Periodic scale: Difference between revisions

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 == Mathematical definition ==
-A periodic scale may be defined in mathematical language as a type of [[Wikipedia: Quasiperiodic function|quasiperiodic function]] from the [[Wikipedia: Integer|integers]] to musical intervals; the integers in this case formalize the notion of "scale degrees". Musical intervals may be written either additively or multiplicatively, and we will assume an additive notation is used, and that intervals are given by positive or negative real numbers with values in cents. In this case, a periodic scale ''s'' has a nonzero quasiperiod ''P'' and repetition interval ''O'' satisfying the following conditions
+A periodic scale may be defined in mathematical language as a type of [[Wikipedia: Quasiperiodic function|quasiperiodic function]] from the [[Wikipedia: Integer|integers]] to musical intervals; the integers in this case formalize the notion of "scale degrees". Here, the intervals are given in cents from an arbitrary "root" note. In this case, a periodic scale ''s'' has a nonzero quasiperiod ''P'' and repetition interval ''O'' satisfying the following conditions
 <math>(1)\ s[0] = 0</math>