1. Harmonic Models (2) CS 275B/Music 254

2. 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

3. 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)

4. CS 275B/Music 2542015 Eleanor Selfridge-Field Acoustical properties of the Circle of Fifths Ozgur Izmirli (CT), c. 2006 4

5. 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

6. CS 275B/Music 2542015 Eleanor Selfridge-Field Krumhansl: Cognitive Foundations of Musical Pitch (1990) 6

7. CS 275B/Music 2542015 Eleanor Selfridge-Field Well Tempered Clavier (Purwins) 7

8. 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

9. 9 Volk’s Inner metric structure CS 275B/Music 254

10. Inner vs outer metric sturcture CS 275B/Music 2542015 Eleanor Selfridge-Field10

11. 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

12. CS 275B/Music 2542015 Eleanor Selfridge-Field12

13. 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

14. 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

15. Gjerdingen website 2015 Eleanor Selfridge-Field15CS 275B/Music 254 Northwestern University

16. 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)

17. 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

18. 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

19. 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

20. 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

21. Examples: Suspensions 2015 Eleanor Selfridge-Field21  Fourth suspensions  Seventh suspensions  Ninth suspensions Mutated bass “Major,” “minor” fourths CS 275B/Music 254

22. Examples: Rhythmic variation 2015 Eleanor Selfridge-Field22  Limping suspensions  Rhythmic enrichment CS 275B/Music 254

23. 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

24. 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