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BAIN MUSC 525 Post-Tonal Music Theory Straus Chapter 3 Some Additional Relationships Joseph Straus, Introduction to Post-Tonal Theory, 3rd ed. (Upper Saddle River, NJ: Prentice Hall, 2005). TERMS & CONCEPTS Common-Tone Theorems Common tones under T n (pp. 79-82) Tritone maps unto itself under T 6 (p. 80) Rahn TCS vector Common tones under T n I (pp. 83-85) Index vector matrix (p. 84, see Fig. 3-7) Index vector (Fig. 3-6, p. 85) Rahn TICS vector Aspects of Symmetry Transpositional symmetry (pp. 82-83) Degree of transpositional symmetry (p. 83) Inversional symmetry (pp. 85-91) Geometric analogy for "mirror" inversion (p. 87) Center of symmetry - Pitch symmetrical (p. 87) - Pitch-class symmetrical (pp. 87-88) Degree of inversional symmetry (p. 90) Straus degree of symmetry notation (p. 90) Self-mapping operations (pp. 90-91) Number of distinct members in a set class (p. 91) Composing-Out Linear projections (pp. 103-06) Set Relations Z-relation (pp. 91-93) The all-interval tetrachords: - 4-Z15 & 4-Z29 (pp. 91-92) Complement relation (p. 93-96) - Literal complement - Abstract complement - Self-complementary hexachords (p. 95) Complementary set classes - Proportional distribution of ic (p. 93) - Same degree of symmetry (p. 93) Aggregate (p. 94) Inclusion relations (p. 96-98) - Literal subset/superset - Abstract subset/superset Power set - 2 c Inclusion lattice (p. 96) Contour relations (pp. 99-102) CSEG (p. 99) CSEG-class (pp. 100-101) Set Properties Maximal ic property (p. 95) Transpositional combination - TC property (pp. 98-99) Inversional symmetry & inversionally-related subsets (p. 98) Atonal Voice-Leading Theories Pitch-class counterpoint (pp. 107-08) Transformational voice leading (pp. 107-10) Fuzzy-T n (pp. 108-10) Voice-leading space (pp. 111-112) References Bain, Reginald. Atonal Assistant. Available online at: <http://www.reginaldbain.com> Buchler, Michael. Setmaker. Available online at: <http://myweb.fsu.edu/mbuchler/setmaker.html>. Forte, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973. Morris, Robert D. Bob's Atonal Theory Primer. Available online at: <http://ecmc.rochester.edu/rdm/downloads.html>. ______________. Class Notes for Atonal Theory. Lebanon, NH: Frog Peak, 1991. Rahn, John. Basic Atonal Theory. New York: Longman, 1980. Tymoczko, Dmitri. Chord Geometries. Available online at: <http://music.princeton.edu/~dmitri/ChordGeometries.html>.

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BAIN MUSC 525 Post-Tonal Music Theory

Straus Chapter 3

Some Additional Relationships

Joseph Straus, Introduction to Post-Tonal Theory, 3rd ed. (Upper Saddle River, NJ: Prentice Hall, 2005).

TERMS & CONCEPTS

Common-Tone Theorems Common tones under Tn (pp. 79-82) Tritone maps unto itself under T6 (p. 80) Rahn TCS vector Common tones under TnI (pp. 83-85) Index vector matrix (p. 84, see Fig. 3-7) Index vector (Fig. 3-6, p. 85) Rahn TICS vector Aspects of Symmetry Transpositional symmetry (pp. 82-83) Degree of transpositional symmetry (p. 83) Inversional symmetry (pp. 85-91) Geometric analogy for "mirror" inversion (p. 87) Center of symmetry - Pitch symmetrical (p. 87) - Pitch-class symmetrical (pp. 87-88) Degree of inversional symmetry (p. 90) Straus degree of symmetry notation (p. 90) Self-mapping operations (pp. 90-91) Number of distinct members in a set class (p. 91)

Composing-Out Linear projections (pp. 103-06)

Set Relations Z-relation (pp. 91-93) The all-interval tetrachords: - 4-Z15 & 4-Z29 (pp. 91-92) Complement relation (p. 93-96) - Literal complement - Abstract complement - Self-complementary hexachords (p. 95) Complementary set classes - Proportional distribution of ic (p. 93) - Same degree of symmetry (p. 93) Aggregate (p. 94) Inclusion relations (p. 96-98) - Literal subset/superset - Abstract subset/superset Power set - 2c Inclusion lattice (p. 96) Contour relations (pp. 99-102) CSEG (p. 99) CSEG-class (pp. 100-101) Set Properties Maximal ic property (p. 95) Transpositional combination - TC property (pp. 98-99) Inversional symmetry & inversionally-related

subsets (p. 98) Atonal Voice-Leading Theories Pitch-class counterpoint (pp. 107-08) Transformational voice leading (pp. 107-10) Fuzzy-Tn (pp. 108-10) Voice-leading space (pp. 111-112)

References Bain, Reginald. Atonal Assistant. Available online at: <http://www.reginaldbain.com> Buchler, Michael. Setmaker. Available online at: <http://myweb.fsu.edu/mbuchler/setmaker.html>. Forte, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973. Morris, Robert D. Bob's Atonal Theory Primer. Available online at:

<http://ecmc.rochester.edu/rdm/downloads.html>. ______________. Class Notes for Atonal Theory. Lebanon, NH: Frog Peak, 1991. Rahn, John. Basic Atonal Theory. New York: Longman, 1980. Tymoczko, Dmitri. Chord Geometries. Available online at:

<http://music.princeton.edu/~dmitri/ChordGeometries.html>.

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