Mathematics of MOS: Difference between revisions
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=== Binary generated scales with #L coprime to #s within each period are MOS === | === Binary generated scales with #L coprime to #s within each period are MOS === | ||
This proof justifies the common description of "stack until binary" for MOS building and Erv Wilson's terminology | This proof justifies the common description of "stack until binary" for MOS building and Erv Wilson's terminology ''moment of symmetry'' where MOS sizes are "moments" in time (when stacking) where the "symmetry" of binarity holds. | ||
By ''generatedness'', we mean that every interval in the scale is of the form ''jg'' + ''kp'' where ''g'' is a generator, ''p'' is the period, and ''j, k'' ∈ '''Z''', and that either ''g'' or ''−g'' occurs on every note. We claim that any interval class not ''p''-equivalent to 0 has ''exactly'' 2 sizes in any scale satisfying the antecedent. | By ''generatedness'', we mean that every interval in the scale is of the form ''jg'' + ''kp'' where ''g'' is a generator, ''p'' is the period, and ''j, k'' ∈ '''Z''', and that either ''g'' or ''−g'' occurs on every note. We claim that any interval class not ''p''-equivalent to 0 has ''exactly'' 2 sizes in any scale satisfying the antecedent. | ||