The Hexachordal Theorem: A Mathematical Look at Interval Relations in Twelve-Tone Composition
Steven K. Blau · Mathematics Magazine · 1999
mentary six-member subsets A and B. Each subset has (6) = 15 pairs of members; the interval between any pair of numbers is the (positive) difference between them, subject to the equivalence n 12 n. So, for the pair (1, 11) the interval may be said to be either 10 or 2. A convenient way to represent a complementary pair of interval sets, which makes visually apparent the equivalence just described, is to present a clock face with six A's and six B's, as follows: