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

is built upon all eighth notes of measures 7-19. Since the continuous sequence of eighth notes (which derives from the metric interplay of the wind instruments and the cello) in measures 7-19 stops at the last eighth note of measure 19, we can observe a gap in the middle of figure 38.

Figure 39:

Metric weight of measures 1-32, $l = 63$

The next differentiation of the metric weight by decreasing the values of $l$ occurs in the metric weight for $l = 63$ (see figure 39) which clarifies the prominent role of the third beats of the measures. The first local meter of length $k = 63$ starts on the first beat of measure 1 and consists of the first and fourth eighth notes of all measures of this segment, the second local meter starts on the second eighth note of the first measure and consists of the second and fifth eighth notes of all measures. Hence the first and third beats of the measures participate in these local meters, whereas the second beats do not. Therefore the highest layer within the metric weight is built upon the first and third beats in the finest metric weight for $l = 2$ as well. The reason for the occurrence of the mentioned local meters is mainly due to the gaps in a quasi continuous motion of eighth notes deriving from the interplay of the wind instruments and the cello. One gap is located in measure 19 as already mentioned, two others are located at the last eighths of measures 4 and 6 respectively (see figure 37).

Figure 40:

Metric weight of measures 1-32 for the cello

The isolated analysis of the cello in figure 40 illustrates that the gaps within the motion of eighth notes even prevents the occurrence of layers corresponding to the outer metric structure within a large segment of this instrumental part. Within the last measures two layers can be separated, but within the highest layer no differentiation can be observed. Hence metric coherence cannot be stated. On the other hand, the melodic contour of the cello in many cases is able to mediate the structure of the time signature $3 4$ .