27ed4 - Revision history

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:21:49Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:21, 1 August 2025
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	The Nelindic temperament is described in it's own article on [[Nelinda]].		The Nelindic temperament is described in it's own article on [[Nelinda]].
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Edonoi]]~~

Fredg999 category edits: Removing from Category:Ed4 using Cat-a-lot

2025-07-31T21:18:56Z

Removing from Category:Ed4 using Cat-a-lot

← Older revision		Revision as of 21:18, 31 July 2025
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	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
	~~[[Category:Ed4]]~~

BudjarnLambeth: Added harmonics

2024-10-02T09:29:22Z

Added harmonics

← Older revision		Revision as of 09:29, 2 October 2024
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	This tuning also lends itself to Tetrarchy temperament, effectively 7-limit [[Archytas clan\|Archytas temperament]] for the [[4/1\|tetratave]]. In this case, the major mossecond (5 mossteps) represents [[9/7]] and the minor mossecond (3 mossteps), a very accurate [[7/6]]. The generator is a sharp diatonic fifth (711.11¢), contextually a perfect mosthird (8 mossteps). The TE tuning gives a tetratave of 2393.9334 cents.		This tuning also lends itself to Tetrarchy temperament, effectively 7-limit [[Archytas clan\|Archytas temperament]] for the [[4/1\|tetratave]]. In this case, the major mossecond (5 mossteps) represents [[9/7]] and the minor mossecond (3 mossteps), a very accurate [[7/6]]. The generator is a sharp diatonic fifth (711.11¢), contextually a perfect mosthird (8 mossteps). The TE tuning gives a tetratave of 2393.9334 cents.

			== Harmonics ==
			{{Harmonics in equal
			\| steps = 27
			\| num = 4
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 27
			\| num = 4
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}

	== Intervals ==		== Intervals ==

Ayceman: /* Intervals */

2024-01-03T18:30:54Z

Intervals

← Older revision		Revision as of 18:30, 3 January 2024
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	! colspan="2" \|Tetrarchy 3L 4s		! colspan="2" \|Tetrarchy 3L 4s
	! rowspan="2" \|Cents		! rowspan="2" \|Cents
	! ~ Ratios		! rowspan="2" \|~ Ratios
	\|-		\|-
	!Note		!Note
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	!Note		!Note
	!Interval name		!Interval name
	!
	\|-		\|-
	\| 0		\| 0

Dummy index: /* Tetrarchy */

2023-08-05T06:58:50Z

Tetrarchy

← Older revision		Revision as of 06:58, 5 August 2023
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	=== Tetrarchy ===		=== Tetrarchy ===
			Tetrarchy is a [[Domain basis #Canonical form\|noncanonical form]] of quarchy.

	* [[Subgroup]]: 4.3/2.9/7		* [[Subgroup]]: 4.3/2.9/7
	* [[Comma list]]: [[64/63]]		* [[Comma list]]: [[64/63]]
	* [[Mapping~~]]: [⟨1~~ 0 -1~~], ⟨0~~ 1 4]]		* {{Mapping\|legend=1\|1 0 -1\|0 1 4}}
	* [[Support\|Supporting]] ETs: [[17ed4\|17]], 27		* [[Support\|Supporting]] ETs: [[17ed4\|17]], 27
	* [[POTE tuning]]: ~[[3/2]] = 709.3213		* [[POTE tuning]]: ~[[3/2]] = 709.3213

CompactStar at 20:59, 20 July 2023

2023-07-20T20:59:59Z

Show changes

Ayceman: /* Temperaments */ Reg temp finder link

2023-07-20T16:15:53Z

Temperaments: Reg temp finder link

← Older revision		Revision as of 16:15, 20 July 2023
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	== Temperaments ==		== Temperaments ==
	There rank-2 temperament interpretation of the 3L 4s is called Tetrarchy. The name is derived from „tetratave Archytas”, as it's the double octave interpretation of 7-limit Archytas. This scale tempers [[64/63\|Archytas' comma]] (64/63), as [[3/2]] stacked twice approximates 16/7, stacked thrice, it approximates 24/7, and stacked 4 times: 36/7, which is 9/7 above the tetratave.		There rank-2 temperament interpretation of the 3L 4s is called Tetrarchy ([http://x31eq.com/cgi-bin/rt.cgi?limit=4_3%2F2_9%2F7&ets=q17_q27&tuning=po&subgroup=on regular temperament finder link]). The name is derived from „tetratave Archytas”, as it's the double octave interpretation of 7-limit Archytas. This scale tempers [[64/63\|Archytas' comma]] (64/63), as [[3/2]] stacked twice approximates 16/7, stacked thrice, it approximates 24/7, and stacked 4 times: 36/7, which is 9/7 above the tetratave.

	=== Tetrarchy ===		=== Tetrarchy ===

Ayceman: /* Intervals */

2023-07-20T16:05:28Z

Intervals

← Older revision		Revision as of 16:05, 20 July 2023
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	The following table of intervals uses both the 7-note 6L 1s [[MOS scale]] of Nelindic for the naturals (simple A-G notation and standard sharps/flats for the [[chroma]]) and the 7-note 3L 4s scale (standard A-G notation using the typical [[Genchain mode numbering\|genchain]] from [[mosh]]) for Tetrarchy. The 6L 1s scale can be extended to the 13-note (7L 6s) scale, these would include all of the sharps except for F#. Due to the L/s ratio of 3:1, in the 13-note case, most former diminished intervals become minor, most former minor intervals become augmented, and most former augmented intervals become major. Similarly, the 3L 4s scale can be extended to a 7L 3s scale, by dividing the long intervals into sets of 3 and 2 mossteps.		The following table of intervals uses both the 7-note 6L 1s [[MOS scale]] of Nelindic for the naturals (simple A-G notation and standard sharps/flats for the [[chroma]]) and the 7-note 3L 4s scale (standard A-G notation using the typical [[Genchain mode numbering\|genchain]] from [[mosh]]) for Tetrarchy. The 6L 1s scale can be extended to the 13-note (7L 6s) scale, these would include all of the sharps except for F#. Due to the L/s ratio of 3:1, in the 13-note case, most former diminished intervals become minor, most former minor intervals become augmented, and most former augmented intervals become major. Similarly, the 3L 4s scale can be extended to a 7L 3s scale, by dividing the long intervals into sets of 3 and 2 mossteps.

	{\| class="wikitable center-all left-2 ~~right~~-4"		{\| class="wikitable center-all left-2 left-4"
	! rowspan="2" \| Steps		! rowspan="2" \| Steps
	! colspan="2" \| Nelindic 6L 1s		! colspan="2" \| Nelindic 6L 1s
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	\|266.67		\|266.67
	\| 7/6		\| 7/6
			\|-
	\| '''4'''		\| '''4'''
	\| '''B'''		\| '''B'''
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	\|1955.56		\|1955.56
	\| 28/9, 40/13		\| 28/9, 40/13
			\|-
	\| '''23'''		\| '''23'''
	\| '''G'''		\| '''G'''

Ayceman: /* Intervals */

2023-07-20T16:02:31Z

Intervals

← Older revision		Revision as of 16:02, 20 July 2023
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	\|266.67		\|266.67
	\| 7/6		\| 7/6
	~~\|- style="background: #eee"~~
	\| '''4'''		\| '''4'''
	\| '''B'''		\| '''B'''
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	\|1955.56		\|1955.56
	\| 28/9, 40/13		\| 28/9, 40/13
	~~\|- style="background: #eee"~~
	\| '''23'''		\| '''23'''
	\| '''G'''		\| '''G'''

Ayceman: Added 3L4s interpretation

2023-07-20T16:00:54Z

Added 3L4s interpretation

Show changes