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

Figure 11:

The hemiolas of measures 78 ff.

Since the hemiolas are located at the edges of the segment of the measures 42-81 the question arises, whether they are mainly responsible for the divergence between inner and outer metric structure within this great segment. This conjecture is tested by excluding these edges of the measures 42-43 and 78-81, figure 12 shows the result of the corresponding analysis for the measures 44-77. Obviously this metric weight reveals a very different shape and is not characterized by the periodicity corresponding to time signature $4 4$ . Hence the observed periodicity within the segment of measures 44-78 in figure 9 is mainly due to the influence of the hemiolas.

The metric weight in figure 12 concerning the measures 44-59 (the first part before the caesura in the middle of the figure) does not show layers corresponding to the >strong< and >weak< beats of the time signature $3 4$ , since the second and fifth eighths gain the greatest metric weights in most cases. Hence by shifting the bar line (see figure 13), a correspondence with the time signature $6 8$ can be observed in the section before the caesura: first and fourth beats get the greatest weights. The metric weight in figure 13 after the caesura (measures 60-77) shows two different tendencies. In some measures one may distinguish layers corresponding to the three strong beats and three weak beats of the meter $3 4$ , whereas in other measures great metric weights on the fourth eighths prevent the occurrence of these layers. The evaluation of this segment in figure 12 results on the other hand in great metric weights on the third beats of the measures, as already observed in the part before the caesura.

Hence the metric weight of the measures 44-77 is characterized on the one hand by an ambiguity between $3 4$ and $6 8$ and on the other by a great metric weight on the third instead of the first beat.

Figure 12:

Metric weight of measures 44-77

Figure 13:

Metric weight of figure 12 with shifted bar lines

Both characteristics correspond to observations in Epstein (1987). The following quotation concerns the great metric weights on the third beats:

»As the big D major section after measure 44 develops to a climax at measure 59, the rhythmic nature of the motive is again unclear. It appears at measure 59 with great downbeat force - the resolution of a long dominant passage, further intensified by a crescendo. However, its attack is on the third beat of