Ternary scale theorems: Difference between revisions
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# If ''n'' is odd, ''s'' is abstractly SV3 (i.e. SV3 for almost all tunings). | # If ''n'' is odd, ''s'' is abstractly SV3 (i.e. SV3 for almost all tunings). | ||
# If ''n'' is odd, {{nowrap|''s'' {{=}} ''a'''''X''' ''b'''''Y''' ''b'''''Z'''}} is obtained from some mode of the (primitive) MOS ''a'''''X''' 2''b'''''W''' by replacing all the '''W'''s successively with alternating '''Y'''s and '''Z'''s (or alternating '''Z'''s and '''Y'''s for the other chirality, fixing the mode of ''a'''''X''' 2''b'''''W'''). The two alternants differ by replacing one '''Y''' with a '''Z'''. In other words, ''s'' is ''odd-regular'' in our classification of MV3 scales. | # If ''n'' is odd, {{nowrap|''s'' {{=}} ''a'''''X''' ''b'''''Y''' ''b'''''Z'''}} is obtained from some mode of the (primitive) MOS ''a'''''X''' 2''b'''''W''' by replacing all the '''W'''s successively with alternating '''Y'''s and '''Z'''s (or alternating '''Z'''s and '''Y'''s for the other chirality, fixing the mode of ''a'''''X''' 2''b'''''W'''). The two alternants differ by replacing one '''Y''' with a '''Z'''. In other words, ''s'' is ''odd-regular'' in our classification of MV3 scales. | ||
=== Proof === | === Proof === | ||