Investigations in Metric
Coherence concerning Brahms
and Stravinsky
Anja Fleischer
Interdisciplinary Research Group for
Mathematical Music Theory
Technical University Berlin
sponsored by Volkswagen-Foundation
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Definition of Metric Coherence
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Metric weight: RUBATO® - Software for Musical Analysis and
Performance
Application of the concept for analysis
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Haydn: Presto from Sonata Hoboken XVI: 24
Brahms: 2. Symphony
Stravinsky: The Rite of Spring
Model of inner metric analysis
Metric weight
RUBATO®
Inner metric structure
Outer metric structure
Symphony C Major K. 551
1. Movement (4/4)
Wolfgang A. Mozart
Excerpt from Metric weight W2,2 of the exposition
(bars1-55)
Tanzen und Springen (3/4)
Hans Leo Haßler
W2,2
2. Symphony, 1. movement
Johannes Brahms
W2,2
Metric Coherence
• correspondence between inner and outer metric
structure
• presupposition:occurrence of regularity (weight
layers corresponding to specific periods)
• a metric subscale of outer metric hierarchy
significant in the inner metric weight
• phase-coincidence, phase-displacement
B-Minor-Mass
Johann Sebastian Bach
Gloria: all vocal parts (part from analysis of the whole piece)(3/8)
Patrem omnipotentem: Soprano (part from analysis of the whole piece)
Guillaume Dufay
Mass: Se la face ay pale
Kyrie II, Soprano
Metrical Ambiguities
Haydn
Presto from Sonata Hoboken XVI: 24
Excerpt from Metric weight W2,2 (3/4)
Excerpt from Metric weight W2,2 (4/4)
Metric weight W2,2 of measures 1-40 (3/4)
Metric weight W2,2 of measures 1-40 (4/4)
Metric weight W2,2 of measures 1-40 (3/4) of the right hand
Metric weight W2,2 of measures 1-40 (4/4) of the right hand
Metric weight W2,2 of measures 1-40 (3/4) of the left hand
Metrical Ambiguities: Brahms
Context
Segmentation
Voicing
Brahms: 2. Symphony
Segmentation
Brahms: 2. symphony, first movement, exposition (3/4)
1-43
44-117
118-186
The question here is the often discussed one of whether the
opening two measures of the motive are downbeat-upbeat or vice
versa. … No answer is definitive for these two measures. D. Epstein
Brahms:2. symphony, first movement, exposition (3/4)
Brahms:2. symphony, first movement, exposition (3/4)
Interpretation as 4/4
As the big D major section after measure 44 develops to a climax at measure 59, the
rhythmic nature of the motive is again unclear. It appears at measure 59 with great
downbeat force … . However, its attack is on the third beat of the preceding measure,
robbing this attack of a congruent emphasis with the local metrical downbeat of
measure 59 itself.
David Epstein
Mozart: K 551: exposition (4/4)
1-55: excerpt from analysis
1-55: separate analysis of the
segment
Voicing
Brahms: 2. symphony, first movement, exposition (3/4)
44-77: wind instruments
Brahms:2. symphony, first movement, exposition (3/4)
44-77: cello and bass
44-77: first violins
Brahms:2. symphony, first movement, exposition (3/4)
44-77: cello and bass
This new phrase is also unclear ... Is it to be heard
as 6/8 or as 3/4 ?... The phrase is one of
the most ambiguous moments in the movement.
David Epstein
Brahms:2. symphony, first movement, exposition (3/4)
44-77: first violins
The Rite of Spring
Igor Stravinsky
Danse Sacrale
Part B: Measures 149-167 (rhythmical accompaniment)
C.f.: Fabien Levy: Fascination du signe et de la figure remarquable en analyse musicale
a5
b4
b4
c4
Metric weight W2,2 of part B (measures 149-167) for
rhythmical accompaniment
Mystic Circles of the Young Girls
W2,2 of the entire piece
W2,2 of the melody (measures 1-45)
W2,2 of the melody (measures 1-8)
For further information see dissertation:
Anja Fleischer
Analytic interpretation.
Steps towards the Exploration of a Research Field
exemplified on Metric Structures
(order the book or download pdf under
http://www.dissertation.de)