Tonal trends and α-motif in the first movement of Brahms’ String Quartet op. 51 nr. 1

Abstract

In this paper, we study the first movement of Brahms’ op. 51 nr. 1 in two musical dimensions. On the one hand, we investigate tonal trends and tonal extremes. On the other, we study the positions of Forte's (and Huron's) α-motif in relation to the musical form. We find that α-motives are especially prevalent in the development section. We also combine these two musical dimensions to see whether the α-motives have some relation to tonal trends. They proved to occur more prominently in remote tonal regions than in those near the main tonality.

Keywords:

• comparison structure analysis
• tonal distance
• motivic analysis
• tonal principal component

Acknowledgements

I would like to deeply thank Chantal Buteau for all her invaluable help with the content and writing of the paper, especially on the mathematical formalization of the approach. I would also like to thank Conklin for all his particularly useful comments and suggestions.

Notes

Later, Aarden and Temperley proposed improvements to the original Krumhansl-Kessler (KK) key profiles by deriving their weights straight from the music itself 24 25.

If the vertical harmony consists of six pc and the segmentation cardinality n _seg has been defined as 5, we get 6 different pc sets for that particular note onset time. The number of combinations is the binomial coefficient , where n is the number of objects from which you can choose and k is a number to be chosen.

The version of the model used in this study is found in 4.

In this study, the bar numbering of the movement follows the score in 26.

It is assumed that with our sample sizes the mean is normally distributed.

In this study, we define these sections as encompassing the following bars: Exposition 1–81, Development 82–132, Recapitulation 133–223 and Coda 224–260.

Similar hypothesis tests were performed for segmentation cardinalities from 3 to 7, which led to small p-values, except for Forte's α-motif and segmentation cardinalities 6 and 7.

With 1,000,000 random samples.