On the Interval Content of Invertible Hexachords
David I Lewin · Journal of Music Theory · 1976
By the content of a collection P of pitch classes, I shall refer here (as in Lewin 1960) to that function p which assigns, to each p.c. n, the number p(n) of ways in which the can be (directedly) spanned by ordered pairs of pitch classes from within P. This construct is essentially Allen Forte's interval (see Forte 1973), with two distinctions that will be useful in the present connection. First, my p(6) is twice the value of the tritone entry on Forte's vector. He counts, for example, C-and-Fsharp-both-within-P as one occurrence of a tritone, while I count two ways of spanning a tritone by members of P: C-to-F-sharp and F-sharp-to-C. Second, I* consider p to be defined on all arguments from 0 through 11, while Forte's vector stops at the argument 6. I do so even though p(7) equals p(5), p(8) equals p(4), p(9) equals p(3), etc. While my entries for arguments 7 through 11 are redundant in this sense, it will be useful to have them available, in the light of certain algebraic formulas to come. In the present context, I shall mean by invertible hexachord a collection H of six pitch classes, such that H can be