Blackdye: Difference between revisions
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The fifth (3L + M + 2S) of blackdye must be a diatonic fifth. | 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 [[2L 3s|2L' 3s']] 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 [[2L 3s|2L' 3s']] with L' = ML and s' = SL.) | ||
== Tunings == | == Tunings == | ||