Jacobin chords - Revision history

Eliora: clarify

2023-06-16T21:53:37Z

clarify

← Older revision		Revision as of 21:53, 16 June 2023
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	'''Jacobin chords''' are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].		'''Jacobin chords''' are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].

	Since the temperament is very complex, even the simplest jacobin chords are 55-odd-limit. There are		Since the temperament is very complex, even the simplest jacobin chords are 55-odd-limit, although they don't contain a lot of notes, just complex intervals. There are
	* 1-11/8-16/11 with steps 11/8-55/52-11/8;		* 1-11/8-16/11 with steps 11/8-55/52-11/8;
	* 1-64/55-11/8 with steps 64/55-13/11-16/11, and its inverse		* 1-64/55-11/8 with steps 64/55-13/11-16/11, and its inverse

FloraC: Rework. Some of them weren't essentially tempered

2023-06-08T03:10:36Z

Rework. Some of them weren't essentially tempered

← Older revision		Revision as of 03:10, 8 June 2023
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	Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].		'''Jacobin chords''' are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].

	~~There are seven chords in total involving this comma. The notation assumes each interval~~ is the ~~interval from the chord and not from the tonic~~. There are ~~5 triads:~~		Since the temperament is very complex, even the simplest jacobin chords are 55-odd-limit. There are
			* 1-11/8-16/11 with steps 11/8-55/52-11/8;
			* 1-64/55-11/8 with steps 64/55-13/11-16/11, and its inverse
			* 1-13/11-11/8 with steps 13/11-64/55-16/11.

	* 1/1 - 55/52 - 11/8 - 11/8		For tetrads, there are
	* 1/1 - 64/55 - 13/11 - 16/11		* 1-11/8-16/11-104/55 with steps 11/8-55/52-13/10-55/52;
	* 1/1 - 13/10 - 16/11 ~~- 128~~/~~121~~		* 1-13/11-11/8-104/55 with steps 13/11-64/55-11/8-55/52, and its inverse
	* 1/1 - 13/11 - 8/5 - ~~128~~/~~121~~		* 1-64/55-11/8-16/11 with steps 64/55-13/11-55/52-11/8;
	* 1/1 - 5/4 - 11/8 - ~~121~~/~~104~~		* 1-64/55-11/8-104/55 with steps 64/55-13/11-11/8-55/52, and its inverse
			* 1-13/11-11/8-16/11 with steps 13/11-64/55-55/52-11/8.
	~~And 2 tetrads which both span two octaves:~~

	* 20/13 - 11/8 - 11/8 - 11/~~8 across 4/1~~
	* 13/11 - 8/5 - 16/11 - 16/11 ~~across 4~~/1

			[[Category:55-odd-limit]]
	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]

Eliora at 21:51, 7 June 2023

2023-06-07T21:51:27Z

← Older revision		Revision as of 21:51, 7 June 2023
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	Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, 6656/6655.		Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, [[6656/6655]].

	There are seven chords in total involving this comma. The notation assumes each interval is the interval from the chord and not from the tonic. There are 5 triads:		There are seven chords in total involving this comma. The notation assumes each interval is the interval from the chord and not from the tonic. There are 5 triads:

Eliora at 21:51, 7 June 2023

2023-06-07T21:51:14Z

← Older revision		Revision as of 21:51, 7 June 2023
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	Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, 6656/6655.		Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, 6656/6655.

	There are ~~five~~ chords ~~known~~. The notation assumes each interval is the interval from the chord and not from the tonic.		There are seven chords in total involving this comma. The notation assumes each interval is the interval from the chord and not from the tonic. There are 5 triads:

	* 1/1 - 55/52 - 11/8 - 11/8		* 1/1 - 55/52 - 11/8 - 11/8
Line 8:		Line 8:
	* 1/1 - 13/11 - 8/5 - 128/121		* 1/1 - 13/11 - 8/5 - 128/121
	* 1/1 - 5/4 - 11/8 - 121/104		* 1/1 - 5/4 - 11/8 - 121/104

			And 2 tetrads which both span two octaves:

			* 20/13 - 11/8 - 11/8 - 11/8 across 4/1
			* 13/11 - 8/5 - 16/11 - 16/11 across 4/1

	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]
			[[Category:Tetrads]]

Eliora at 21:41, 7 June 2023

2023-06-07T21:41:50Z

← Older revision		Revision as of 21:41, 7 June 2023
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	[[Category:Jacobin]]		[[Category:Jacobin]]
	[[Category:Essentially tempered ~~dyadic~~ chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

Eliora: Created page with "Jacobin chords are essentially tempered dyadic chords tempered by the jacobin comma, 6656/6655. There are five chords known. The notation assumes each interval is the int..."

2023-06-07T21:41:28Z

Created page with "Jacobin chords are essentially tempered dyadic chords tempered by the jacobin comma, 6656/6655. There are five chords known. The notation assumes each interval is the int..."

New page

Jacobin chords are [[essentially tempered dyadic chord]]s tempered by the jacobin comma, 6656/6655.

There are five chords known. The notation assumes each interval is the interval from the chord and not from the tonic.

* 1/1 - 55/52 - 11/8 - 11/8
* 1/1 - 64/55 - 13/11 - 16/11
* 1/1 - 13/10 - 16/11 - 128/121
* 1/1 - 13/11 - 8/5 - 128/121
* 1/1 - 5/4 - 11/8 - 121/104

[[Category:Jacobin]]
[[Category:Essentially tempered dyadic chords]]
[[Category:Triads]]