Neutral and interordinal intervals in MOS scales: Difference between revisions
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Tags: Mobile edit Mobile web edit |
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=== Lemma 1 === | === Lemma 1 === | ||
Let n and k be integers, and let x be a real number such that kx is not an integer. Then floor((n+k)x) − floor(nx) ≥ floor(kx). | Let n and k be integers, and let x be a real number such that kx is not an integer. Then floor((n + k)x) − floor(nx) ≥ floor(kx). | ||
==== Proof ==== | ==== Proof ==== | ||
floor((n+k)x) − floor(nx) = -1 + ceil((n+k)x) + ceil( | floor((n + k)x) − floor(nx) = -1 + ceil((n + k)x) + ceil(−nx) ≥ ceil((n + k)x − nx) − 1 = ceil(kx) − 1 = floor(kx). | ||
=== Discretizing Lemma === | === Discretizing Lemma === | ||