Neutral and interordinal intervals in MOS scales: Difference between revisions
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* The parent mos, which is bL(a-b)s, has steps Ls and L. In this context, since aLbs is assumed to have hardness 2/1, bL(a-b)s has hardness 3/2 thus is proper. | * The parent mos, which is bL(a-b)s, has steps Ls and L. In this context, since aLbs is assumed to have hardness 2/1, bL(a-b)s has hardness 3/2 thus is proper. | ||
=== | === Discretizing Lemma (?) === | ||
Consider an m-note [[maximal evenness|maximally even]] mos of n-edo. Then a k-step of aLbs is either floor( | Consider an m-note [[maximal evenness|maximally even]] mos of n-edo. Then a k-step of aLbs is either floor(kn/m)\n or ceil(kn/m)\n. | ||
==== Proof ==== | ==== Proof ==== | ||
The circular word formed by stacking k-steps of the mos is itself a maximally even mos, considered as a subset of a kn-note equal tuning. One step of a n m'-note maximally even mos of an n'-note equal tuning is either floor(n'/m')\n' or ceil(n'/m')\n', implying the lemma. | |||
=== Statemwnt of the theorem === | === Statemwnt of the theorem === | ||