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.

'''''S7r2c1''''' - 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.

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== Properties ==

One significant characteristic that differs from most tunings is that each successive lower octave has more notes. At first sight, the different progressions don't seem to say much. It helps to analyze each tuning by looking at its full interval matrix, revealing that some ~~spirals~~ have many more types of minor thirds, while others have more fifths. Some completely dodge certain harmonics, regardless of how many "strings" you add; some combinations just never happen.

One significant characteristic that differs from most tunings is that each successive lower octave has more notes. At first sight, the different progressions don't seem to say much. It helps to analyze each tuning by looking at its full interval matrix, revealing that some strings have many more types of minor thirds, while others have more fifths. Some completely dodge certain harmonics, regardless of how many "strings" you add; some combinations just never happen.

The most important part is the number of sides, which will expose different chords at each row, some configurations make progressions more intuitive. The most altered part of the progression are the initial segments, since its the result of truncating the spiral, they are the most affected. from these different truncation different patterns still emerge. The rest of the progression are mostly equal, relatively, in most configurations. From a string length perspective,(already away from the center, with less error in the truncation) the progression is almost arithmetic, seems to increase at constant but there is an increasing unnoticeable ratio.

TODO: Add images!

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* [https://kepleriandreams.github.io An open-source, virtual playable spiral harp] by [[User:Jbcristian|J.B. Cristian]]

[[Category:Instruments]]

[[Category:Tuning]]

@@ 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.
+'''''S7r2c1''''' - 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.
@@ Line 74: / Line 74: @@
 == Properties ==
-One significant characteristic that differs from most tunings is that each successive lower octave has more notes. At first sight, the different progressions don't seem to say much. It helps to analyze each tuning by looking at its full interval matrix, revealing that some spirals have many more types of minor thirds, while others have more fifths. Some completely dodge certain harmonics, regardless of how many "strings" you add; some combinations just never happen.
+One significant characteristic that differs from most tunings is that each successive lower octave has more notes. At first sight, the different progressions don't seem to say much. It helps to analyze each tuning by looking at its full interval matrix, revealing that some strings have many more types of minor thirds, while others have more fifths. Some completely dodge certain harmonics, regardless of how many "strings" you add; some combinations just never happen.
+The most important part is the number of sides, which will expose different chords at each row, some configurations make progressions more intuitive. The most altered part of the progression are the initial segments, since its the result of truncating the spiral, they are the most affected. from these different truncation different patterns still emerge. The rest of the progression are mostly equal, relatively, in most configurations. From a string length perspective,(already away from the center, with less error in the truncation) the progression is almost arithmetic, seems to increase at constant but there is an increasing unnoticeable ratio.
 TODO: Add images!
@@ Line 85: / Line 87: @@
 * [https://kepleriandreams.github.io An open-source, virtual playable spiral harp] by [[User:Jbcristian|J.B. Cristian]]
+[[Category:Instruments]]
 [[Category:Tuning]]