Mathematics of MOS: Difference between revisions
| Line 238: | Line 238: | ||
See [[Recursive structure of MOS scales#Proofs]]. | See [[Recursive structure of MOS scales#Proofs]]. | ||
=== Maximally even scales are MOS === | === Maximally even scales are MOS === | ||
Let ME(''m'', ''n'') be as in [[Maximal evenness]]. An arbitrary k-step in ME(''m'', ''n'') has size floor((''i'' + ''k'')''n''/''m'') − floor(''in''/''m''), and | Let m < n, gcd(m, n) = d, and ME(''m'', ''n'') be as in [[Maximal evenness]]. An arbitrary k-step in ME(''m'', ''n'') has size floor((''i'' + ''k'')''n''/''m'') − floor(''in''/''m''), and | ||
<math>\lfloor in/m \rfloor + \lfloor kn/m\rfloor - \lfloor in/m\rfloor = \lfloor kn/m\rfloor ≤ \lfloor(i+k)n/m \rfloor - \lfloor in/m \rfloor | <math>\lfloor in/m \rfloor + \lfloor kn/m\rfloor - \lfloor in/m\rfloor = \lfloor kn/m\rfloor ≤ \lfloor(i+k)n/m \rfloor - \lfloor in/m \rfloor | ||