Blackdye: Difference between revisions
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== Properties == | == Properties == | ||
# | # Assuming positive step sizes, the fifth (3L + M + 2S) of blackdye must be a diatonic fifth.<!-- | ||
#* (To see this: Consider the chain of fifths generated by the fifth. The diatonic chroma = 7 fifths - 4 octaves = 21L + 7M + 14S - (20L + 8M + 12S) = L - M + 2S. Since L - M >= 0, this must always be nonnegative, so the fifth must be >= 4\7. The fifth cannot be sharper than 3\5, since it generates the [[2L 3s|2L' 3s']] subset of blackdye with L' = ML and s' = SL.)--> | #* (To see this: Consider the chain of fifths generated by the fifth. The diatonic chroma = 7 fifths - 4 octaves = 21L + 7M + 14S - (20L + 8M + 12S) = L - M + 2S. Since L - M >= 0, this must always be nonnegative, so the fifth must be >= 4\7. The fifth cannot be sharper than 3\5, since it generates the [[2L 3s|2L' 3s']] subset of blackdye with L' = ML and s' = SL.)--> | ||
# | # Assuming positive step sizes, the fifth is: | ||
#* sharper than 700¢, if L + 3S > 2M | #* sharper than 700¢, if L + 3S > 2M | ||
#* equal to 700¢, if L + 3S = 2M | #* equal to 700¢, if L + 3S = 2M | ||