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with Schönberg concerning the phrase lengths as being the cause of the observed displacements:
»Phrases of irregular or variable length are, to be sure, a significant aspect of Brahms’s language ... But they differ fundamentally from actual metrical displacement.«3 Frisch instead regards notes’ placements as being responsible for metric displacements, as in the case of the piano quintet in F-Minor Op. 34, 1:
»Because the notated third beat is empty in bars 90-5 and the first beat is empty in bars 87-95 ... , they tend to sound like weak second and fourth beats respectively. That is, notated beats 2 and 4 are perceived as 1 and 3. The bar line has thus drifted still further to the right ... .«4 Epstein’s (1987) above mentioned quotation considers »metric displacement« as well. The following quotation suggests that Epstein might apply this term in a similar way as Schönberg and Frisch did:
»Rhythmic ambiguity also serves a broader design: by disguising and in several ways deemphasizing rhythmic downbeats, the music in its longest spans is kept continually on a quasi-upbeat footing, with few points of stability.«5 The mentioned deemphasizing of rhythmic downbeats might be achieved by placing notes on weak beats and rests on strong beats, as Frisch argued concerning the piano quintet. However, since Epstein adumbrates »several ways«, one might detect other compositional methods being responsible for ambiguities as well. In this article we want to apply the method of inner metric analysis to Brahms’ Symphonies in order to describe these several ways of producing ambiguities and compare the results to the observations made by the above mentioned music theorists.
2 Inner metric analysisThe inner metric analysis, as implemented in the RUBATO-Software for Musical Analysis and Performance, is based on the investigation of regularities within the set of notes’ onsets of a given piece of music. It has been described in detail in Mazzola (2002), Fleischer (2003), Fleischer (2002a) and Fleischer (2002b), here we want to give just a brief overview. Inner metric analysis results in a metric weight for each note and is concerned with the metric structure expressed by the actual notes of a composition without taking into consideration the information given by the time signature. The latter refers to the outer metric structure, which is characterized by a metric hierarchy of accents depending on the time signature and bar lines. Inner metric analysis is based on the regularities within the set of all onsets of the notes of a given piece. These regularities are described by means of local |