Recursive structure of MOS scales: Difference between revisions

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 It is clear that the MOS nL 1s has a unique generator, L (or its inversion). However, the previous proof showed that reduction reflects generators, and so by induction all MOS scales have a single generator.
-=== Child MOSes exist ===
-{{todo|expand|inline=1}}
-Going from a MOS scale aL bs and applying rules L → Ls, s → s ''or'' L → L, s → Ls, we end up with the child scales aL (a+b)s or (a+b)L bs. The layout of these scales is such that the [[#Stepwise version|stepwise algorithm]] immediately says these two are MOS too: in both cases, first we either exactly de-apply the rules given here, and end up with the parent scale which was chosen to be a MOS, or we get to an L↔s reversed scale with b L’s and a s’s which should end up being MOS too, for some clear reason not stated here right now yet.
 == See also ==