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Basic concepts of pitch and interval. Octave equivalence -- Enharmonic equivalence -- Pitch and pitch class -- Integer notation -- Arithmetic modulo 12 (mod 12) -- Intervals (calculated in semitones) -- Pitch intervals (ordered and unordered) -- Ordered pitch-class intervals -- Unordered pitch-class intervals -- Interval class -- Interval-class content -- Interval-class vector -- Spacing and register -- Model analyses. Anton Webern, "Wie bin ich froh!" from Three songs, op. 25 -- Arnold Schoenberg, "Nacht" (Night), from Pierrot Lunaire, op. 21 -- Guided analyses. Anton Webern, Symphony, op. 21, second movement, theme -- Arnold Schoenberg, Piano Concerto, op. 42, first movement -- Igor Stravinsky, "Musick to heare," from Three Shakespeare songs -- Ruth Crawford Seeger, Diaphonic suite no. 1 (for oboe or flute), first movement -- Edgard Varèse, Octandre, first movement -- Milton Babbitt, "The widow's lament in springtime" -- Luciano Berio, Sequenza I (for solo flute) -- Kaija Saariaho, NoaNoa (for flute and live electronics) -- Elliott Carter, Riconoscenza per Goffredo Petrassi (for solo violin) -- Ursula Mamlok, Variations for solo flute, theme -- Pitch-class sets. Pitch-class sets -- Normal form. Putting a set into normal form ; Using the pitch-class clockface -- Transposition (Tn). Line (or series) of pitches ; Line (or series) of pitch classes ; Set of pitch classes ; Levels of transposition ; Transposing a pitch-class set ; Recognizing sets related by transposition ; Nodes, arrows, and networks ; Inverse -- Inversion (In). Index number (sum) ; Line (or series) of pitches ; Line (or series) of pitch classes ; Set of pitch classes -- Inversion (I(x/y)) -- Set class -- Prime form -- List of set classes -- Model analyses. Arnold Schoenberg, Book of the Hanging Gardens, op. 15, no. 11 -- Béla Bartók, String quartet no. 4, first movement -- Guided analyses. Ruth Crawford Seeger, Piano prelude no. 9 -- Anton Webern, Concerto for nine instruments, op. 24, second movement -- Igor Stravinsky, Agon, "Pas de deux" -- Anton Webern, Five movements for string quartet, op. 5, no. 2 -- Milton Babbitt, Semi-simple variations, theme -- Igor Stravinsky, Three pieces for string quartet, no. 2 -- Some additional properties and relationships. Common tones under transposition (Tn). Interval-class content -- Some special set classes (major scale and whole-tone scale) -- Transpositional symmetry. Interval-class vector -- Some special set classes -- The pitch-class clockface -- Degrees of transpositional symmetry -- Common tones under inversion (In). Calculating common tones under inversion -- Common tones as a source of musical continuity -- Inversional symmetry. Intervallic palindrome (mirror image) -- Pitch symmetry and pitch-class symmetry -- Degrees of inversional symmetry -- Symmetry and set class -- Z-relation. Z-correspondents -- The two "all-interval" tetrachords -- Complement relation. Interval content -- Literal and abstract complements -- List of set classes -- Hexachords -- Inclusion relation (subsets and supersets). Subsets of the same type -- Inclusion lattice -- Projecting subsets in pitch space -- Literal and abstract subsets and supersets -- Transpositional combination (TC) -- Contour relations. Contour segment (CSEG) -- CSEG-class -- Contours of dynamics and durations -- Model analyses. Anton Webern, Movements for string quartet, op. 5, no. 4 -- Alban Berg, "Schlafend trägt man mich," from Four songs, op. 2, no. 2 -- Guided analyses. Igor Stravinsky, Agon, "Bransle Gay" -- Arnold Schoenberg, Six little piano pieces, op. 19, no. 2 -- George Crumb, Vox Balaenae (Voice of the whale), "Vocalise (for the beginning of time)" -- György Ligeti, Étude 1 1: En suspens -- Anton Webern, Five pieces for orchestra, op. 10, no. 4 -- Motive, voice leading, and harmony. Composing-out -- Interval cycles. Cyclic linear motion ; Cyclic harmonies ; Maximal evenness ; Combination cycles -- Voice leading. Transposition and inversion ; Fuzzy transposition and inversion (with offset) -- Set-class space. Voice-leading space for tritones ; Voice-leading space for tetrachords ; Harmonic quality -- Contextual inversion. Chain and space for (O14) ; Chain and space for B-G-A-Bb -- Triadic post-tonality. Triadic transformation ; Other progressions of triads -- Model analyses. Stravinsky, The Rite of Spring, Part 1, introduction -- Anton Webern, Little Pieces for Cello and Piano, op. 11, no. 1 -- Guided analyses. Thomas Adès, The Tempest, Act III, scene 5 -- Karlheinz Stockhausen, Klavierstück III -- Béla Bartók, String quartet no. 3, Prima parte -- Elliott Carter, Scrivo in Vento -- Witold Lutoslawski, Funeral Music, first movement -- Arnold Schoenberg, Five Piano Pieces, op. 23, no. 3 -- Alfred Schnittke, Hymnus II (for cello and double bass) -- Centricity and referential pitch collections. Tonality and centrality -- Inversional axis. Inversional symmetry in pitch space ; Inversional wedges ; Inversional symmetry in pitch-class space (axis of symmetry) ; Motion from axis to axis -- Diatonic collection -- Octatonic collection -- Whole-tone collection -- Hexatonic collection -- Collectional and centric interaction -- Model analyses. Igor Stravinsky, Petrushka, scene 1 -- Béla Bartók, Piano Sonata, first movement, first theme and second theme -- Guided analyses. Igor Stravinsky, Oedipux Rex -- Igor Stravinsky, Orpheus -- Igor Stravinsky, "In a foolish dream," from The Rake's Progress -- Béla Bartók, Mikrokosmos, no. 109, "From the island of Bali" -- Béla Bartók, Mikrokosmos, no. 101, "Diminished fifth" -- Ellen Taaffe Zwilich, String quartet no. 2, second movement -- Peter Maxwell Davies, Eight songs for a Mad King, no. 3, "The lady-in-waiting: Miss Musgrave's fancy" -- Claude Debussy, "Voiles" -- Anton Webern, Six Bagatelles, op. 9, no. 5 -- Olivier Messiaen, "Amen du Désir," from Visions de l'Amen (for two pianos) -- Joan Tower, "Vast antique cubes," from No Longer Very Clear (for piano solo) -- Basic concepts of twelve-tone music. Twelve-tone series. Set and series ; Role of the series -- Basic operations. Content and order ; Prime ordering ; Transposition ; Retrograde ; Inversion ; Retrograde-inversion ; Series class (row class) ; 12 x 12 matrix ; "Twelve-count" ; Composing with a series -- Segmental subsets. Direct presentation ; Indirect presentation -- Invariants. Invariant dyads ; Invariant trichords ; Invariant dyads between series forms -- Varieties of twelve-tone music. Webern and derivation ; Schoenberg and hexachordal combinatoriality ; Stravinsky and rotational arrays ; Crawford Seeger and multilevel rotation ; Babbitt and trichordal arrays -- Model analyses. Anton Webern, String quartet, op. 28, first movement, variation 4 -- Arnold Schoenberg, Piano Piece, op. 33a, first theme -- Guided analyses. Arnold Schoenberg, Suite for Piano, op. 25, gavotte -- Igor Stravinsky, In Memoriam Dylan Thomas, prelude ("Dirge-Canons") -- Anton Webern, Quartet, op. 22, first movement -- Luigi Dallapiccola, Goethe Lieder, no. 2, "Die Sonne kommt!" -- Luigi Dallapiccola, Quaderno Musicale di Annalibera, "Contrapuntus Secundus (canon contrario motu)" -- Igor Stravinsky, Epitaphium -- Ursula Mamlok, Panta Rhei, third movement -- Charles Wuorinen, Twelve Pieces, no. 3 -- Anton Webern, Concerto for nine instruments, op. 24, third movement -- Arnold Schoenberg, String quartet no. 4, first movement -- Igor Stravinsky, Requiem Canticles, "Exaudi" -- Ruth Crawford Seeger, Three songs, "Prayers of steel" -- Milton Babbitt, Du, song no. 1 ("Wiedersehen") -- List of set classes. |
