Investigations in Metric Coherence concerning Brahms and Stravinsky

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Investigations in Metric Coherence concerning
Brahms and Stravinsky
Anja Fleischer Interdisciplinary Research Group
for Mathematical Music Theory Technical
University Berlinsponsored by
Volkswagen-Foundation
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• Definition of Metric Coherence
• Metric weight RUBATO - Software for Musical
  Analysis and Performance
  
  
• Application of the concept for analysis
• Haydn Presto from Sonata Hoboken XVI 24
• Brahms 2. Symphony
• Stravinsky The Rite of Spring

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Model of inner metric analysis Metric weight
RUBATO
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Inner metric structure
Outer metric structure
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Symphony C Major K. 551 1. Movement
(4/4) Wolfgang A. Mozart
Excerpt from Metric weight W2,2 of the
exposition (bars1-55)
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Tanzen und Springen (3/4) Hans Leo Haßler
W2,2
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2. Symphony, 1. movement Johannes Brahms
W2,2
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Metric Coherence

• correspondence between inner and outer metric
  structure
• presuppositionoccurrence 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

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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)
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Guillaume Dufay Mass Se la face ay pale Kyrie
II, Soprano
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Metrical Ambiguities
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Haydn Presto from Sonata Hoboken XVI 24
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Excerpt from Metric weight W2,2 (3/4)
Excerpt from Metric weight W2,2 (4/4)
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Metric weight W2,2 of measures 1-40 (3/4)
Metric weight W2,2 of measures 1-40 (4/4)
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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
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Metrical Ambiguities Brahms
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Context
Segmentation
Voicing
Brahms 2. Symphony
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Segmentation
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Brahms 2. symphony, first movement, exposition
(3/4)
1-43
44-117
118-186
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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
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Brahms2. symphony, first movement, exposition
(3/4)
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Brahms2. symphony, first movement, exposition
(3/4)
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Interpretation as 4/4
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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
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Mozart K 551 exposition (4/4)
1-55 excerpt from analysis
1-55 separate analysis of the segment
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Voicing
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Brahms 2. symphony, first movement, exposition
(3/4)
44-77 wind instruments
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Brahms2. symphony, first movement, exposition
(3/4)
44-77 cello and bass
44-77 first violins
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Brahms2. 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
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Brahms2. symphony, first movement, exposition
(3/4)
44-77 first violins
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The Rite of Spring Igor Stravinsky
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Danse Sacrale
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Part B Measures 149-167 (rhythmical
accompaniment)
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C.f. Fabien Levy Fascination du signe et de la
figure remarquable en analyse musicale
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a5
b4
c4
b4
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Metric weight W2,2 of part B (measures
149-167) for rhythmical accompaniment
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Mystic Circles of the Young Girls
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W2,2 of the entire piece
W2,2 of the melody (measures 1-45)
W2,2 of the melody (measures 1-8)
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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)