Rothenberg propriety

Rothenberg propriety is a concept in the theory of musical scales.

“Rothenberg calls a scale 'strictly proper' if it possesses a generic ordering, 'proper' if it admits ambiguities but no contradictions, and 'improper' if it admits contradictions.”

Examples

It's easy to see the concept in action at the 7-step diatonic scale (5L 2s) as rendered in three different EDOs:

• 12edo (2-2-1-2-2-2-1) is proper but not strictly proper because of the ambiguities of d5 (1+2+2+1=6) and A4 (2+2+2=6) in three-step and five-step intervals.
• 17edo (3-3-1-3-3-3-1) is improper because of the contradiction in d5 (1+3+3+1=8) being smaller than A4 (3+3+3=9).
• 19edo (3-3-2-3-3-3-2) is strictly proper.

See also

• Wikipedia: Rothenberg propriety
• MOS scale