Spiral tunings: Difference between revisions

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

'''''~~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.

'''''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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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, the progression is almost arithmetic, seems to increase at constant but there is an increasing unnoticeable ratio.

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 16: / Line 16: @@
 '''''S1m1.05946''''' - One-sided spiral with a margin of the twelfth root of 2.
-'''''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.
+'''''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 76: / Line 76: @@
 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, the progression is almost arithmetic, seems to increase at constant but there is an increasing unnoticeable ratio.
+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!