In all cases, I assume that the sequence of pitch classes ascending diagonally from left to right in the grid forms a cycle analogous to the cycle of fifths in C12.
(To take C12 as an example, a seven-tone segment of the cycle of fifths complies with this rule, but a nine-tone segment does not.)
This has profound implications for the creation of new diatonic scales, in that a diatonic scale can be seen not as a reordered segment of a "cycle of fifths" or its microtonal equivalents, but a compact struct ure in a grid space of two alternating intervals.
In particular, Wilson's concern to make clear distinctions between movements II and IV tends to obscure an important unifying process in which each movement moves from a compositional strategy based on the cycle of fifths to one centred on what Lendvai would have described as 'alpha' harmony.
In bars 1--5 the material may easily be related to a cycle of fifths concluding on D: F[sharp]--C[sharp]--G[sharp]--D[sharp]--A[sharp]--E[sharp]--B[sharp]--G--D.
1a--c bring together the relationships I have proposed to form a matrix where two inversionally related seven-note segments of the cycle of fifths are aligned at sum 10 such that they each contain F and B, which form one pair of axes for the collection, the other being D--G[sharp].(29) The closely related sum 4 alignment (it has the same axes), which turns the sum 10 version 'inside out', is given for comparison.
The cello presents two five-note, overlapping segments of the cycle of fifths (C--G--D--A--E in bars 10--16 and F--C--G--D--A in bars 17--20).
The timpani opens the work with an idea built around the cycle of fifths ending on C[sharp], a dominant preparation for the second entry of the motto theme on F[sharp], and a lengthy G in the first piano similarly prepares for the entry of the second on C.
A more satisfactory analysis of the foreground would need to explore the major third/minor third confrontation between the C major triads and the projected octatonic set and why the harmonies beneath Wilson's goal notes are not octatonic but seem instead to present segments of the cycle of fifths and generate Z tetrachords.(50) Once again two pairs of i.c.'s--5, 6 and 3, 4--have important structural roles, but with a very different effect from that at the opening.