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Technically any sequence of notes within the octave is a scale, including the chromatic scale (111111111111). The French composer Olivier Messiaen did some investigation into how many scales can be built, I think the number is a bit over 800. Of course most scales sound weird to unaccostumed ears.



And that’s just within 12 tone systems! Scales don’t have to repeat over the octave, see Wendy Carlos’ work in this area.




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