Neutral and interordinal intervals in MOS scales: Difference between revisions
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=== Discretizing Lemma === | === Discretizing Lemma === | ||
Consider an m-note [[maximal evenness|maximally even]] mos of n-edo. Then a k-step of that mos is either floor(nk/m)\n or ceil(nk/m)\n. | Consider an m-note [[maximal evenness|maximally even]] mos of n-edo, and let 1 <= k <= m-1. Then a k-step of that mos is either floor(nk/m)\n or ceil(nk/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 an m'-note maximally even mos of an n'-note equal tuning is either floor(n'/m')\n'<equave> or ceil(n'/m')\n'<equave>, implying the lemma. | 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 an m'-note maximally even mos of an n'-note equal tuning is either floor(n'/m')\n'<equave> or ceil(n'/m')\n'<equave>, implying the lemma. | ||