Generator-offset property: Difference between revisions
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If a 3-step size scale word ''ax by cz'' is | If a 3-step size scale word ''ax by cz'' is | ||
# unconditionally SV3 (strict variety 3, i.e. every k-step except multiples of the equave comes in ''exactly'' 3 sizes), | # unconditionally SV3 (strict variety 3, i.e. every k-step except multiples of the equave comes in ''exactly'' 3 sizes), | ||
# has ''odd'' | # has ''odd'' length, | ||
# has gcd(''a'', ''b'', ''c'') = 1, | # has gcd(''a'', ''b'', ''c'') = 1, | ||
# is not of the form ''xyzyx'' or ''xyxzxyx'', | # is not of the form ''xyzyx'' or ''xyxzxyx'', | ||
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If a 3-step size scale word is | If a 3-step size scale word is | ||
# unconditionally SV3 (strict variety 3, i.e. every k-step except multiples of the equave comes in ''exactly'' 3 sizes) | # unconditionally SV3 (strict variety 3, i.e. every k-step except multiples of the equave comes in ''exactly'' 3 sizes) | ||
# has ''even'' | # has ''even'' length, and | ||
# is not of the form ''mx my mz'', | # is not of the form ''mx my mz'', | ||
then it is of the form ''W''(''x'', ''y'', ''z'')''W''(''y'', ''x'', ''z'') for some word ''W'' in 3 variables. | then it is of the form ''W''(''x'', ''y'', ''z'')''W''(''y'', ''x'', ''z'') for some word ''W'' in 3 variables. | ||