Harmonic Models (2)
CS 275B/Music 254
Harmonic Models: Overview
Geometric models
18th-century Germany Henichen Euler 19th-century Germany Riemann Krumhansl (1990) Purwins (2000-2006) Chew (2000-2006) Acoustic models Metric and spectral models Harmony foundation as basis for composition
2 2013 Eleanor Selfridge-Field CS 275B/Music 254
Geometric Models
Geometric models
Heinichens Circle of Fifths (1728)
18th-century Germany Henichen Euler 19th-century Germany Riemann Krumhansl (1990) Purwins (2000-2006) Chew (2000-2006)
Chews spiral array (2000)
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Acoustical properties of the Circle of Fifths
Modern arrangement of Circle of Fifths 4
Ozgur Izmirli (CT), Computing in Musicology 15 (2008): differential utilization of key regions in WTC fugues
2013 Eleanor Selfridge-Field CS 275B/Music 254
Toroidal model of tonality
Weber (18th cent) key chart
Hendrik Purwins, Technische Univ., Berlin, (c. 2000)
Derived from transformation of 18th-century German grids to three-dimensional mappings
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Krumhansl:
Cognitive Foundations of Musical Pitch (1990)
Probe-tone experiment results: How well to subjects judge how well a single tone Relates to a musical passage? Intercultural studies show that judgments vary by mode (major/minor).
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Well Tempered Clavier (Purwins)
Key frequency in Gould performances of Bachs WTC
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Spectral Weights (in association with metric weights)
Schumann Waltz Op. 124, N. 15, mm. 1-4
Work of Anja Volk (Utrecht Univ.)
inner metric structure [outer metric structure = meter]
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Volks Inner metric structure
Periodicity of different metric types
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Inner vs outer metric sturcture
10
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Spectral weights
start
period
length
Work of Anja Volk (Utrecht Univ.)
inner metric structure [outer metric structure = meter] Spectral weights (additive from inner metric weight grid)
11
2013 Eleanor Selfridge-Field
CS 275B/Music 254
12
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Inner metric structure (summary)
Prozess -Ausgangspunkt ist midi-Reprsentation d.Stckes, am Ende erhlt man fr jede Note ein metrisches Gewicht, dass die metr. Bedeutung dieses Tones kodieren soll -metr. Analyse bercksichtigt nun lediglich die Einsatzzeiten der Tne, vergit Tonhhe und Dauern -sucht nach Regularitten in den EZ, indem nach wiederholenden Einsatzzeitenabstnden gesucht wird -d.h. ermittelt werden die sog. Lokalen Metren, dies sind Raster oder Kmme von Tnen im gleichen Einsatzzeitenabstand -metr. Gewicht einer EZ berechnet sich als gewichtete Summe aus allen lokalen Metren, an denen sie beteiligt ist (man mit die Regularitten) -hchstes metr. Gewicht auf G entspricht nicht unserer Erwartung; -Frage: was kann man denn erwarten von diesem Ansatz?
Authors summary of process
13
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Partimenti: Harmonic foundation as basis of composition
18th Neapolitan practice of composition Sanguinetti (2012): The Part of Partimento Robert Gjerdingen (2010):
http://facultyweb.at.northwestern.edu/music/gjerdingen/partimenti/collections/Durante/diminuiti/index.htm
14
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Gjerdingen: Partimenti website
Northwestern University
15
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Sanguinetti: Partimento book
The Rule of the Octave Suspensions Elaborations of the Rule of the Octave Relationships to compositional genres How to create your own partimenti
The Art of Partimento (OUP, 2012)
16
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Sanguinetti, 2
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
17
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Sanguinetti, 3
The Rule of the Octave How to harmonize an octave
Ascending/descending Major/minor
Suspensions
In the soprano: by the 4th, by the 7th, by the 9th In the bass: by the 2nd Elaborations of the Rule of the Octave
Relationships to compositional genres How to create your own partimenti
18
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Sanguinetti, 4
The Rule of the Octave
How to harmonize an octave
Ascending/descending Major/minor
Suspensions
In the soprano: by the 4th, by the 7th, by the 9th In the bass: by the 2nd Interpolations in the bass line Variations, diminutions in any part Motives, subjects et al.
Elaborations of the Rule of the Octave
Relationships to compositional genres How to create your own partimenti
19 2013 Eleanor Selfridge-Field CS 275B/Music 254
Examples: Ascending, descending scales
Octave, ascending, 3 positions
Ascending, minor, 1st position
Descending, major, 1st position
Positions:
Treble starting on the first, 3rd, 5th
20
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Examples: Suspensions
Fourth suspensions
Ninth suspensions
Fourth suspensions Fourth suspensions
Seventh suspensions
As in exachordal theory, a mutated bass thrusts the harmonic action into a new key. Mutated bass Major, minor fourths
4th, 7th, 9th suspensions pertain to treble
21
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Examples: Rhythmic variation
Limping suspensions
Rhythmic enrichment
22
2013 Eleanor Selfridge-Field
CS 275B/Music 254
Examples: Patterned basses
Sequential bass
Patterns based elaboration
Rising by 3rds, falling by step
Falling by 4ths, rising by step
23
2013 Eleanor Selfridge-Field
CS 275B/Music 254
