Generator sequence: Difference between revisions
m →Related concepts: Added conjectures regarding ternary scales with 3-interval WFGSes |
m →Conjectures: "3-interval" is ambiguous here... |
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If a ternary [[billiard scale]] has a WFGS, the WFGS must use either two or three distinct generators, since ternary billiard scales are MV3 or MV4 and the closing generator is excluded from the generator sequence. | If a ternary [[billiard scale]] has a WFGS, the WFGS must use either two or three distinct generators, since ternary billiard scales are MV3 or MV4 and the closing generator is excluded from the generator sequence. | ||
=== Conjectures === | === Conjectures === | ||
'''Conjecture:''' There are only finitely many ternary scales with a 3 | '''Conjecture:''' There are only finitely many ternary scales with a WFGS of length 3. | ||
'''Conjecture:''' There exist no ternary scale with more than 14 notes that has a WFGS of length 3. | |||
== MOS substitution == | == MOS substitution == | ||
[[MOS substitution]] is a procedure that yields ternary scales with binary generator sequences. | [[MOS substitution]] is a procedure that yields ternary scales with binary generator sequences. | ||