Harmonic vectors and stylistic analysis: a computer-aided analysis of the first movement of Brahms’ String Quartet Op. 51-1

Abstract

The theory of the harmonic vectors, originally developed by Nicolas Meeùs, primarily between 1988 and 1992, is a theory of harmony based on a novel type of classification of harmonic root progressions. ‘Charles’, a software to automate calculations, is used here to present a vectorial analysis of the first movement of Brahms’ first String Quartet. Resulting from the analysis, the harmonic style of Brahms is discussed and characterized, as well as the use of his harmonic language compared with other Romantic composers. A hypothesis on the connections between dissonances and the preferential movement of particular chords allows a discussion about the particular influence of modality on Brahms’ harmonic language. It is argued that Brahms’ harmonic language is perhaps closer to the French composers of his time rather than the more geographically close ones.

Keywords:

• analysis of harmonic progressions
• comparative stylistic analysis
• formalization

Acknowledgements

I am particularly grateful to Allegra Kuklowsky and Dominique Deshayes for reading the entire manuscript and correcting my many mistakes and to Christina Anagnostopoulou and Chantal Buteau for their fruitful suggestions during the proofreading of this article.

Notes

Neither Salzer, Schoenberg, or Meeùs takes into account the inversions of chords – except for the cadential second inversion.

For a global explanation and discussion see 5, especially Sections 3–9. Schoenberg proposed a grouping of three pairs of root progressions: up a fourth and down a third, down a fourth and up a third, and both second root motions.

Op. 2-1. The discussion is limited to bars 1–8.

And it remains generally constant: for instance, the rate is 50% in the exposition of the first movement of the Fifth Symphony. These results have been partly exposed in 12.

See 8, a research based upon an analysis of all recitatives in all Mozart's operas with about 10,000 harmonic vectors.

‘Brahms the progressive’ is an essay written by Schoenberg in 1933 and rewritten in 1947 23.

As can be seen in almost all of his works, for instance, in the four first bars of songs like Chanson d'amour, op. 27, no 1 or Le Plus Doux Chemin, Op. 87, no 1 12.

Tables 6 and 7, sum of all boxes including ‘to fourth ↑ ’ or ‘from fourth ↑’.

Table 7, sum of the nine lower-right corner boxes.

In 22, N. Biamonte has listed Isaac, Senfl, Palestrina, Lassus, Eccard, Praetorius, Schütz among others.