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Harmonic Models (2) CS 275B/Music 254
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Harmonic Models: Overview 2015 Eleanor Selfridge-Field2 Geometric models 18 th -century Germany Heinichen Euler 19 th -century Germany Riemann Krumhansl (1990) Purwins (2000-2006) Chew (2000-2006) Acoustic models Metric and spectral models Harmony as improvisation platform CS 275B/Music 254
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Geometric Models 2015 Eleanor Selfridge-Field3 Geometric models 18 th -century Germany Heinichen Euler 19 th -century Germany Riemann Krumhansl (1990) Purwins (2000-2006) Chew (2000-2006) CS 275B/Music 254 Heinichen’s Circle of Fifths (1728) Chew’s spiral array (2000)
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CS 275B/Music 2542015 Eleanor Selfridge-Field Acoustical properties of the Circle of Fifths Ozgur Izmirli (CT), c. 2006 4
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CS 275B/Music 2542015 Eleanor Selfridge-Field Toroidal model of tonality Weber (18 th cent) key chart Hendrik Purwins, Technische Univ., Berlin, (c. 2000) 5
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CS 275B/Music 2542015 Eleanor Selfridge-Field Krumhansl: Cognitive Foundations of Musical Pitch (1990) 6
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CS 275B/Music 2542015 Eleanor Selfridge-Field Well Tempered Clavier (Purwins) 7
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Work of Anja Volk (Utrecht Univ.) inner metric structure [outer metric structure = meter] Schumann Waltz Op. 124, N. 15, mm. 1-4 Spectral Weights (in association with metric weights) CS 275B/Music 2542015 Eleanor Selfridge-Field8
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9 Volk’s Inner metric structure CS 275B/Music 254
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Inner vs outer metric sturcture CS 275B/Music 2542015 Eleanor Selfridge-Field10
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Work of Anja Volk (Utrecht Univ.) inner metric structure [outer metric structure = meter] Spectral weights start period length Spectral weights CS 275B/Music 2542015 Eleanor Selfridge-Field11
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CS 275B/Music 2542015 Eleanor Selfridge-Field12
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Inner metric structure - Ausgangspunkt ist midi-Repräsentation d.Stückes, am Ende erhält man für jede Note ein metrisches Gewicht, dass die metr. Bedeutung dieses Tones kodieren soll -metr. Analyse berücksichtigt nun lediglich die Einsatzzeiten der Töne, vergißt Tonhöhe und Dauern -sucht nach Regularitäten in den EZ, indem nach wiederholenden Einsatzzeitenabständen gesucht wird -d.h. ermittelt werden die sog. Lokalen Metren, dies sind Raster oder Kämme von Tönen im gleichen Einsatzzeitenabstand -metr. Gewicht einer EZ berechnet sich als gewichtete Summe aus allen lokalen Metren, an denen sie beteiligt ist (man „mißt“ die Regularitäten) -höchstes metr. Gewicht auf G entspricht nicht unserer Erwartung; -Frage: was kann man denn erwarten von diesem Ansatz? CS 275B/Music 2542015 Eleanor Selfridge-Field13
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Partimenti: Harmony as foundation of improvisation 2015 Eleanor Selfridge-Field14 18 th Neapolitan practice of composition Sanguinetti (2012): The Part of Partimento Robert Gjerdingen (2010): http://faculty- web.at.northwestern.edu/music/gjerdingen/partimenti/collections/Durante/diminuiti/index.htm http://faculty- web.at.northwestern.edu/music/gjerdingen/partimenti/collections/Durante/diminuiti/index.htm CS 275B/Music 254
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Gjerdingen website 2015 Eleanor Selfridge-Field15CS 275B/Music 254 Northwestern University
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Sanguinetti: Overview 2015 Eleanor Selfridge-Field16 The Rule of the Octave Suspensions Elaborations of the Rule of the Octave Relationships to compositional genres How to create your own partimenti CS 275B/Music 254 The Art of Partimento (OUP, 2012)
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Sanguinetti, 2 2015 Eleanor Selfridge-Field17 The Rule of the Octave How to harmonize an octave Ascending/descending Major/minor Suspensions Elaborations of the Rule of the Octave Relationships to compositional genres How to create your own partimenti CS 275B/Music 254
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Sanguinetti, 3 2015 Eleanor Selfridge-Field18 The Rule of the Octave How to harmonize an octave Ascending/descending Major/minor Suspensions In the soprano: by the 4 th, by the 7 th, by the 9 th In the bass: by the 2nd Elaborations of the Rule of the Octave Relationships to compositional genres How to create your own partimenti CS 275B/Music 254
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Sanguinetti, 4 2015 Eleanor Selfridge-Field19 The Rule of the Octave How to harmonize an octave Ascending/descending Major/minor Suspensions In the soprano: by the 4 th, by the 7 th, by the 9 th In the bass: by the 2nd Elaborations of the Rule of the Octave Interpolations in the bass line Variations, diminutions in any part Motives, subjects et al. Relationships to compositional genres How to create your own partimenti CS 275B/Music 254
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Examples: Ascending, descending scales 2015 Eleanor Selfridge-Field20 Octave, ascending, 3 positions Ascending, minor, 1 st position Descending, minor, 1 st position CS 275B/Music 254
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Examples: Suspensions 2015 Eleanor Selfridge-Field21 Fourth suspensions Seventh suspensions Ninth suspensions Mutated bass “Major,” “minor” fourths CS 275B/Music 254
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Examples: Rhythmic variation 2015 Eleanor Selfridge-Field22 Limping suspensions Rhythmic enrichment CS 275B/Music 254
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Examples: Patterned basses 2015 Eleanor Selfridge-Field23 Sequential bass Patterns based elaboration Rising by 3rds, falling by step Falling by 4ths, rising by step CS 275B/Music 254
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2015 Eleanor Selfridge-Field Coming soon: Generative music theory Generation of harmonization from melody Kemal Ebcioglu (SUNY Buffalo, 1986-1990; IBM) rule (“expert”) systems (100 for thesis, 300 in post-thesis work) Generation of 5000 chorales David Cope (UC Santa Cruz, 1980-2005) 24
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