Z-Related Sets

These are sets that have different prime form, but whose interval class vectors are the same. For example: (0146) and (0137) are different prime forms, but they both have an interval class vector of [111111].

Inclusion (subsets and supersets)

A pc set contains within it examples of pc sets of smaller ordinal numbers. For example: contained within the pc set {2,3,4,6,7} would be the pc sets {2,3,4}, {4,6,7}, {3,4,6}, {2,3,4,6} as well as several others.

Complementation

The complement of a pc set is the set containing all the remaining pcs not in the first set. For example: a seven note set will exclude five pcs. The set containing those five pcs is the complement of the original seven note set. Given the set {5,6,7,9,10,11,1}, the complement would be {0,2,3,4,8}.

Invariance

The concept of invariance has to do with commn tones between pc sets. Two or more pc sets are said to hold some pcs invariant if they have those pcs in common. For example: the sets {1,2,3,6,7} and {2,3,5,8,9} hold pcs 2 and 3 invariant, that is, pcs 2 and 3 are common tones between these two pc sets. This should be determined at the level of the normal order rather than the prime form.

Similarity Relations

This refers to the relative similarity between the interval class vectors fo different sets. While there are numerous mathematical formulae that approach this topic we Will simply do this via inspection.