7/6-4/3, and its inverse
* 1-7/6-24/19-3/2 with steps 7/6-13/12-19/16-4/3;
* 1-19/16-18/13-3/2 with steps 19/16-7/6-13/12-4/3, and its inverse
* 1-13/12-24/19-3/2 with steps 13/12-7/6-19/16-4/3;
* 1-7/6-18/13-3/2 with steps 7/6-19/16-13/12-4/3, and its inverse
* 1-13/12-9/7-3/2 with steps 13/12-19/16-7/6;
* 1-3/2-7/4-36/19 with steps 3/2-7/6-13/12-19/18, and its inverse
* 1-3/2-19/12-12/7 with steps 3/2-19/18-13/12-7/6;
* 1-3/2-7/4-24/13 with steps 3/2-7/6-19/18-13/12, and its inverse
* 1-3/2-13/8-12/7 with steps 3/2-13/12-19/18-7/6;
* 1-3/2-13/8-36/19 with steps 3/2-13/12-7/6-19/18, and its inverse
* 1-3/2-19/12-24/13 with steps 3/2-19/18-7/6-13/12;
* 1-9/7-3/2-13/8 with steps 9/7-7/6-13/12-16/13, and its inverse
* 1-7/6-3/2-24/13 with steps 7/6-9/7-16/13-13/12;
* 1-9/7-3/2-19/12 with steps 9/7-7/6-19/18-24/19, and its inverse
* 1-7/6-3/2-36/19 with steps 7/6-9/7-24/19-19/18;
* 1-18/13-3/2-7/4 with steps 18/13-13/12-7/6-8/7, and its inverse
* 1-13/12-3/2-12/7 with steps 13/12-18/13-8/7-7/6;
* 1-18/13-3/2-19/12 with steps 18/13-13/12-19/18-24/19, and its inverse
* 1-13/12-3/2-36/19 with steps 13/12-18/13-24/19-19/18;
* 1-24/19-3/2-7/4 with steps 24/19-19/16-7/6-8/7, and its inverse
* 1-19/16-3/2-12/7 with steps 19/16-24/19-8/7-7/6;
* 1-24/19-3/2-13/8 with steps 24/19-19/16-13/12-16/13, and its inverse
* 1-19/16-3/2-24/13 with steps 19/16-24/19-16/13-13/12.

Otherwise they work with a major second:
* 1-9/8-19/16-9/7 with steps 9/8-19/18-13/12-14/9, and its inverse
* 1-9/8-7/4-36/19 with steps 9/8-14/9-13/12-19/18;
* 1-9/8-19/16-18/13 with steps 9/8-19/18-7/6-13/9, and its inverse
* 1-9/8-13/8-36/19 with steps 9/8-13/9-7/6-19/18;
* 1-9/8-18/13-7/4 with steps 9/8-16/13-24/19-8/7, and its inverse
* 1-9/8-9/7-13/8 with steps 9/8-8/7-24/19-16/13.

If we allow the 21-odd-limit, we have these additional tetrads:
* 1-21/16-18/13-3/2 with steps 21/16-19/18-13/12-4/3, and its inverse
* 1-13/12-8/7-3/2 with steps 13/12-19/18-21/16-4/3;
* 1-21/16-3/2-36/19 with steps 21/16-8/7-24/19-19/18, and its inverse
* 1-8/7-3/2-19/12 with steps 8/7-21/16-19/18-24/19;
* 1-9/8-21/16-18/13 with steps 9/8-7/6-19/18-13/9, and its inverse
* 1-9/8-13/8-12/7 with steps 9/8-13/9-19/18-7/6;
* 1-9/8-21/16-36/19 with steps 9/8-7/6-13/9-19/18, and its inverse
* 1-9/8-19/16-12/7 with steps 9/8-19/18-13/9-7/6.

[[Category:21-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triad]]
[[Category:Tetrad]]
[[Category:Ramanujanismic]]