During the Modernist period many composers tried to move away from tonality as the controlling structural principle and sought other means of giving their music unity, continuity, and direction. Russian composers showed little interest in serialism, which is more a compositional convenience than a way of building an audible musical structure. Chapters 8 and 9 treated their use of symmetry and the harmonic coloring of new scale patterns as a basis of form. Apart from these new resources composers looked for new applications for old techniques. With few exceptions, which will be dealt with in chapter 13, Russian Modernists did not seek to abandon tonality altogether but to share the burden for structural responsibility between a number of different parameters. This chapter examines some of these experiments; and it concludes with an analysis of two sets of pieces by Lourié in which many of the aspects of style dealt with in earlier chapters are drawn together and demonstrated against the background of a largerscale design.

In one form of construction all the material is derived from the opening bars, as in Skriabin’s Prelude Op. 74 No. 2, analyzed in Examples 11-la and b. Like all the Op. 74 Preludes, this piece is highly concentrated, and every detail can be related to the opening two-bar modal melody.¹ A larger-scale demonstration of the same technique is found in Sonata No. 1 by Mosolov and Sonata Op. 12 by Shostakovich, two compositions in which the opening motifs are subjected to a process of continuous variation; and in Skriabin’s Sonata No. 10 (to be discussed in chapter 12). Examples 11-2 and 11-3 show the motifs on which the Mosolov and Shostakovich works are based.

Another constructional principle, that of building a piece from a number of fixed intervals, is illustrated by Skriabin’s Prelude Op. 74 No. 4. Although a slight difference of texture may be detected in the middle, the whole piece is closely integrated, with a central link leading to a modified repeat of the opening. The Prelude is based on the major and minor 3rd, and its form may be described as the process whereby the opening A major/minor triad (with the minor 3rd on top) is transformed into the final chord, where C-sharp is in the upper voice.

The Prelude begins with a three-bar phrase, A (Example 11-4), which incorporates a segment, Ax; it is repeated after a link, C. Phrase B (bars 7-11) is the same as the end of A and the following link, but transposed up a major 3rd. B is also repeated and then broken down so that it becomes identical with C in bars

10-13. As a result of further compression the treble of C (marked F in bars 3-4) is reduced to a series of two-beat figures which are transposed through a sequence of major 3rds in bars 12-16. The left-hand descending figure (bars 12-14) is also transposed down a major 3rd, but, as it is six beats long, it forms a number of different intervals with the treble. The piece has a motif near the beginning based on a diminished 7th (marked E in the reduction). There are two essential steps in the transformation of the opening chord into the final one: the first is the use of melodic figure F, which consists of a minor 3rd leading to a major 3rd and occurs fourteen times in the treble—four times at the central climax (bars 8-13), where it is formed from the same pitch classes that appear in the final chord. The second is the modification and semitone transposition of Ax, so that figure E now ends on C-sharp (bars 21-24). A close examination of the surface features of the score reveals a great number of harmonic and melodic occurrences of the major and minor 3rd, sometimes in rapid alternation—as in the four-against-three patterns between the alto and bass in bars 4, 9, 11, and 12. If the inversions of these intervals are included they account for a major part of the substance of the piece.

In a work of no more than moderate length a high degree of unity may be achieved by using the same rhythmic and melodic patterns throughout, providing they have sufficient life and character to retain the listener’s interest. The last movement of Sonatina Op. 7 is a case in point; all its sections make use of the same material. Starting in bar 12 (Example ll-5a), there is no break in the toccatalike flow of eighth notes (and sixteenths) until bar 59, where a new figure enters quietly (Example 11-5b). At first this sounds like a new section, but eight bars later the old material returns and persists as far as bar 101. Following a big climax and a pause, another section commences, similar to the opening but incorporating a rhythm from the second section in its third bar (Example 11-5c). In bar 129, after another pause a new theme marked “tranquillo” enters (Example 11-5d). It is difficult for the listener to tell whether this pause or the previous one (bar 101) marks the beginning of the middle part of the movement. There are two more breaks (bars 139 and 141) and an abortive reference to the first bar at its original pitch (bar 142). Then the music sets off with imitative entries of the material of bar 1 transposed a minor 3rd. Finally, after fourteen bars, the opening theme again returns at the original pitch, but it does so as part of a continuous texture which has been developing during those fourteen bars. The effect is rather comic as we are kept guessing as to where we are in the unfolding of the form; this effect is consistent with the light-hearted character of the melodic and rhythmic material.

Skriabin was particularly successful in handling these seamless joints. His composition Vers la flamme may be interpreted as the artist’s seeking for the realization of an at first dimly perceived creative goal. Or, more grandiosely, as his own search for ultimate truth, which would be revealed along with cataclysmic events he expected to occur when his Mysterium was finally performed. The idea contained in the title suggests an ongoing process or continuous progression which raises a problem of musical form. Skriabin deals with this, not only by a process of continuous harmonic resolution (Example 2-28), but by a carefully designed overlap between the middle part and the repeat of the opening material. In bar 95 (Example 11-6) the bass E effects a return to the original pitch while the texture of the middle section continues unaltered. Next, in bar 97, a repeated eighth-note figure is introduced; it remains prominent throughout the remainder of the piece. The opening theme returns in bar 107, after the E pitch and new figuration are well established. Skriabin has thus been able to produce a balanced structure while maintaining a feeling of unbroken progression, which the spirit and title of the piece demand.

The same ideal of continuous progression underlies many of Skriabin’s late works. It is evident in Op. 58, where the function of the first chord is only revealed with the appearance of the final bass B. It is heard in the striving toward E in Op. 59 No. 1 and in the resolution, at bar 54, of the enigmatic sonority of bar 1 in Op. 59 No. 2 (see Example 2-27 and related discussion). The delayed tonics and subdominant openings of some of Skriabin’s early works are manifestations of the same process. A sense of arrival is also given by the long-term harmonic relationships discussed in chapter 6 and by the departure from and return to a particular harmonic resonance, as sometimes used by both Skriabin and Roslavets.

Another problem which exercised the minds of Russian composers at this time was that of building an effective climax without the conflict of strongly defined tonal areas or the use of modulation to build intensity. Again responsibility had to be shared by surface features of the music, which therefore assume greater structural importance than formerly. In Skriabin’s Sonata No. 10 the feeling of climax is achieved by the use of the trill, from its quiet introduction at the end of the first subject to its shattering effect in the central episode. Example 11-7 shows a similar instance from Sonata Op. 15 by Sabaneev, in which a tremendous climax is achieved without resort to any tonal device.

The first movement of Lopatnikov’s Sonatina, which was examined in chapter 9 for its fairly complex use of scale patterns in the exposition, achieves its climax with a simple C major triad in bar 48 (Example 11-8). In leading up to it the composer has contrived to lengthen the stride of the music. Instead of the frequent changes of scale heard in the exposition, bars 38-40 are entirely whole-tone and make use of both whole-tone scales, after which the remaining seven bars are mainly chromatic as far as the climactic chord at bar 48. The eighth-note chords at the beginnings of bars 42-48 also have the effect of lengthening the musical stride (in contrast with the almost constant flow of sixteenth notes in the earlier part of the movement). The sustained half notes in bars 38-40 (which coincide with the whole-tone passage) also contribute to the effect; so do the whole notes leading up to the important E chord in bar 46 and the more-extended chromatic lines—in place of the constant changes of direction in the exposition.

Other ways employed to achieve a climax included increasingly rapid entries of a figure, as in the middle of Prelude Op. 74 No. 4 by Skriabin (Example 114), and a polyphonic interchange of motifs, as in Roslavets’s Poem (1916), quoted in Example 11-9. The greater intensity of the central section is largely achieved by this means.

Passages of relative stability and instability play an important part in the structuring of music in the Modernist period. Works in which the tonal gravitation is weak in the stable areas demand a lack of tonal centricity in the unstable parts. It was shown in chapter 7 that this was brought about not by avoiding traditional relationships and chords but by balancing tertiary harmonies in such a way as to create a tonally neutral effect. The structure of Lourié’s Sonatina is articulated as much by the alternation of passages of stability and instability as by the underlying tonal scheme, with melodic return playing only a minimal role. It is basically binary in form, with the first part opening in B-flat and moving to D, and the second part opening in C and also moving to D at the end. The alternation of stable and unstable areas superimposes a quasi-rondo effect on this basic structure. There are two stable passages in each half, and they are all marked by the kind of ostinato texture and figuration that occurs in the opening bars (Example 11–10a). The melodic material is formed from neighboring tones of the left-hand figurations and is different at each recurrence, except at the beginning of the second half of the piece, which resembles the opening. The three unstable areas are all quite different from each other but demonstrate the kind of harmonic technique that is shown in bars 7-10, where the cross-currents are indicated in the music reduction (Example 11–10b).

Lourie’s Syntheses No. 3 (Example 11-11c) is also structured in terms of stable and unstable areas, the former based on the pitches F and D and having a generally harmonic texture, the latter marked by more-linear writing. In the first bar the staccato sixteenths are heard against the background of the sustained D and F, and this sets the pattern for the whole piece. The notes of this first bar can be arranged into various groups, as shown in Example 11-1la, each of which bears a certain harmonic relationship to the whole notes D and F, as indicated in Example 11–11b. The structure of the piece is based on the different ways in which these harmonic groups can be combined and the range of ambiguities that results.

In the music reduction (Example 11-12) no attempt has been made to show the time values or to follow exactly the original horizontal or vertical groupings. Rather the purpose is to draw the notes of each bar together into significant harmonic or melodic formations and thereby show their relationship to the overall design. In addition, various pitch groups may be drawn toward one of the five notes or combinations of Example 11-1 la by virtue of some traditional connection. Thus, for example, a dominant-structured 7th is attracted toward the note a 5th below its root. This happens at the end of bar 3 (see Example 11-11c), where the dominant 7th on the top staff is brought into association with the minor 3rd on E-flat on the middle staff, so that the two form an enlarged E-flat harmonic area, labeled 3 in Example 11-1la. In turn the whole E-flat complex is heard against the bass F as an extension of the principle established in bar 1 and mentioned in the last paragraph. Further, any irregular combination of pitches which tends toward a certain note or chord of resolution may as a result be drawn into one of these numbered combinations. An example is the beginning of bar 4, where the chord on the middle staff contains neighboring tones of the F 7th below, and so enlarges the field of influence of the root F. Occasionally a significant melodic line may lead to or suggest a certain note and thus come within the general area of that pitch. This is heard in the line leading to E-flat on the middle staff of bar 3: through E-flat it is brought into association with the bass F (there is also a strong hint of F within the line itself because of the chromatic descent and neighboring tones G-flat and E).

The relatively stable areas of this piece are bars 2-4, based on F; bars 8-10, based on D; and bars 17-18, based on D and F in combination. The less-stable areas often have some significant melodic lines to give them direction and may be more complex or harmonically vague. Bar 2 begins with the bass F supported by its 5th and 7th, coupled with harmonic area 2 (Example 11-11a) and a fragment of 5 (Example 11-12). This already suggests possible connections between the three, since the D could be an added 6th within an F chord, and the B-flat and D-flat can be interpreted as neighbors of A and C. The bar continues with a direct linear juxtaposition of 1 and 2 with 3 (Example 11-12). Here, in the music reduction, the dotted beams indicate the notes treated as nonharmonic and the solid beams those treated as harmony notes. The two hands express opposite points of view on the matter: the very short left-hand notes against the sustained right-hand line are reminiscent of bar 1 and allow the final treble F to stand alone, so that the overall effect of the bar is of the pitch F holding everything together. Bar 3 has already been mentioned: the alto descends to E-flat and the bass returns to F, the first three chords on the top staff of Example 11-11c relate ambiguously to both pitches as possible roots.

In bars 4 and 5 the harmonic area of F is enlarged to include the whole complex of five pitch areas shown in Example 11-lla: F is supported by its 5th and minor 7th in the bass; there are neighboring-tone additions to the F triad on the middle staff; and there are references to areas 2, 3, 5, and 4 in bars 4-5 (see Example 11-12). The left-hand part of bar 5 requires special comment: the halfnote chords relate to the low F of bar 4, but because they are now introduced ff, they have a strongly disruptive effect and serve as a transition to the unstable section consisting of bars 6 and 7.

These bars are more loosely constructed, and the reduction suggests that the control here is more linear, although the constant use of multiple octave transposition somewhat disguises that fact. Viewed this way the arpeggios are by no means the random configurations they appear to be; laid out as they are in the score, the individual tones are more easily heard in relation to the sustained background, against which they form various harmonic or neighboring-tone relationships (the former are marked X in Example 11-12). There are a number of chromatic and tritone formations in these bars. An allusion to group 3 may be asserted in reference to the right-hand part at the beginning of bar 7, but this is not structurally important, as in this context it does not clearly relate to either of the main pitches, F and D.

Bars 8-10 are the next stable area, this time based on D. The direct juxtaposition of D with E-flat is a reminder of the opening of bar 1. In this bar E-flat is associated with the triad on its 5th (B-flat) on the top staff, as an enlargement of area 3 (Example 11-1la), and the whole is heard in relation to the dominant-structured chord on D, ornamented here as elsewhere with its minor 3rd and major 7th. Bar 9 seems to be complex but is based mainly on areas 1 and 3, while the prominent bass F-sharp relates to D of the preceding and following bars.

Bars 10-16 form the middle section of the work, and little needs to be added to what is shown in the reduction except to point out (1) the various references to rhythmic figures drawn from bars 1 and 6 and a melodic allusion to bar 3 in bar 14; and (2) the use again (as in bars 6 and 7) of horizontal features including more marked employment of melodic lines.

In the final section F and D are brought together in the bass. The F is prominent by virtue of its pitch and placement early in the bar (the printing in bar 17 is confusing—the chord is more clearly presented in the following bar) and the D by being marked with emphasis. A further feature which helps to draw attention to the F and D is the peculiar rhythm: the initial F sounds like a downbeat but suddenly (with the 5th eighth note) the chords are brought into phase with the beat, as written, thus producing a syncopated effect when the F and D are heard in the bass for the second time. The four-bar coda brings into comparison the melodic and harmonic features of bar 3 with the rhythm of bar 14 and relates them now to the D bass, instead of the F as formerly. The move, in the bass, from D to D-flat has little to do with the immediate context, but it is part of the wider construction of the whole collection, which will be dealt with later in this chapter.

The constructional principle behind Deshevov’s Meditations Op. 3 No. 7 (Example 11-13) is related to the matter of alternating passages of stability and instability, but in this case there is a continuous alternation of tension and relaxation on a miniature scale. The overall progression of this piece is from C in bar 1 to F in bar 19, and this agrees with the fact that the C bass at the opening has a slight dominant sound. The bass Cs at the beginning represent relaxation and the C-sharps tension. The dominant effect of C is not strong enough to make it sound unstable; on the contrary it is stable in relation to the alternate C-sharp.

The whole piece is constructed on the basis of this relationship. The cadence across the bar line at bars 7-8 is emphasized by amending the rhythmic alternation of C and C-sharp in bars 6 and 7 so that the first beat of bar 8 falls unexpectedly on a point of relaxation. The contrary-motion approach in the right hand to C (which is established as the central pitch) assists the cadential effect, and the elision of the C serves to maintain forward movement. There is another cadence at bars 10-11, and again an adjustment to the alternation of C and C-sharp brings the C unexpectedly on to the first beat of the bar. The traditional relationship between the F and G on the third beat of bar 10 and the C in bar 11 contributes to the cadential effect. The overall rising contour of this phrase and the more rapid movement in the right hand give it a greater tension than in bars 1-7.

There is no interference with the alternations of C and C-sharp in the long descending phrase in bars 11-17. Consequently, the delayed arrival of the treble line at C in bar 17 coincides with the unstable C-sharp in the bass. This produces a contradictory and slightly disturbing situation, which is emphasized by repetition in the following bar.

This moment of greatest tension is released in the final eight bars. They sound like a coda for two reasons: because the pitch range is level in contrast to the contrary-motion rising or falling contours of the earlier phrases; and because the tendency of G-flat to move to F (which corresponds to the earlier relationship of C-sharp to C) is balanced by the sounding of F and B together. The cadential relationship of a tritone and a semitone between B, F, and C is thus locked into a permanent situation of stable tension which is allowed to fade out at the end.

Prokofiev’s Op. 22 No. 11 (Example 11-14) is similar in that the ostinato has continuous alternations of tension and relaxation, represented at the beginning by A-sharp and B. Prokofiev, however, is less radical than Deshevov. He does not structure his phrases by these means but uses traditional cadences.

Sets of Pieces

The two compositions of Op. 1 by Boris Aleksandrov illustrate many of the techniques discussed earlier and demonstrate some simple methods of uniting separate pieces into a coherent set. Neither has a contrasted middle section, but each consists of a single idea repeated after a central link and followed by a coda. In the first piece this link runs from bar 19 to bar 34 and in the second from bar 17 to bar 39. The principal feature in both is the composer’s use of the major/minor 2nd both decoratively and in the structure.

In the first piece tritones are important in the harmonic relationships, and six of these are marked in eighth notes on the middle staff of the music reduction (Example 11-15). F-sharp/C is particularly important: it occurs at bars 6-7, just before the music returns to G at the end of the first phrase; in bar 10, where it forms a tritone and semitone relationship with the F in bar 13; and in bars 2526 and 27, where it assists in the move to G, with which it forms the same pattern.

The play on the major/minor 2nd is introduced right at the outset, where the harmonic rhythm on A and G seems to be at variance with the meter (Example 11-16). With the change to a more-linear style in bar 3, most of the inflections can be heard as neighboring tones of the underlying G triad. The interval of a 2nd is developed structurally with the move to F in bar 13, the whole-tone ascent (D, E, F-sharp) in bars 19-24, the parallel lines of bars 24-26, and the harmonic compression in bar 28, which leads to the return of the opening G. At the end there is an ambiguity involving the major 2nd G/A in the right hand of bars 4951: either the G is an unresolved appoggiatura of F-sharp or the A is an added tone in the chord of G. The first two chords of the penultimate bar have both been heard previously with colorful effect in bars 5 and 31-33. In each case they can be heard as neighboring-tone ornamentation of the underlying chords of G or D. Chords of B-flat and C in bar 52 are also related to the whole-tone harmonic compression of bar 26.

The overall progression of the second piece, Scherzo (Example 11-17) is from F-sharp to A, but, as with the first, the detailed structure relies on neighboring tones and harmonic relationships of the major and minor 2nd. There is also a connection with the Dance in that F-sharp and A are neighbors of G, which was central to that piece. The A triad is brought into relationship with F-sharp early in the Scherzo, at bars 3-7. When the opening theme returns at bar 39 it is a semitone down, but the extension of the theme at bar 45 also moves down by only a semitone, leading to an expanded repetition of bars 9-26 at the original pitch. The whole piece is dominated by the progression F-sharp, E, A as far as bar 17 and F, E, A from bar 39 to the end.

The first phrase of the Scherzo is bounded by the chord of F-sharp appearing in bars 1 and 7, in both cases followed immediately by an augmented triad. Within this framework the triad of A minor is decorated by other triads bearing a major or minor 2nd relationship to it. The second phrase is limited to six bars bounded by the chord of E, with the related augmented triad this time appearing during the course of the phrase (in bar 13), and this, together with other triads, provides neighboring-tone decoration of the chord of G. The second phrase is thus a varied version of the first. In bars 15 and 16 there is a minor 2nd clash between the inverted pedal and the chord of B-flat below, and in bars 18-23 a series of 7th chords (decorated by various neighboring tones) whose roots descend in minor 3rds to reach D-sharp in bar 24.

A number of similarities unite the two pieces (Example 11-15): at bar 32 of the Scherzo the harmony and the bass progression to F-sharp are similar to bar 26 of the Dance, and both occur in a prominent position in the buildup toward the return of the opening themes. The compression of two 5ths, separated by a semitone, in bar 83 of the Scherzo is related to the compression in bar 28 of the Dance, though it occurs at a later stage in the piece. The third similarity is the insertion of the chords of F-sharp and C in the cadential progression in bars 8487: it is similar to the insertions in bar 52 of the Dance and also relates to the earlier piece in that the tritone F-sharp/C was important there.

In Syntheses No. 1 by Lourié the opening and closing bass C has a slight dominant sound. The low bass (Example 11-18) hardly gets away from that pitch and its chromatic neighbors. Syntheses No. 2 (Examples 5-32a and b) begins with the bass progression F-C, and the first bar sounds like a series of neighboring-tone gravitations toward the chord of F. The chord of bar 2 is a dressed-up dominant minor 9th (without its minor 7th), at least until the bass moves down to B (or B-flat in bar 4). These bars are twice restated before the three-bar coda, so that this piece too has a framework of F tonality.

It has already been shown that F and D are the two main pitches of Syntheses No. 3 and that in No. 4 F forms a common ground between the pitch centers of B-flat and D-flat. F is frequently heard in the very highest notes of the harmony (Examples 10-19a and b). It was also demonstrated that in No. 5 the low bass alternates between the two chromatic neighbors of F (Example 6-12), though F itself is not stated in the bass (this is also the case in No. 1).

The tendency toward a common center of pitch is tenuous and perhaps to many people scarcely noticeable in performance. Lourie has supplemented it by several other means of uniting the set into a coherent whole. As has been pointed out, the final note or notes in the bass of each piece appear, in some cases, to have no relationship to the internal structure. No. 2 ends with B-flat/B, No. 3 with D-flat, No. 4 with D, and No. 5 with E-flat. This pitch collection (including the final C of No. 1) is reflected in the ascending chromatic series in the bass, rising from B-flat to E-flat, which opens No. 5 (Example 6-12). In every piece there are frequent occurrences of short chromatic lines of three to six notes, usually (but not always) descending. Given sufficient familiarity with Lourie’s experimental construction, these can be related audibly to the ascending line mentioned here.

Another unifying figure is the [0,1,4] set. This little motif is present everywhere. It is interesting to compare it with Skriabin’s Prelude Op. 74 No. 4. The figure crops up frequently in Russian music, perhaps not surprisingly, as it is a basic unit of the octatonic scale, for which Russians show a special fondness.²

This motif brings us to another feature of these pieces—the unity of harmony and melody. In chapter 10 it was noted that Lourié’s Syntheses No. 1 contains bichords based on the tritone or the semitone. These relationships occur frequently in both melodic and harmonic progressions. The semitone is particularly evident in the constant use of unresolved neighboring tones. The same is true of the major/minor 3rd figure mentioned in the last paragraph; many of the chords have both major and minor 3rds. There are then a number of features both stylistic and structural uniting this collection.

One of the most problematical compositions of the Russian Modernist period is Lourifé’s Forms in the Air which is written without bar lines and uses two to five incomplete staves. The composition is divided into small cells, most of which are not difficult to distinguish, as they are marked off by breaks, pauses, and commas and differentiated by texture and by motivic and harmonic content. The “forms” to which the title refers may be either the cells or the subtle and constantly changing resonances. The construction of these “forms” and the relationships between them are very enigmatic at the beginning but become noticeably clearer as the work proceeds. Hence it will be helpful to examine the last movement first.

The first cell in the third piece (Example 11-19c) is a compression of the chords of C and D-flat with an additional F-sharp, which opposes the tonal pull of the dominant-structured 7th on C and is also a neighbor (G-flat) of the D-flat triad. The melody, marked mf, appears to go its own way but conforms to the C chord at the beginning and end of the cell and has its F in common with the chord on the upper staves.

Cells 2, 3, 11, 12, and 15 are similar, except that in 2, 11, and 15 the D-flat is supported by the A-flat triad. Cell 4 is basically an augmented 6th and implies a possible resolution to C as well as the establishment of D-flat in the bass. Cells 6 and 14 are similar to 4, but in 14 the resolution to C is completed. Of the remaining cells, 7, 8, and 9 make a neighboring-tone approach to A in the low bass (B-flat, B-flat/G, A); and 10, 14, and 16 all end on A. A clear picture emerges of D-flat, C, and A being central to the structure of the last movement.

The second piece (Example 11–19b) is not so straightforward, and one has to take careful note of Lourié’s dynamics in assessing the pitch structure. Immediately evident are the emphasis given to E-flat in cell 8 and the fact that this emphasis is carried over into the following cell, with the E-flat minor triad in the lower voice and the three last accented notes. Another emphatic progression is the neighboring-tone approach to C in cells 6 and 7: half notes on D-flat and B in the second half of cell 6, and D-flat in the bass with C at the end of cell 7.³ Cell 1 has some emphasis on the initial A but otherwise is a G chord with a chromatic neighboring-tone focus on its 5th. Cell 2 combines elements of the chords of G and C, with C coming through clearly mf as the pitch center. Cell 5 begins strongly with the 7th chord of G but seems to move gradually toward F-sharp by the third eighth note, as the right-hand chord fades. The dominant-structured chord on G emerges at the end of the movement (cell 13), but in performance it is not clearly recognized until the last note ppp. The remaining cells are more vague but B-flat seems to emerge in cell 11. It may be concluded that C, supported by G, is again important in the second movement, though with some opposition from F-sharp in cells 5 and 12. E-flat marks the central climax.

The first piece (Example 11-19a) is more complex than the third, especially in the first half. Cell 9 is the D-flat triad with neighboring tones of its major 3rd, and cell 8 is the triad of E-flat with neighboring tones of its root. Cells 6 and 7 each have a quasi-trill effect in which the tonal pull moves from D-flat to C.⁴ Cell 7 is opposed by its tritone in the bass of the cells preceding and following. Some anticipation of this play on D-flat and C may perhaps be detected in cell 4 in the minor 7th on A-flat on the middle staff, the segment of D-flat scale toward the end, and the 5th C/G. The top staff of cells 2 and 3 and the third staff down of cell 2 are based on the triad of C with a segment of C scale in the bass and again some opposition from G-flat in the 2nd staff down. Cell 1 (Example 7-18) is the most complex of all. What stands out, if the composer’s dynamics are observed, is the initial tritone A-flat/D (echoed by the quarter-note chords), the triad of E-flat in the bass line, the three-note figure C, A, D-flat beginning near the end of the middle staff, and the four-note figure at the conclusion in the treble. The cell begins and ends with A in the bass. Of all these notes only the A-flat and D are not important later; their function in this cell is to help maintain a tonally neutral setting against which the composition can develop. D-flat, C, A, and E-flat are central to the whole work. The movement ends on E, which note begins to assume importance in cell 9.

Characteristic of this work are the pauses at the ends of some cells, most frequently in the last piece, where the construction becomes clearer. These allow the listener time to become aware of the main centers of pitch. In the first movement the pauses following cells 6 and 8 allow the gravitational attraction of D-flat and E-flat respectively to be heard. In both these cells the last note to be played has a tendency to rise a semitone while, in contrast, the last D-flat in cell 9 is stable. In the second movement (Example 11–19b) there are only two pauses: at the central climax in cell 8, which draws attention to the stable 4th E-flat/B-flat; and at the end, where the final F, as part of a G chord, arouses an expectation of C to follow.

In the last piece (Example 11-19c) the pause after cell 2 follows a complex passage in which one of the main pitches (C) is heard in the bass. Another principal note, D-flat, is sounded with its triad in the upper texture and the related A-flat triad at the end in the bass (see also cells 11 and 15); and the final C/B-flat sounds inconclusive in this context. The next pause, following cell 3, reveals the C tending to rise to D-flat, as at the end of cell 6 in the first movement. At the conclusion of cell 9 the A sounds like the 3rd of an F-sharp triad, but at the end of the movement the A has become stable. An important change in the final cell, compared with cells 3 and 12, is that an F on the second staff down has been changed to A, allowing the D-flat to function as a major 3rd. This final cell now bears a close resemblance to the end of cell 1 of the first movement (following the quarternote chords, Example 7-18), thus completing the circle.

Example 11–19d shows the main pitch centers of the three pieces. A emerges clearly at the end with the other most important pitches being C and D-flat. A is contrasted with the strong central E-flat in the second movement, and C is sometimes opposed by F-sharp. Time values indicate relative emphasis: the longer the time value the greater the emphasis. D-flat, C, and A clearly predominate, with the tritone opposition of E-flat and A also important.

The pitch structure of Forms in the Air is supplemented by a number of motivic references, shown in Example 11-19e, along with the movement and cell number in which they first occur. No chart of later occurrences is given, as they are surface features and clearly evident in the score.

Of these motifs certainly the most important, because it is not limited to the surface features, is the [0,1,4] set. It is to be found everywhere as a harmonic and melodic feature and also in relationships between the main pitch centers of the work. Example 11–19f shows that these pitch centers form a segment of the octatonic scale, and a number of minor 3rds with adjacent semitone exist among them. Several cells have an affinity with the octatonic scale. The first five quarter notes of time of cell 10 in Example 11-19a contains seven notes of the octatonic scale plus E. It has been noted above that the first piece cadences on E, and it is not uncommon to find the octatonic scale associated with a pitch center external to the scale; for example, the beginning of Lourié’s Syntheses No. 1 (Example 639; see also Example 3-2c). Cell 12 of the second piece is octatonic, with the exception of the last group of notes on the top staff. In the last piece the second part of cell 3 (which recurs several times) is octatonic with the exception of the bass C. Cell 4 (with all its repeats) also consists of six notes of the octatonic scale. It appears that the harmonic coloring and motivic content of the octatonic scale is a unifying element in the work.

Various cross-references can be found between the three pieces; for example, the varied treatment of the augmented 6th formations in cell 6 of the first and cell 4 and its recurrences in the last, and the use of the augmented 6th interval (G-flat/E) in cell 8 of the first piece, which is the same as the one in cell 6 but treated in a different harmonic context.

Other cross-references concern melodic features. The opening of cell 4 in the second piece (B-flat/E) anticipates the tritone at the beginning of cell 8, and the intervals between the first three notes of cell 11 are the same as between D-flat, G, and C in the middle staff of cell 10. The last movement has a number of such features, some of which are drawn from earlier in the work. The pitch content of the middle line in cell 1 is identical with that toward the end of the last cell of the preceding movement (second staff down, commencing from the high G flat), and the figure G-flat, B, D is an inversion of what appears there. The rising figure of a minor 3rd and whole tone from the same staff of cell 1 (D, F, G) is also heard twice (transposed) in the previous cell—D-flat, E-flat, G-flat (retrograde inversion) and B, D, E—and is worked into a symmetrical pattern in cell 5 of the third piece, G, B-flat, C, E-flat. The pattern of two major 3rds and a minor 3rd at the beginning of the top staff in this cell is related to the descending line at the beginning of the bottom staff in cell 10 of the first movement.

The figure on the second staff down in cell 3 of the first movement is heard at the same pitch in cells 2, 11, and 15 in the last piece and (transposed) in the middle staff of cell 4 of the first piece and elsewhere (see also Example 11–19f). In its final form, as it appears in the last three notes of the work (Example 11-19c), it coincides with the three main centers of pitch shown at the beginning of and throughout Example 11–19d.

Cells 2-4 of the first piece are united by their similarity of shape. The descending contour of the first four 32nd notes in these cells is also taken up by the eighth notes of cell 5. Especially noticeable is the widening interval between the first two notes of each group. There are also examples of the varied treatments of specific intervals, such as the minor 2nds in cells 5-9 of the first piece.

Forms in the Air represents a further advance in techniques in the same direction as taken in Syntheses. The detailed dynamics indicated by Lourié suggest that he is again interested in the play of subtle resonances and directional tendencies of pitch. He was evidently anxious that these should be enjoyed in their own right, unhampered by strongly tonal gravitations or by the straitjacket of metrical regularity. Lourié’s instructions for accents and tenuto are just as remarkable as his dynamics. The subtlety of his music at this time could exist only in a style free of rigid formulae.