Set Theory Flashcards
What is a pitch set?
A way of describing a set of notes in a way that is unordered (that is, the order/register doesn’t matter) and thus universal for the same set of notes in any transposition, inversion or retrograde.
What is a subset?
A smaller set that can be extracted from a bigger set. (01) is a subset of (013).
What is a superset?
A larger set, from which subsets can be drawn. (012345) is a superset from which (024) can be drawn.
What is dyad, trichord, tetrachord, pentachord, hexachord etc?
A set with 2 notes is a dyad I.e. (04). A set with 3 notes is a trichord (013) and so on and so on.
What is an interval vector?
Notated <000000>. Describes the interval content of a set. Each integer simply states how many of each interval up to a tritone there are.
< minor 2nd major 2nd minor 3rd major 3rd perfect 4th tritone >
What is Z relation?
Two sets that have the same interval vector are said to be ‘Z related’. There are only a few of these. (0146) and (0137) are Z-related.
What is a literal compliment?
Two sets of pitches which literally form a twelve-tone aggregate (I.e. C D E F G A B and C# D# F# G# A#)
What is an abstract compliment?
The pitch sets of two sets which would (in the correct transposition) give a literal compliment. For the above example, (0,1,3,5,6,8,10) and (0,2,4,7,9) are abstract compliments. Other examples of abstract compliments are:
(0,2,4,6,8,10) is an abstract compliment of itself.
(0,1,2,3,4,5) is an abstract compliment of itself.
(0) and (0,1,2,3,4,56,7,8,9,10), or (0,1) and (0,1,2,3,4,5,6,7,8,9), or (0,1,2) and (0,1,2,3,4,5,6,7,8), or (0,1,2,3) and (0,1,2,3,4,5,6,7) or (0,1,2,3,4) and (0,1,2,3,4,5,6) etc.
