Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

3.3 Third Movement

Figure 36:

Metric weight of measures 1-32 of the third movement

The third movement Allegretto grazioso (Quasi Andantino) is segmented into sections of different time signatures as well. Measures 1-32, 107-125 and 190-240 are notated as $3 4$ , measures 33-106 as $2 4$ and measures 126-189 as $3 8$ . Here we discuss the first segment of each time signature (measures 1-32, 33-106 and 126-189).

Figure 37:

The beginning of the third movement

The greatest metric weights within the analysis of the first segment (measures 1-32 in $3 4$ ) in figure 36 are located on the first and third beats of the measures. The second layer is built upon the second beats of the measures, the weak beats (second, fourth and sixth eighth note) form a lower layer. Hence the metric weight reflects the hierarchy of strong and weak beats of the outer metric structure, but the first and third beats compete within the highest layer of the strong beats. The great metric weights on the third beats correspond on the one hand to the accents in the score (see figure 37) in the beginning.

Figure 38:

Metric weight of measures 1-32, $l = 76$

The reason for the prominence of the weight of the third beats on the other hand can be explored by incrementing the value of $l$ . The metric weight calculated with $l = 76$ in figure 38 enables us to differ three local meters. The longest local meter of length $k = 95$ is built upon the first beats of all measures, a second one of length $k = 77$ is built upon all eighth notes of measures 20-32, a third one of length $k = 76$