Inner metric analysis and its perceptual evaluation

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Inner metric analysis and its perceptual
evaluation
Anja FleischerInterdisciplinary Research Group
for Mathematical Music Theory Technical
University Berlinsponsored by
Volkswagen-Foundation
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Inner metric analysis
Perceptual evaluation
Music theory Empiric science

• Investigating phenomena immediately related to
  perception and which therefore can be tested with
  the help of empiric interviews

• models of structure of the score (mathematical
  model of metrics)

• Model of perception

• Syntactic/paradigmatic relations between signs
  of the score

• Neutral level (Nattiez)

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Inner metric analysis
Perceptual evaluation
Music theory Empiric science
Analytic Interpretation
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Analytic Interpretation

• Adorno, Riemann The task of the performer is to
  elucidate the structure of a piece of music to
  the audience, to communicate his understanding of
  the piece to the listener.

• use analytic information as help for decisions
  concerning the performance of the piece

• use resulting performance in listening experiments

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Analytic Interpretation
Experimental approach
RUBATO- Software for Musical Analysis and
Performance
Inner metric analysis
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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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3. Symphony op. 90 1. Movement (6/4) Johannes
Brahms
Excerpt from Metric weight W2,2 of the
exposition (bars1-35)
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Sing we and chant it (3/4) Thomas Morley
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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3. Symphony Robert Schumann
1. movement
Analyse der Exposition 3/2-Takt
David Epstein that the first six measures of
the opening, in their metric organization ...
make unclear whether the music is to be perceived
as 3/4 or as 3/2 (Beyond Orpheus)
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3. Symphony Robert Schumann
Analysis of the Exposition 3/4
Analysis of the Exposition 3/2
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3. Symphony Robert Schumann
Detail of the analysis of the Exposition 3/4
Detail of the analysis of the Exposition 3/2
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B-Minor-Mass Johann Sebastian Bach
Patrem omnipotentem Soprano (part from analysis
of the whole piece)
Crucifixus all vocal parts (3/2)
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Analytic Interpretation

• Metric weights
  Performance
• Do metric weights with a high degree of coherence
  produce performances which express the
  metric structure of the piece more clearly to the
  listener?

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score
performance
Metric coherence
analysis
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Listening experiments
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Metric weights of different degree of coherence
of the same piece
Last measures of the altus of Gratias Analysis
of the whole piece lt---gt Analysis of the part
Beginning of Credo, all vocal parts Analysis of
the whole piece for vocal parts lt---gt Analysis of
the whole piece for separate vocal parts
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Credo analyses of single vocal parts
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Credo all vocal parts
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Listening experiments

• relationship between metric coherence and the
  understanding of the corresponding interpretation
  by the listeners detected
• metric weights of higher degree of coherence led
  to a more convincing interpretation regarding the
  question in how far the metric structure was
  expressed properly

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Inner metric analysis
Perceptual evaluation
Music theory Empiric science
Analytic Interpretation

• correspondence between perceptual evaluation of
  listeners and the shape of the analytical
  performance --gt relation between model of metric
  structure of the score and the understanding of
  listeners

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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)