/sci/ - Science & Math

Träumerei: From the score it is clear that this composition may be divided into four parts [math]P_j[/math], [math]j=1,2,3,4[/math], corresponding to the onset intervals [math]I_1 =[0,8] [/math] and [math]I_j =((j−1)·8,j·8] [/math], [math]j = 2, 3, 4[/math], respectively. Also is it obvious that these four parts are similar to each other, and that [math]P_3[/math] differs most from the other parts. In fact, [math]P_2[/math] is, by definition, an exact replicate of [math]P_1[/math] (except for the slightly different up-beat). In figures 43.5.a through 43.5.c, the weights for the four parts are plotted on top of each other, i.e., onset time is taken modulo 8. The weights are indeed almost identical to each other. Interestingly, the fact that [math]P_3[/math] differs most from the other parts shows only for the melodic weights. Also, the scatter plots do not indicate any strong relationship between the three weight functions. The sample correlations are all in the range [math][−0.01, 0.09][/math].