Generator-offset property: Difference between revisions

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 * is generator-offset (chain lengths off by 1)
 * has odd length ''n''
-* the generator is subtended constantly.
 Then the scale is SGA.
-Note: The third condition is required. Without it, this is false for the 5-note scale 0 250 300 700 750 1200 with alternants 700 and 50: the 1-steps form the chain 250 50 400 50 450 and the 2-steps form the chain 300 450 700 250 500.
 ==== Proof ====
 Assume that the generator is a ''k''-step and ''k'' is even. (If ''k'' is not even, invert the generator.) On some tonic p we have a chain of ceil(''n''/2) notes and on some other note ''p' = p'' + offset (not on the first chain) we'll have floor(''n''/2) notes.