Ternary scale theorems: Difference between revisions
m →Proof: The equave complement is also a generator |
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## If len(S) is even, then ''S'' is equivalent to a word constructed from taking the brightest mode of the MOS 2''a'''''X''' 2''b'''''Z''' with ''a'' odd and gcd(''a'', ''b'') = 1, and replacing every other '''X''' with '''Y'''. | ## If len(S) is even, then ''S'' is equivalent to a word constructed from taking the brightest mode of the MOS 2''a'''''X''' 2''b'''''Z''' with ''a'' odd and gcd(''a'', ''b'') = 1, and replacing every other '''X''' with '''Y'''. | ||
# All primitive balanced ternary scales are MV3. | # All primitive balanced ternary scales are MV3. | ||
# Balanced primitive ternary scales not of type (3) are always SV3. | # Balanced primitive ternary scales not of type (3) are always SV3. | ||
# Balanced primitive ternary scales of type (2) have a generator sequence of period 2. | # Balanced primitive ternary scales of type (2) have a generator sequence of period 2. | ||
=== Theorem 6.2 (Classification of MV3 scales) === | === Theorem 6.2 (Classification of MV3 scales) === | ||