Some New Constructs Involving Abstract PCSets, and Probabilistic Applications

Abstract

In general, I shall use the terminology the cited article. Briefly: X,Y,Z etc. will denote pcsets, that is, unordered collections pitch sets. Individual pitch classes will be denoted by lower case letter names c, c#, d etc., and also by certain letters such as x,y and z for variable or unknown pcs in formulas and arguments. A,B, etc. will denote members the group canonical transformations, those operations on pcs which transform any pcset X into pcset accepted as equivalent in given abstract context. A pcset Xl is a form of pcset X2 if there is some canonical transformation A such that Xl = A(X2); in this case X2 will also be form X1. The chord type X, denoted by /X/, is the family all forms X. The number C(j,n) is the number distinct non-ordered combinations j things that can be extracted from set containing n things.

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