Generator-offset property: Difference between revisions
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== Conjectures == | == Conjectures == | ||
=== Conjecture | === Conjecture -1 (falsified) === | ||
An odd generator-offset scale is SGA. | An odd generator-offset scale is SGA. | ||
==== Counterexamples ==== | ==== Counterexamples ==== | ||
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A 7-note counterexample: 0 210 220 700 710 920 930 1200 | A 7-note counterexample: 0 210 220 700 710 920 930 1200 | ||
=== Conjecture | === Conjecture 2 === | ||
If a non-multiperiod 3-step size scale word is | If a non-multiperiod 3-step size scale word is | ||
# unconditionally MV3, | # unconditionally MV3, | ||
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# and is not of the form ''xyzyx'' or ''xyxzxyx'', | # and is not of the form ''xyzyx'' or ''xyxzxyx'', | ||
then it is AG. (a converse to Theorem 1 + Conjecture 2) | then it is AG. (a converse to Theorem 1 + Conjecture 2) | ||
=== Conjecture 3 === | |||
An SGA scale is always pairwise-well-formed. That is, the result of identifying any two step sizes of an SGA scale is always a non-multiperiod mos. | |||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:AG scales| ]]<!--Main article--> | [[Category:AG scales| ]]<!--Main article--> | ||