Fractal scale: Difference between revisions
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| 1 | | 1 | ||
| 2:3:1 | | 2:3:1 | ||
| | | 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 | ||
| | | 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 | ||
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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. | ||
Here is the example for the order-3 golden ratio (φ) fractal scale: | |||
{| 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 | ||
! Mode binary numbering | |||
! Division pattern | ! Division pattern | ||
! [[FRACNAMS]] | ! [[FRACNAMS]] | ||
| Line 296: | Line 298: | ||
! 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 | ||
| Line 302: | Line 305: | ||
| 8 13 18 21 26 29 32 34 | | 8 13 18 21 26 29 32 34 | ||
|- | |- | ||
| 0,0,1 | |||
| 1 | | 1 | ||
| 1:φ, 1:φ, φ:1 | | 1:φ, 1:φ, φ:1 | ||
| Line 308: | Line 312: | ||
| 5 13 16 21 24 29 31 34 | | 5 13 16 21 24 29 31 34 | ||
|- | |- | ||
| 0,1,0 | |||
| 2 | | 2 | ||
| 1:φ, φ:1, 1:φ | | 1:φ, φ:1, 1:φ | ||
| Line 314: | Line 319: | ||
| 5 8 16 21 24 26 31 34 | | 5 8 16 21 24 26 31 34 | ||
|- | |- | ||
| 0,1,1 | |||
| 3 | | 3 | ||
| 1:φ, φ:1, φ:1 | | 1:φ, φ:1, φ:1 | ||
| Line 320: | Line 326: | ||
| 3 8 13 21 23 26 29 34 | | 3 8 13 21 23 26 29 34 | ||
|- | |- | ||
| 1,0,0 | |||
| 4 | | 4 | ||
| φ:1, 1:φ, 1:φ | | φ:1, 1:φ, 1:φ | ||
| Line 326: | Line 333: | ||
| 5 8 11 13 21 26 31 34 | | 5 8 11 13 21 26 31 34 | ||
|- | |- | ||
| 1,0,1 | |||
| 5 | | 5 | ||
| φ:1, 1:φ, φ:1 | | φ:1, 1:φ, φ:1 | ||
| Line 332: | Line 340: | ||
| 3 8 10 13 18 26 29 34 | | 3 8 10 13 18 26 29 34 | ||
|- | |- | ||
| 1,1,0 | |||
| 6 | | 6 | ||
| φ:1, φ:1, 1:φ | | φ:1, φ:1, 1:φ | ||
| Line 338: | Line 347: | ||
| 3 5 10 13 18 21 29 34 | | 3 5 10 13 18 21 29 34 | ||
|- | |- | ||
| 1,1,1 | |||
| 7 | | 7 | ||
| φ:1, φ:1, φ:1 | | φ:1, φ:1, φ:1 | ||
| Line 345: | Line 355: | ||
|} | |} | ||
{{todo| | {{todo|improve definition|complete section|inline=1|comment=Add specific and detailed definitions.}} | ||
== Formulas == | == Formulas == | ||