"Sacrificial Dance"
In stunning contrast to the separate, climactic block of the Introduction at nos. 87–89, the opening section of the "Sacrificial Dance" conforms to the first of the two rhythmic types outlined in Chapter 4. Labeled A, B, and C in Example 79, three blocks are placed in rapid juxtaposition; within each of these blocks the lines or parts repeat according to the same rhythmic periods and are hence synchronized unvaryingly in vertical coincidence; and the invention has principally to do with the reordering, expansion, or contraction of these blocks and their motivic subdivisions upon successive restatements. Earlier, in Example 36 in Chapter 3, attention
Example 79:
"Sacrificial Dance"
Example 79
(continued)
was drawn to the two motives of Block B and to the upbeat-downbeat contradictions to which subsequent repeats of these motives were subjected in relation to a background 
periodicity.
No less apparent in Example 79, however, is the adherence at the outset of the "Sacrificial Dance" to The Rite 's by now standard pitch formulae. There is, first, the punctuating dominant seventh of Block A, here (D C A F 
), which refers to Collection II, and with the disposition of this unit exposing an upper, incomplete (D C (B) A) tetrachord. Typical, too, is the superimposition of this dominant seventh over a lower pitch number 11, which yields the 0–5, 11 vertical span, here in terms of D-A, E 
. Moreover, the rapid collectional shifts characteristic of Part II are apparent in Block B, where the dominant sevenths, enclosed within 0–11 spans, imply first Collection II, then Collections III and I, and finally Collection II again with (C A F D), which thus frames the succession. Finally, in Block C the referential commitment to Collection II is restored and enhanced. With an F-G span fixed in the upper parts, Collection II's major triads at F, B, D, and A unfold underneath.
Indeed, Block C is in this respect favorably understood as a continuation of the collectional implications of Block A. Shown in Example 80, Blocks A and C are composed of four relatively static layers of material: (1) the (E G B ) triad, where G , as the enharmonic equivalent of F , may be inferred from the punctuating (D C A F ) dominant seventh; (2) the F-A figure later in Block C; (3) Collection II's descending triads, which begin with the (D C A F ) dominant seventh of the opening bar; and (4) the D-F motion in the bass. Moreover, while the 1943 revision deleted the B from the opening chord (as is shown by the bracketed measure in Example 79), its relationship to the (E G B ) triad later on in Block C is clear. B
Example 80:
"Sacrificial Dance"
ensures (E G B )'s presence in the initial chord of Block A, which serves as the source of the upper parts further along in Block C. (As noted earlier, in Example 13 in Chapter 2, B also enhances the long-range connection between the "Augurs of Spring" chord and the "Sacrificial Dance.") And while, as a triadic unit, (E G B ) refers to Collection III rather than to Collection II, E and G are nonetheless a part of Collection II. Only B is foreign to Collection II in Block C, a matter to which we shall presently be turning for further comment.
What thus emerges in Blocks A and C (Example 80) is the superimposition of the fixed (E G B ) triad over Collection II's F-A figure, its descending triads at F, B, D, and A , and finally its D-F motion in the timpani and bass. More significantly, the D-F motion in the bass echoes the principal progression in the treble parts: the progression from D of the (D C A F ) dominant seventh to F of the F-A figure, and, an octave lower, from D of the same dominant seventh to F of the (F A C) triad. The resultant "parallel octaves," as it were, are shown by the dotted lines in Example 80.
Subsequent transpositions of the opening section of the "Sacrificial Dance" are traced in Example 81. Earlier, in Example 65, the origin of the first of these transpositions at no. 167, down a half step from (D C A F ) to (D B A F), was traced to the upper C -B and C -B-G parts in the chords at nos. 157 and 166 + 2. (See the circled pitches in Examples 65 and 66.) Of special note here is the second and final version at no. 186, where the octatonic implications of Block C's descending triads are more explicitly brought into play. Transposed to Collection III, the material in the upper parts is omitted at nos. 193 and 194, with the triadic progression now harmonized with dominant sevenths rather than major triads. (Note that the familiar disposition of the dominant seventh can apply only at C, A, and F , at
Example 81:
"Sacrificial Dance"
those pitches in the C-B -A-G-F succession that are among the (C, A, F , E ) symmetrically defined partitioning elements of Collection III, the roots of this collection's four triads and dominant-seventh chords.) Finally, the three transpositions are plotted in condensed form in Example 82. Here, the motion embedded in the upper parts of Block C, F-A-B at no. 148, is mirrored (inverted) by these long-range transpositions, which in the upper parts read D-D -A. Thus, too, the transpositions implicate Collections II, I, and III, respectively.
But to return for a moment to the opening statement of Block A. Even the non-octatonic pitches in this initial stretch, the non—Collection II D , for example, derive from intercollectional relations of significance in Part II. Thus, as shown in Example 83, the two 0–11 verticals embedded in the initial "cluster" simultaneity, D-E and C-D , are traceable to the oscillating E -E and D -D verticals at no. 87 + 1. The difference is that while these two (0, 2) whole step—related verticals define a collectional shift in the Introduction, they are wedded in the "Sacrificial Dance" as part of a single simultaneity. And in each case the verticals jointly yield the "chromatic" (0 1 2 3) tetrachord (shown in Example 83), with pitch number 2 lying outside the octatonic ordering, the D lying outside Collection II in Block A.
Example 82:
"Sacrificial Dance" (transpositions)
Example 83:
"Sacrificial Dance"
Ultimately of greater consequence, however, are the two upper and lower 2s or whole steps of this (0 1 2 3) tetrachord: that is, in Block A, D-C and E -D . (See, again, the brackets in Example 83.) For instead of the two 0–11 verticals, it is these two 2s or whole steps to which the collectional shifts in subsequent passages
of the "Sacrificial Dance" make reference.[7] Thus, further along, at no. 158, shown in Example 83, the two oscillating 0–5, 11 verticals in the strings, D-A, E and C -G , D, define a shift from Collection II to Collection I. This is neatly synchronized with the octatonic implications of the (G G F F) tetrachord's two 2s or whole steps, G -F and G-F in the trumpets: for Collection II, G -(G)-F is superimposed over D-A, E , while for Collection I, G-(F )-F is superimposed over C -G , D. By such means seemingly non-octatonic, "chromatic" elements in these passages derive from intercollectional shifts, and the octatonicism that may here be inferred acquires its special intricacy.