Inner metric analysis and its perceptual evaluation Anja Fleischer Interdisciplinary Research Group for Mathematical Music Theory Technical University Berlin sponsored by Volkswagen-Foundation

Music theory Empiric science models of structure of the score (mathematical model of metrics) Investigating phenomena immediately related to perception and which therefore can be tested with the help of empiric interviews Inner metric analysisPerceptual evaluation Model of perception Syntactic/paradigmatic relations between signs of the score Neutral level (Nattiez)

Music theory Empiric science Inner metric analysisPerceptual evaluation Analytic Interpretation

use analytic information as help for decisions concerning the performance of the piece use resulting performance in listening experiments 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.

Analytic Interpretation Inner metric analysis RUBATO- Software for Musical Analysis and Performance Experimental approach:

Model of inner metric analysis Metric weight RUBATO ®

Inner metric structure Outer metric structure

3. Symphony op Movement (6/4) Johannes Brahms Excerpt from Metric weight W 2,2 of the exposition (bars1-35)

Sing we and chant it (3/4) Thomas Morley W 2,2

2. Symphony, 1. movement Johannes Brahms W 2,2

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

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)

3. Symphony Robert Schumann Analysis of the Exposition: 3/4 Analysis of the Exposition: 3/2

3. Symphony Robert Schumann Detail of the analysis of the Exposition: 3/4 Detail of the analysis of the Exposition: 3/2

B-Minor-Mass Johann Sebastian Bach Patrem omnipotentem: Soprano (part from analysis of the whole piece) Crucifixus: all vocal parts (3/2)

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

score performance analysis Metric coherence

Listening experiments

Metric weights of different degree of coherence of the same piece Last measures of the altus of Gratias: Analysis of the whole piece Analysis of the part Beginning of Credo, all vocal parts: Analysis of the whole piece for vocal parts Analysis of the whole piece for separate vocal parts

Credo: analyses of single vocal parts

Credo: all vocal parts

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

correspondence between perceptual evaluation of listeners and the shape of the analytical performance --> relation between model of metric structure of the score and the understanding of listeners Music theory Empiric science Inner metric analysisPerceptual evaluation Analytic Interpretation

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