5L 2s: Difference between revisions
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1 1 0 1 1 1 0 = 1 1 1 1 1 | 1 1 0 1 1 1 0 = 1 1 1 1 1 | ||
==A continuum of tunings== | == A continuum of tunings: the 5L 2s scale tree == | ||
So if 4\7 (four degrees of 7edo) is at one extreme and 3\5 (three degrees of 5edo) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12edo: | So if 4\7 (four degrees of 7edo) is at one extreme and 3\5 (three degrees of 5edo) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12edo: | ||