Spiral tunings: Difference between revisions

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'''''S1m1.05946''''' - One-sided spiral with a margin of the twelfth root of 2.

'''''S7x1.~~1y1c1~~''''' - Seven-sided spiral with a margin of 1 (omitted), ~~starting away from the center at x = 1.1, y = 1~~, and constant increment c = 1. When omitted, spirals ~~start at x = 0, y =~~ 0, c = 1.

'''''S7x1.1r2''''' - Seven-sided spiral with a margin of 1 (omitted), with an initial radius of 2, and constant increment c = 1. When omitted, spirals initial radius is 0, c = 1.

'''''iS6m1''''' - Inverted six-sided spiral with a margin of 1.

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''Margin:'' usually 1 (to mimic spider-webs). This property can be (unnecessarily) employed to generate [[Equal divisions of the octave|equal-division systems]]. For example, the angle is calculated with "PI * 2 / spiralSides," so when sides are 1, 1/2, or 1/4, etc., it leaves the margin as the sole control for segment length increase. For instance, a one-sided spiral with a radius of approximately 1.05946 (twelfth root of 2) generates a 12 equal division system. From this perspective, equal-division systems can be seen as a subset of spirals.

~~''Starting coordinates''~~: usually 0~~, 0. Starting the spiral away from the center~~ opens another dimension of progression; however, it seems to mostly affect the initial segments, and the rest of the spiral converges quickly with its version ~~starting at 0,~~ 0.

Initial radius: usually 0 Using a different initial radius opens another dimension of progression; however, it seems to mostly affect the initial segments, and the rest of the spiral converges quickly with its version with radius 0.

''Inversion'': This parameter doesn't affect the progression but rather how the progression is treated, as string length or as frequency.

@@ Line 16: / Line 16: @@
 '''''S1m1.05946''''' - One-sided spiral with a margin of the twelfth root of 2.
-'''''S7x1.1y1c1''''' - Seven-sided spiral with a margin of 1 (omitted), starting away from the center at x = 1.1, y = 1, and constant increment c = 1. When omitted, spirals start at x = 0, y = 0, c = 1.
+'''''S7x1.1r2''''' - Seven-sided spiral with a margin of 1 (omitted), with an initial radius of 2, and constant increment c = 1. When omitted, spirals initial radius is 0, c = 1.
 '''''iS6m1''''' - Inverted six-sided spiral with a margin of 1.
@@ Line 26: / Line 26: @@
 ''Margin:'' usually 1 (to mimic spider-webs). This property can be (unnecessarily) employed to generate [[Equal divisions of the octave|equal-division systems]]. For example, the angle is calculated with "PI * 2 / spiralSides," so when sides are 1, 1/2, or 1/4, etc., it leaves the margin as the sole control for segment length increase. For instance, a one-sided spiral with a radius of approximately 1.05946 (twelfth root of 2) generates a 12 equal division system. From this perspective, equal-division systems can be seen as a subset of spirals.
-''Starting coordinates'': usually 0, 0. Starting the spiral away from the center opens another dimension of progression; however, it seems to mostly affect the initial segments, and the rest of the spiral converges quickly with its version starting at 0, 0.
+Initial radius: usually 0 Using a different initial radius opens another dimension of progression; however, it seems to mostly affect the initial segments, and the rest of the spiral converges quickly with its version with radius 0.
 ''Inversion'': This parameter doesn't affect the progression but rather how the progression is treated, as string length or as frequency.