Generator-offset property: Difference between revisions
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Now we only need to see that AG + odd cardinality => unconditionally MV3. But the argument in case 2 above works for any interval class (unconditional MV3 wasn't used), hence any interval class comes in at most 3 sizes regardless of tuning. | Now we only need to see that AG + odd cardinality => unconditionally MV3. But the argument in case 2 above works for any interval class (unconditional MV3 wasn't used), hence any interval class comes in at most 3 sizes regardless of tuning. | ||
== Conjectures == | == Conjectures == | ||
=== Conjecture 2 === | |||
If a non-multiperiod 3-step size scale word is | |||
# MV3, | |||
# has odd cardinality, | |||
# is not of the form mx my mz, | |||
# and is not of the form xyxzxyx, | |||
then it is AG. | |||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:AG scales| ]]<!--Main article--> | [[Category:AG scales| ]]<!--Main article--> | ||