Fractal scale: Difference between revisions

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== Examples ==

=== 2-step divisions ===

A series of [[octave]]-repeating fractal scales can be created using the [[golden ratio]] (here treated as [[~~acoustic~~ phi]]) and the octave. Various [[edo]]s approximate this series to a certain degree of precision. The example below uses the first nine terms of the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21, 34, 55) to approximate golden fractal scales in [[55edo]].

A series of [[octave]]-repeating fractal scales can be created using the [[golden ratio]] (here treated as [[logarithmic phi]]) and the octave. Various [[edo]]s approximate this series to a certain degree of precision. The example below uses the first nine terms of the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21, 34, 55) to approximate golden fractal scales in [[55edo]].

{| class="wikitable"

|+ Golden (1:φ:2) fractal scales, as approximated by 55edo

|+ Golden (<math>1:2^{\phi-1}:2</math>) fractal scales, as approximated by 55edo

! Order

! Number of steps

Line 50:

| 8 13 18 21 26 29 32 34 39 42 45 47 50 52 54 55

|}

The fractal scale of <math>1:\sqrt{2}:2</math> is accurately consistent with edo to the power of 2 (e.g. 16edo).

[[User:R-4981|R-4981]] calls the order-4 <math>1:2^{1/\sqrt{3}}:2</math> fractal scale [[redbull]].

@@ Line 10: / Line 10: @@
 == Examples ==
 === 2-step divisions ===
-A series of [[octave]]-repeating fractal scales can be created using the [[golden ratio]] (here treated as [[acoustic phi]]) and the octave. Various [[edo]]s approximate this series to a certain degree of precision. The example below uses the first nine terms of the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21, 34, 55) to approximate golden fractal scales in [[55edo]].
+A series of [[octave]]-repeating fractal scales can be created using the [[golden ratio]] (here treated as [[logarithmic phi]]) and the octave. Various [[edo]]s approximate this series to a certain degree of precision. The example below uses the first nine terms of the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21, 34, 55) to approximate golden fractal scales in [[55edo]].
 {| class="wikitable"
-|+ Golden (1:φ:2) fractal scales, as approximated by 55edo
+|+ Golden (<math>1:2^{\phi-1}:2</math>) fractal scales, as approximated by 55edo
 ! Order
 ! Number of steps
@@ Line 50: / Line 50: @@
 | 8 13 18 21 26 29 32 34 39 42 45 47 50 52 54 55
 |}
+The fractal scale of <math>1:\sqrt{2}:2</math> is accurately consistent with edo to the power of 2 (e.g. 16edo).
 [[User:R-4981|R-4981]] calls the order-4 <math>1:2^{1/\sqrt{3}}:2</math> fractal scale [[redbull]].