Parallelogram substring scale: Difference between revisions
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== Ternary scales with this property == | == Ternary scales with this property == | ||
=== Examples === | |||
* All non-Fraenkel balanced MV3 scales | * All non-Fraenkel balanced MV3 scales | ||
* All ''a'''''x'''(''b'''''y'''(''a'' - ''b'')'''z''') MOS substitution scales | * All ''a'''''x'''(''b'''''y'''(''a'' - ''b'')'''z''') MOS substitution scales | ||
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**# ''h'' is a generator of the filling MOS | **# ''h'' is a generator of the filling MOS | ||
**# |''g''|<sub>'''X'''</sub> = |''h''| where '''X''' is the slot letter of the template MOS | **# |''g''|<sub>'''X'''</sub> = |''h''| where '''X''' is the slot letter of the template MOS | ||
=== Non-examples === | |||
* All multiperiod MOS substitution scales | |||
== Open problems == | == Open problems == | ||
# Classify all MOS-substitution quasi-parallelogram scales. | # Classify all MOS-substitution quasi-parallelogram scales. | ||
# Classify all ternary quasi-parallelogram scales. Conjecture: All ternary quasi-parallelogram scales are MOS substitution scales. | # Classify all ternary quasi-parallelogram scales. Conjecture: All ternary quasi-parallelogram scales are MOS substitution scales. | ||
[[Category:Pages with open problems]] | [[Category:Pages with open problems]] | ||