User:CompactStar/8edso - Revision history

Fredg999: Categories

2025-03-26T19:20:52Z

Fredg999: Fredg999 moved page 8edso to User:CompactStar/8edso: OR-3

2025-03-26T19:20:03Z

Fredg999 moved page 8edso to User:CompactStar/8edso: OR-3

← Older revision	Revision as of 19:20, 26 March 2025
(No difference)

Lériendil: super-pitch belongs in novelty tbh

2025-03-18T11:43:04Z

super-pitch belongs in novelty tbh

← Older revision		Revision as of 11:43, 18 March 2025
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	{{~~niche~~}}		{{Novelty}}
	'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.		'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.

BudjarnLambeth: Niche

2025-03-18T03:03:15Z

Niche

← Older revision		Revision as of 03:03, 18 March 2025
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	{{~~Novelty~~}}		{{niche}}
	'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.		'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.

Fredg999: Marked as novelty (same reason as Super-pitch)

2023-07-25T05:46:58Z

Marked as novelty (same reason as Super-pitch)

← Older revision		Revision as of 05:46, 25 July 2023
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			{{Novelty}}
	'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.		'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.

CompactStar at 22:15, 1 July 2023

2023-07-01T22:15:26Z

← Older revision		Revision as of 22:15, 1 July 2023
Line 8:		Line 8:
	!Step		!Step
	!Linear value		!Linear value
			!Cents
	!Tetrative intervals		!Tetrative intervals
	!Common JI approximation		!Common JI approximation
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	\|0		\|0
	\|1		\|1
			\|0.000
	\|		\|
	\|[[1/1]] exact		\|[[1/1]] exact
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	\|1		\|1
	\|1.11149118		\|1.11149118
			\|182.996
	\|		\|
	\|[[10/9]]		\|[[10/9]]
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	\|2		\|2
	\|1.22436140		\|1.22436140
			\|350.435
	\|log(log(5)) = [[5/1]] reduced		\|log(log(5)) = [[5/1]] reduced
	\|[[5/4]], [[11/9]]		\|[[5/4]], [[11/9]]
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	\|3		\|3
	\|1.33973255		\|1.33973255
			\|506.334
	\|		\|
	\|[[4/3]]		\|[[4/3]]
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	\|4		\|4
	\|1.45878181		\|1.45878181
			\|653.717
	\|		\|
	\|[[16/11]], [[19/13]]		\|[[16/11]], [[19/13]]
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	\|5		\|5
	\|1.58278746		\|1.58278746
			\|794.961
	\|log(3) = [[3/1]] reduced		\|log(3) = [[3/1]] reduced
	\|[[8/5]], [[11/7]], [[19/12]]		\|[[8/5]], [[11/7]], [[19/12]]
Line 43:		Line 50:
	\|6		\|6
	\|1.71318047		\|1.71318047
			\|932.013
	\|		\|
	\|[[12/7]]		\|[[12/7]]
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	\|7		\|7
	\|1.85160598		\|1.85160598
			\|1066.533
	\|		\|
	\|[[11/6]], [[13/7]]		\|[[11/6]], [[13/7]]
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	\|8		\|8
	\|2		\|2
			\|1200.000
	\|		\|
	\|[[2/1]] exact		\|[[2/1]] exact

Eliora at 11:34, 1 July 2023

2023-07-01T11:34:33Z

← Older revision		Revision as of 11:34, 1 July 2023
Line 1:		Line 1:
	'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.		'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.

	8edso is notable for containing a close approximation to [[3/1]] (as well as log<sub>2</sub>(3)) according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the [[Pythagorean tuning]].		8edso is notable for containing a close approximation to [[3/1]] (as well as log<sub>2</sub>(3)) according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the [[Pythagorean tuning]]. Furthermore, it provides good representation of 5/1 as well as log<sub>2</sub>(5), thus being a strong 2.3.5 super-subgroup tuning and therefore being the best candidate for the super-pitch equivalent of [[12edo]].

	== Intervals ==		== Intervals ==
Line 8:		Line 8:
	!Step		!Step
	!Linear value		!Linear value
			!Tetrative intervals
			!Common JI approximation
			\|-
			\|0
			\|1
			\|
			\|[[1/1]] exact
	\|-		\|-
	\|1		\|1
	\|1.11149118		\|1.11149118
			\|
			\|[[10/9]]
	\|-		\|-
	\|2		\|2
	\|1.22436140		\|1.22436140
			\|log(log(5)) = [[5/1]] reduced
			\|[[5/4]], [[11/9]]
	\|-		\|-
	\|3		\|3
	\|1.33973255		\|1.33973255
			\|
			\|[[4/3]]
	\|-		\|-
	\|4		\|4
	\|1.45878181		\|1.45878181
			\|
			\|[[16/11]], [[19/13]]
	\|-		\|-
	\|5		\|5
	\|1.58278746		\|1.58278746
			\|log(3) = [[3/1]] reduced
			\|[[8/5]], [[11/7]], [[19/12]]
	\|-		\|-
	\|6		\|6
	\|1.71318047		\|1.71318047
			\|
			\|[[12/7]]
	\|-		\|-
	\|7		\|7
	\|1.85160598		\|1.85160598
			\|
			\|[[11/6]], [[13/7]]
	\|-		\|-
	\|8		\|8
	\|2		\|2
			\|
			\|[[2/1]] exact
	\|}		\|}

Eliora: categories

2023-07-01T10:50:05Z

CompactStar at 00:48, 1 July 2023

2023-07-01T00:48:55Z

← Older revision		Revision as of 00:48, 1 July 2023
Line 1:		Line 1:
	'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.		'''8 equal divisions of the superoctave''' is a [[super-pitch]] tuning system that tetratively divides the superoctave into 8 equally spaced steps.

	8edso is notable for containing a close approximation to [[3/1]] according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the [[Pythagorean tuning]].		8edso is notable for containing a close approximation to [[3/1]] (as well as log<sub>2</sub>(3)) according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the [[Pythagorean tuning]].

	== Intervals ==		== Intervals ==

Eliora at 15:16, 30 June 2023

2023-06-30T15:16:45Z

← Older revision		Revision as of 15:16, 30 June 2023
Line 2:		Line 2:

	8edso is notable for containing a close approximation to [[3/1]] according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the [[Pythagorean tuning]].		8edso is notable for containing a close approximation to [[3/1]] according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the [[Pythagorean tuning]].

			== Intervals ==
			{\| class="wikitable"
			\|+
			!Step
			!Linear value
			\|-
			\|1
			\|1.11149118
			\|-
			\|2
			\|1.22436140
			\|-
			\|3
			\|1.33973255
			\|-
			\|4
			\|1.45878181
			\|-
			\|5
			\|1.58278746
			\|-
			\|6
			\|1.71318047
			\|-
			\|7
			\|1.85160598
			\|-
			\|8
			\|2
			\|}

← Older revision		Revision as of 19:20, 26 March 2025
Line 67:		Line 67:
	\|[[2/1]] exact		\|[[2/1]] exact
	\|}		\|}

	~~[[Category:Equal divisons of the superoctave]]~~
	~~[[Category:Tetration]]~~
	~~[[Category:Transcendental]]~~

← Older revision		Revision as of 10:50, 1 July 2023
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	\|2		\|2
	\|}		\|}

			[[Category:Equal divisons of the superoctave]]
			[[Category:Tetration]]
			[[Category:Transcendental]]