Z-relation
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In musical set theory, a Z-relation, also called isomeric relation, is a relation between two pitch-class sets in which the two sets have the same intervallic content (i.e. they have the same interval vector), but they are of different Tn-type and Tn/TnI-type. That is to say, one set cannot be derived from the other through transposition or inversion.
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, but the notion seems to have first been considered by Howard Hanson. Hanson termed this the isomeric relationship, defining two such sets to be isomeric.
Some argue that the "relation" is often so remote as to be imperceptible, but certain composers have exploited the Z-relation in their work.
[edit] References
- Allen Forte, The Structure of Atonal Music, Yale University Press, 1977,
- Howard Hanson, Harmonic Materials of Modern Music, Appleton-Century-Crofts, 1960
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