…Scriabin op.67 by Mario Mazzoli, second part…

Ex.13

            The passage of measures seventeen to twenty bears the same inner relationships of that of measures thirteen to sixteen, as it is a literal transposition. The following observations however, strengthen the previous points: the (02468) interpretation of the measure 19 chord is strongly isographic with B in measure one, therefore confirming the hypothesis of  “chordal mixture” described above. The melodic elements of measures nineteen and twenty, respectively, are strongly isographic with A3 and A4, reinforcing the comparison between measure three and four and the correspondent fifteen and sixteen. Example 14 displays these relations.

Ex.14

            The retransition, which consists of musical material either literally transposed or repeated from the A section, features “Klumpenhouwerian” relations identical to those found in the first section of the Prelude. Measure twenty-one is strongly isographic with measure one and the motion from B21 to C 21 is consequently that of a <T3>. A21 (0134) moves to A22 (0358) via <T0>, and the two networks are strongly isographic with A1. To this extent, the transition from measure twenty-one to twenty-two represents an equivalent motion to that which would bring measure one directly into measure four. The same observations are worth for measure twenty-three and twenty-four, excepting that they are in <T6> relation with twenty-one and twenty-two (m.24 is identical to m.4). Measure twentyfive and twentysix can be considered equivalent to measure four, due to the strong isography of their melodic elements, which allows the melodic tetrachord to interchange between (0147) and (0358). Example 15 presents the most significant networks of the retransition.

Ex.15

              As already emphasized, the recapitulation mirrors exactly the A section, excepting for the A3 present in measure thirty instead of A4: Scriabin’s aesthetic choice relies on the above described strong isography of the two components.

            The Coda summarizes the piece by restating the "cadential" measures of the A and A’ sections (m.6 and 12), prolonging C3 instead of substituting it with C12. Measure thirty-five finally concludes the piece affirming the predominance of (013679) in Scriabin’s late music. This super-set of the set-class of C is  actually (with the addition of a note that completes the chain of tritones) strongly isographic with C3, the most frequently employed verticality of the entire Prelude. Example 16 presents the k-net of measure thirty-five.

Ex.16

            At last, we observe how the two four measures phrases in the B section, despite being initially problematic, derive chordal significance from the collections of the first measure and reiterate, in a complex fashion, the structure of the first four measures of the piece. We also observe that the vertical deployment of  T6 is balanced by the composer’s  horizontal interest in T3, which not only constitutes the basic operation within the melodic elements, but also significantly  illustrates the “hyper” motion between verticalities in the three most different sections of the piece, albeit A, B and retransition. Finally, we may notice how some “hyper networks”[1] built with those verticalities in view of they <T3>’s, seem particularly supportive of this idea: B moves to C via <T3>, and so does B14 to C14; noticing that B and B14 are in <I7>[2] relation and C and C14 are in <I1> relation, we can employ these four elements to build a network of networks that is strongly isographic with the k-net of melodic element A. A similar result occurs when comparing B14 and C14 to B23 and C23. However in this case the “hyper network” will be strongly isographic with A3, implying a <<T6>> motion from the previous hyper network. These last conclusions are presented in example 17.

Ex.17

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