Investigations in Metric Coherence concerning Brahms and Stravinsky Anja Fleischer Interdisciplinary Research Group for Mathematical Music Theory Technical University Berlin sponsored by Volkswagen-Foundation

n Definition of Metric Coherence u Metric weight: RUBATO® - Software for Musical Analysis and Performance n Application of the concept for analysis u Haydn: Presto from Sonata Hoboken XVI: 24 u Brahms: 2. Symphony u Stravinsky: The Rite of Spring

Model of inner metric analysis Metric weight RUBATO ®

Inner metric structure Outer metric structure

Symphony C Major K Movement (4/4) Wolfgang A. Mozart Excerpt from Metric weight W 2,2 of the exposition (bars1-55)

Tanzen und Springen (3/4) Hans Leo Haßler 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

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 W 2,2 (3/4) Excerpt from Metric weight W 2,2 (4/4)

Metric weight W 2,2 of measures 1-40 (3/4) Metric weight W 2,2 of measures 1-40 (4/4)

Metric weight W 2,2 of measures 1-40 (3/4) of the right hand Metric weight W 2,2 of measures 1-40 (4/4) of the right hand Metric weight W 2,2 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)

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)

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 (rhythmical accompaniment)

C.f.: Fabien Levy: Fascination du signe et de la figure remarquable en analyse musicale

a5 b4c4 b4

Metric weight W 2,2 of part B (measures ) for rhythmical accompaniment

Mystic Circles of the Young Girls

W 2,2 of the entire piece W 2,2 of the melody (measures 1-45) W 2,2 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