Wizardharry chords - Revision history

Xenllium at 13:59, 17 July 2023

2023-07-17T13:59:23Z

← Older revision		Revision as of 13:59, 17 July 2023
Line 17:		Line 17:
	* 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.		* 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.

	In the 2.3.5.11 subgroup, the wizardharry temperament contains many possibilities for essentially tempered chords~~, including~~ 12 triads, and even nonads, as 33-odd-limit essentially tempered chords.		In the 2.3.5.11 subgroup, the wizardharry temperament contains many possibilities for essentially tempered chords. It includes 12 triads, and even nonads, as 33-odd-limit essentially tempered chords.

	For triads, there are five additional pairs of chords in inverse relationship:		For triads, there are five additional pairs of chords in inverse relationship:
Line 27:		Line 27:

	Remarkable nonads include a pair of chords in inverse relationship:		Remarkable nonads include a pair of chords in inverse relationship:
	* 1-11/10-40/33-4/3-11/8-22/15-50/33-5/3-11/6 with steps of ~~11/10-11/10-11/10-~~33/32-16/15-33/32-11/10-11/10-12/11, and its inverse		* 1-33/32-11/10-25/22-5/4-11/8-3/2-33/20-20/11 with steps of 33/32-16/15-33/32-11/10-11/10-12/11-11/10-11/10-11/10, and its inverse
	* 1-11/10-40/33-5/4~~-4/3~~-11/8-50/33-5/3-11/6 with steps of 11/10-11/10-33/32-16/~~15-33/32~~-11/10-11/10-11/10-12/11.		* 1-33/32-25/22-5/4-11/8-3/2-33/20-20/11-15/8 with steps of 33/32-11/10-11/10-11/10-12/11-11/10-11/10-33/32-16/15.

	Equal temperaments with wizardharry chords include {{Optimal ET sequence\| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.		Equal temperaments with wizardharry chords include {{Optimal ET sequence\| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.

Xenllium at 13:33, 17 July 2023

2023-07-17T13:33:32Z

← Older revision		Revision as of 13:33, 17 July 2023
Line 1:		Line 1:
	'''Wizardharry chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the wizardharry comma, [[4000/3993]].		'''Wizardharry chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the wizardharry comma, [[4000/3993]].

	The wizardharry temperament has a [[1L 6s\|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out\|tempered out]]. It contains two triads, four tetrads and two pentads as 33-odd-limit essentially tempered chords.		The wizardharry temperament has a [[1L 6s\|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out\|tempered out]]. It contains two triads, four tetrads and two pentads as 2.3.11/5 [[subgroup]] 33-odd-limit essentially tempered chords.

	The triads are		The triads are
Line 16:		Line 16:
	* 1-11/10-40/33-4/3-22/15 chord with steps of 11/10-11/10-11/10-11/10-15/11;		* 1-11/10-40/33-4/3-22/15 chord with steps of 11/10-11/10-11/10-11/10-15/11;
	* 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.		* 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.

			In the 2.3.5.11 subgroup, the wizardharry temperament contains many possibilities for essentially tempered chords, including 12 triads, and even nonads, as 33-odd-limit essentially tempered chords.

			For triads, there are five additional pairs of chords in inverse relationship:
			* 1-11/10-25/22 with steps of 11/10-33/32-44/25 and its inverse 1-33/32-25/22 with steps of 33/32-11/10-44/25;
			* 1-40/33-11/8 with steps of 40/33-25/22-16/11 and its inverse 1-25/22-11/8 with steps of 25/22-40/33-16/11;
			* 1-11/8-50/33 with steps of 11/8-11/10-33/25 and its inverse 1-11/10-50/33 with steps of 11/10-11/8-33/25;
			* 1-22/15-50/33 with steps of 22/15-33/32-33/25 and its inverse 1-33/32-50/33 with steps of 33/32-22/15-33/25;
			* 1-50/33-11/6 with steps of 50/33-40/33-12/11 and its inverse 1-40/33-11/6 with steps of 40/33-50/33-12/11.

			Remarkable nonads include a pair of chords in inverse relationship:
			* 1-11/10-40/33-4/3-11/8-22/15-50/33-5/3-11/6 with steps of 11/10-11/10-11/10-33/32-16/15-33/32-11/10-11/10-12/11, and its inverse
			* 1-11/10-40/33-5/4-4/3-11/8-50/33-5/3-11/6 with steps of 11/10-11/10-33/32-16/15-33/32-11/10-11/10-11/10-12/11.

	Equal temperaments with wizardharry chords include {{Optimal ET sequence\| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.		Equal temperaments with wizardharry chords include {{Optimal ET sequence\| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.
Line 24:		Line 37:
	[[Category:Tetrads]]		[[Category:Tetrads]]
	[[Category:Pentads]]		[[Category:Pentads]]
			[[Category:Nonads]]
	[[Category:Wizardharry]]		[[Category:Wizardharry]]

Xenllium: Created page with "'''Wizardharry chords''' are essentially tempered chords tempered by the wizardharry comma, 4000/3993. The wizardharry temperament has a 1L 6s|seven-to..."

2023-07-17T10:39:57Z

Created page with "'''Wizardharry chords''' are essentially tempered chords tempered by the wizardharry comma, 4000/3993. The wizardharry temperament has a 1L 6s|seven-to..."

New page

'''Wizardharry chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the wizardharry comma, [[4000/3993]].

The wizardharry temperament has a [[1L 6s|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out|tempered out]]. It contains two triads, four tetrads and two pentads as 33-odd-limit essentially tempered chords.

The triads are
* 1-11/10-40/33 chord with steps of 11/10-11/10-33/20;
* 1-40/33-22/15 chord with steps of 40/33-40/33-15/11.

The tetrads are
* 1-11/10-40/33-4/3 chord with steps of 11/10-11/10-11/10-3/2;
* 1-11/10-40/33-22/15 chord with steps of 11/10-11/10-40/33-15/11, and its inverse
* 1-40/33-4/3-22/15 chord with steps of 40/33-11/10-11/10-15/11;
* 1-40/33-22/15-16/9 chord with steps of 40/33-40/33-40/33-9/8.

The pentads are
* 1-11/10-40/33-4/3-22/15 chord with steps of 11/10-11/10-11/10-11/10-15/11;
* 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.

Equal temperaments with wizardharry chords include {{Optimal ET sequence| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.

[[Category:33-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Wizardharry]]