Fractal scale - Revision history

BudjarnLambeth: /* Modes */ update todo

2024-12-21T06:17:39Z

Modes: update todo

← Older revision		Revision as of 06:17, 21 December 2024
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	\|}		\|}

	{{todo\|~~expand~~\|inline=1\|comment=Add specific and detailed definitions.}}		{{todo\|improve definition\|complete section\|inline=1\|comment=Add specific and detailed definitions.}}

	== Formulas ==		== Formulas ==

R-4981 at 08:37, 29 January 2024

2024-01-29T08:37:04Z

← Older revision		Revision as of 08:37, 29 January 2024
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	\| 1		\| 1
	\| 2:3:1		\| 2:3:1
	\| ~~Scissors~~		\| Paper
	\| 4 6 2 6 9 3 2 3 1		\| 4 6 2 6 9 3 2 3 1
	\| 4 10 12 18 27 30 32 35 36		\| 4 10 12 18 27 30 32 35 36
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	\| 2		\| 2
	\| 3:1:2		\| 3:1:2
	\| ~~Paper~~		\| Scissors
	\| 9 3 6 3 1 2 6 2 4		\| 9 3 6 3 1 2 6 2 4
	\| 9 12 18 21 22 24 30 32 36		\| 9 12 18 21 22 24 30 32 36

Akselai: /* Modes */

2024-01-28T17:31:38Z

Modes

← Older revision		Revision as of 17:31, 28 January 2024
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	{\| class="wikitable"		{\| class="wikitable"
	\|+ Modes of 1:φ logarithmic fractal scales in 34edo		\|+ Modes of 1:φ logarithmic fractal scales in 34edo
	! Mode rotational order (binary numbering)		! Mode rotational order
			! Mode binary numbering
	! Division pattern		! Division pattern
	! [[FRACNAMS]]		! [[FRACNAMS]]
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	! Scale [[degree]]s (34edo)		! Scale [[degree]]s (34edo)
	\|-		\|-
	\| 0,0,0 (0)		\| 0,0,0
			\| 0
	\| 1:φ, 1:φ, 1:φ		\| 1:φ, 1:φ, 1:φ
	\| Brazilian		\| Brazilian
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	\| 8 13 18 21 26 29 32 34		\| 8 13 18 21 26 29 32 34
	\|-		\|-
	\| 0,0,1 (1)		\| 0,0,1
			\| 1
	\| 1:φ, 1:φ, φ:1		\| 1:φ, 1:φ, φ:1
	\| Carolina		\| Carolina
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	\| 5 13 16 21 24 29 31 34		\| 5 13 16 21 24 29 31 34
	\|-		\|-
	\| 0,1,0 (2)		\| 0,1,0
			\| 2
	\| 1:φ, φ:1, 1:φ		\| 1:φ, φ:1, 1:φ
	\| Georgia		\| Georgia
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	\| 5 8 16 21 24 26 31 34		\| 5 8 16 21 24 26 31 34
	\|-		\|-
	\| 0,1,1 (3)		\| 0,1,1
			\| 3
	\| 1:φ, φ:1, φ:1		\| 1:φ, φ:1, φ:1
	\| California		\| California
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	\| 3 8 13 21 23 26 29 34		\| 3 8 13 21 23 26 29 34
	\|-		\|-
	\| 1,0,0 (4)		\| 1,0,0
			\| 4
	\| φ:1, 1:φ, 1:φ		\| φ:1, 1:φ, 1:φ
	\| Cariboo		\| Cariboo
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	\| 5 8 11 13 21 26 31 34		\| 5 8 11 13 21 26 31 34
	\|-		\|-
	\| 1,0,1 (5)		\| 1,0,1
			\| 5
	\| φ:1, 1:φ, φ:1		\| φ:1, 1:φ, φ:1
	\| Montana		\| Montana
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	\| 3 8 10 13 18 26 29 34		\| 3 8 10 13 18 26 29 34
	\|-		\|-
	\| 1,1,0 (6)		\| 1,1,0
			\| 6
	\| φ:1, φ:1, 1:φ		\| φ:1, φ:1, 1:φ
	\| Bigbend		\| Bigbend
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	\| 3 5 10 13 18 21 29 34		\| 3 5 10 13 18 21 29 34
	\|-		\|-
	\| 1,1,1 (7)		\| 1,1,1
			\| 7
	\| φ:1, φ:1, φ:1		\| φ:1, φ:1, φ:1
	\| Omineca		\| Omineca

Akselai: /* Modes */

2024-01-28T17:30:17Z

Modes

← Older revision		Revision as of 17:30, 28 January 2024
Line 291:		Line 291:
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Modes of 1:φ logarithmic fractal scales in 34edo		\|+ Modes of 1:φ logarithmic fractal scales in 34edo
	! Mode rotational order		! Mode rotational order (binary numbering)
	! Division pattern		! Division pattern
	! [[FRACNAMS]]		! [[FRACNAMS]]
Line 297:		Line 297:
	! Scale [[degree]]s (34edo)		! Scale [[degree]]s (34edo)
	\|-		\|-
	\| 0		\| 0,0,0 (0)
	\| 1:φ, 1:φ, 1:φ		\| 1:φ, 1:φ, 1:φ
	\| Brazilian		\| Brazilian
Line 303:		Line 303:
	\| 8 13 18 21 26 29 32 34		\| 8 13 18 21 26 29 32 34
	\|-		\|-
	\| 1		\| 0,0,1 (1)
	\| 1:φ, 1:φ, φ:1		\| 1:φ, 1:φ, φ:1
	\| Carolina		\| Carolina
Line 309:		Line 309:
	\| 5 13 16 21 24 29 31 34		\| 5 13 16 21 24 29 31 34
	\|-		\|-
	\| 2		\| 0,1,0 (2)
	\| 1:φ, φ:1, 1:φ		\| 1:φ, φ:1, 1:φ
	\| Georgia		\| Georgia
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	\| 5 8 16 21 24 26 31 34		\| 5 8 16 21 24 26 31 34
	\|-		\|-
	\| 3		\| 0,1,1 (3)
	\| 1:φ, φ:1, φ:1		\| 1:φ, φ:1, φ:1
	\| California		\| California
Line 321:		Line 321:
	\| 3 8 13 21 23 26 29 34		\| 3 8 13 21 23 26 29 34
	\|-		\|-
	\| 4		\| 1,0,0 (4)
	\| φ:1, 1:φ, 1:φ		\| φ:1, 1:φ, 1:φ
	\| Cariboo		\| Cariboo
Line 327:		Line 327:
	\| 5 8 11 13 21 26 31 34		\| 5 8 11 13 21 26 31 34
	\|-		\|-
	\| 5		\| 1,0,1 (5)
	\| φ:1, 1:φ, φ:1		\| φ:1, 1:φ, φ:1
	\| Montana		\| Montana
Line 333:		Line 333:
	\| 3 8 10 13 18 26 29 34		\| 3 8 10 13 18 26 29 34
	\|-		\|-
	\| 6		\| 1,1,0 (6)
	\| φ:1, φ:1, 1:φ		\| φ:1, φ:1, 1:φ
	\| Bigbend		\| Bigbend
Line 339:		Line 339:
	\| 3 5 10 13 18 21 29 34		\| 3 5 10 13 18 21 29 34
	\|-		\|-
	\| 7		\| 1,1,1 (7)
	\| φ:1, φ:1, φ:1		\| φ:1, φ:1, φ:1
	\| Omineca		\| Omineca

Akselai: /* Modes */

2024-01-28T11:50:29Z

Modes

← Older revision		Revision as of 11:50, 28 January 2024
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	\|}		\|}

	Alternatively, it is possible to choose which rotation of the division pattern to use in the next step. This results in ''M''<sup>''N''</sup> modes for an order-''N'' fractal scale, which are as many modes are there are scale steps:		Alternatively, it is possible to choose which rotation of the division pattern to use in the next step. This results in ''M''<sup>''N''</sup> modes for an order-''N'' fractal scale, which are as many modes are there are scale steps.
	or order-3 golden ratio(φ)~~'s case~~:
			Here is the example for the order-3 golden ratio (φ) fractal scale:

	{\| class="wikitable"		{\| class="wikitable"

Akselai: /* Modes */

2024-01-28T11:49:07Z

Modes

← Older revision		Revision as of 11:49, 28 January 2024
Line 256:		Line 256:

	== Modes ==		== Modes ==
	It is possible for a fractal scale to have various modes. However, unlike [[MOS scales]], the modes of a fractal scale are not ordinary [[rotation]]s of a scale. Instead, modes correspond to the rotations of the ratio used to divide the scale. For example, here are the modes of an order-2 logarithmic fractal scale with scale steps divided into 1:2:3:		It is possible for a fractal scale to have various modes. However, unlike [[MOS scales]], the modes of a fractal scale are not ordinary [[rotation]]s of a scale. Instead, modes correspond to the rotations of the ratio used to divide the scale. This results in ''M'' modes for each order-''N'' fractal scale. For example, here are the modes of an order-2 logarithmic fractal scale with scale steps divided into 1:2:3:

	{\| class="wikitable"		{\| class="wikitable"
Line 285:		Line 285:
	\|}		\|}

			Alternatively, it is possible to choose which rotation of the division pattern to use in the next step. This results in ''M''<sup>''N''</sup> modes for an order-''N'' fractal scale, which are as many modes are there are scale steps:
	or order-3 golden ratio(φ)'s case:		or order-3 golden ratio(φ)'s case:

R-4981: Undo revision 133313 by R-4981 (talk)

2024-01-28T11:44:46Z

Undo revision 133313 by R-4981 (talk)

@@ Line 283: / Line 283: @@
 | 9 3 6 3 1 2 6 2 4
 | 9 12 18 21 22 24 30 32 36
 |}

R-4981: /* Modes */

2024-01-28T11:41:25Z

Modes

@@ Line 283: / Line 283: @@
 | 9 3 6 3 1 2 6 2 4
 | 9 12 18 21 22 24 30 32 36
 |}

R-4981 at 11:35, 28 January 2024

2024-01-28T11:35:33Z

← Older revision		Revision as of 11:35, 28 January 2024
Line 344:		Line 344:
	\|}		\|}

	{{~~Todo~~ \| ~~add~~ specific and detailed definitions ~~\| inline=1~~}}		{{todo\|expand\|inline=1\|comment=Add specific and detailed definitions.}}

	== Formulas ==		== Formulas ==

R-4981 at 11:34, 28 January 2024

2024-01-28T11:34:47Z

← Older revision		Revision as of 11:34, 28 January 2024
Line 344:		Line 344:
	\|}		\|}

	{{Todo\|add specific and detailed definitions}}		{{Todo \| add specific and detailed definitions \| inline=1}}

	== Formulas ==		== Formulas ==