Z-relation - All About All

Z-relation

In musical set theory, a Z-relation is a relation between two sets in which the two sets have the same interval content (i.e. they have the same "interval vector"), but they are of different T_n-type and T_n/T_nI-type.

For example, the two sets {0,1,4,6} and {0,1,3,7} have the same interval vector (<1,1,1,1,1,1>) but they are not transpositionally or inversionally related.

The term originated with Allen Forte, in his Structure of Atonal Music (ISBN 0300021208).

Some argue that the "relation" is so remote as to be imperceptible.