Rank-3 scale: Difference between revisions
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Nonetheless, an ''n''-ary periodic scale is still ''generically'' rank-''n'' (the group generated by the ''n'' step sizes X<sub>''i''</sub> > 0, ''i'' = 1, ..., ''n'' has rank ''n'', not lower, for ''almost all'' choices of X<sub>''i''</sub>, in the same sense that almost all real numbers between 0 and 1 are irrational). | Nonetheless, an ''n''-ary periodic scale is still ''generically'' rank-''n'' (the group generated by the ''n'' step sizes X<sub>''i''</sub> > 0, ''i'' = 1, ..., ''n'' has rank ''n'', not lower, for ''almost all'' choices of X<sub>''i''</sub>, in the same sense that almost all real numbers between 0 and 1 are irrational). | ||
Ternary scales described on this page are generalizations of | Ternary scales described on this page are generalizations of rank-2 scales (MOS scales and permutations thereof, and other scales that have a single generator), which will first be introduced. | ||
== Rank-2 scales == | == Rank-2 scales == | ||