Mathematics of MOS: Difference between revisions
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Suppose that such a scale ''S'' (with {{nowrap|''n'' ≥ 2}} notes) has ''a'' L steps and ''b'' s steps per period ''p'', and has generator ''g''. Since ''S'' is generated, the interval sizes modulo ''p'' that occur in ''S'' are: | Suppose that such a scale ''S'' (with {{nowrap|''n'' ≥ 2}} notes) has ''a'' L steps and ''b'' s steps per period ''p'', and has generator ''g''. Since ''S'' is generated, the interval sizes modulo ''p'' that occur in ''S'' are: | ||
{ | <nowiki>{</nowiki>{{nowrap|(−''n'' + 1)''g''}}, …, −''g'', 0, ''g'', …, {{nowrap|(''n'' − 1)''g''}}<nowiki>}</nowiki>, | ||
and all sizes {0, ''g'', …, {{nowrap|(''n'' − 1)''g''}} | and all sizes {0, ''g'', …, {{nowrap|(''n'' − 1)''g''}}<nowiki>}</nowiki> are distinct. | ||
We thus have: | We thus have: | ||