**Sets**. Ways in which a set can be defined: listing
its elements or selecting a property common to all its elements.
Venn (Euler) diagrams.

- elements of a set
- subsets
- universal or reference set
- complement or negation
- empty or null set
- disjoint sets

**Operations with sets**

- union (either/or): cup
- intersection (both/and): cusp
- negation/complement (but; everything except)
- implies
- logical equivalence

**Laws of Operations with Sets**

- Symmetrical difference or the disjunctive sum (exclusive or)
- DeMorgan's Laws (see Ayres, page 5).

**Musical examples**

- Complementarity of chords and scales (also see Anatol
Vieru -
**:The Book of Modes**)- Debussy - Voiles (piano prelude)
- Luigi Nono - Guernica
- Aurel Stroe - Piano Sonata
- Skriabin - Prometheus, scales and quartal chord
- combinatoriality: Schoenberg - Variations for Orchestra, Theme.

- Complex structures as the result of operatins with sets
- Richard Strauss - Elektra: whole-tone fragment in Elektra's monologue (act 1).
- Messiaen's modes with limited transpositions
- Xenakis - Herma

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