The three subjects discussed in this chapter are all associated with the layered texture often encountered in Russian music, but they may also occur in a more harmonic setting. Polytonality, of the kind found in the third movement of Szymanowski’s String Quartet Op. 37, is rare in Russian music; even when the key signature suggests something of the kind, as in Prokofiev’s Sarcasms No. 3, the aural experience may be different. Although polymodality, as presented here, is related to bichords and bitonality, it is a characteristically Russian phenomenon and owes much to the aspects of folk music discussed in chapters 7, 8, and 9.

Blchords

The formation of a bichord involves two separate groupings within a larger complex. It may be achieved by associating one triad with another or with a 7th chord; by combining an arrangement of 4ths with a traditional harmony; or by a particular voicing of a chord which has been altered by chromatic inflection or by added tones which are then given harmonic status. The principle can be extended to trichords, and, in the most complex examples, further tones can be supplied to achieve a desired resonance. Bichordal voicing will color the basic harmony. If given sufficient independence of pitch, rhythm, or color, the two chords may permit simultaneous emphasis on two tonal centers, and the device can be elevated to the structural level by reflecting some long-term relationship.

The concept of the bichord is often associated with Stravinsky, his use of the device in Petrushka (1911)—where it is possibly intended to illustrate the dual personality of the puppet—being quoted as one of the earliest examples. The effect here is easily assimilated because the pitch collection is identical with that of a dominant-structured minor 9th with added diminished 5th, the kind of harmony Skriabin was using just before 1910 in Prometheus. The bichord in Petrushka is also associated with the octatonic scale and illustrates the coloristic potential of unusual harmonic voicing.¹ It contains the same intervals as the scale used by Aleksandr Krein at bar 59 of his Sonata (Example 9-23). (For a discussion of symmetry, see chapter 8; for a general review of scales, see chapter 9.)

Reference was made in chapter 6 to the trichordal and octatonic arrangement of the first bar in Lourie’s Syntheses. Bar 4 too is built around F, G-flat, and the triad of C. The piece has to be analyzed against the background of this opening complex and the structure of the bass line shown in Example 11-18. In bar 2 there is an F 7th over B-flat (Example 10-1), with a passing reference to the minor 3rd of the latter. Since there was a suggestion of dominant about the initial bass C, this chord may be regarded as tonic over subdominant, an extension of the dominant over tonic bass familiar from Skriabin’s music of around 1910.

A particularly subtle effect is the bichordal arrangement in bar 5. The pitch center of F in the preceding bars suggests that the chord on the two lower staves (with the exception of A and E) is an augmented 6th on D-flat, compressed with its semitone neighboring-tone harmony, the dominant 7th on C. At this slow tempo the listener can clearly hear the relationship. The D-flat chord is distinguished by register and is heard by itself at the end of the bar. The half-note chord is also heard alone for a moment on the second quarter note: one hears both the combined effect and then the alternation.

The chord of bar 6 has a rather Wagnerian sound, like a dominant-structured chord on A with added tones. Lourie’s notation suggests that it is also possible to think of it in terms of A and E-flat. An interesting case of the careful voicing of a harmonic complex is found in bar 7. The harmony may be analyzed as an augmented 6th on B-flat and a triad on C (the sixteenth-note A-flat is heard in relation to F in the following bar). The B-flat and C chords are distinguished by dynamics and texture, and the two notes are symmetrical around F—a procedure already seen in Skriabin, Tcherepnin, and Roslavets. The B and C-sharp in the extreme registers are chromatic neighbors of C (a feature especially characteristic of Lourié) and are part of an emphasis on this pitch which runs throughout the piece. The C chord element is carried over into the next bar, where the whole complex eventually resolves to F and A.

The bichords in Syntheses are mainly coloristic, but the device may also be given some structural importance. Attention was drawn in chapter 8 to the double focus on B and D-sharp in bars 3 and 20 of Skriabin’s Albumleaf Op. 58 (Example 2-5) and to the bichordal arrangement of bars 1 and 17 in Roslavets’s Poem No. 1 (1920) (Example 8-28), the relationship between the two chords being a major 6th (E-flat/C) in the first bar.

Dance Op. 1 by Boris Aleksandrov shows that the two parts of such bichords may be given varying degrees of independence. In bar 12 the notes are grouped into a minor 7th on C in the left hand and a triad on D in the right (Example 1116). This, however, merely gives a certain coloring to what is heard as a major 9th on C, with added 6th and flattened 5th. In bars 24 and 25 the upper and lower chords are distinguished by metrical placing as well as by pitch, and this, together with the repetition of the chords, allows the possibility of hearing two harmonic strands. The harmony at bar 26 is similar to that in bar 12, but the effect is quite different. This is partly because after the F-sharp chord at the end of bar 25 one expects a B to follow. What is heard is a splitting of this B into its neighboring chords C and B-flat. The delayed sounding of the left hand also gives greater prominence to the C, with the result that the A-flat sounds more like G-sharp than a 7th to B-flat. This tonal disruption gives rise to further major 2nd clashes before the music returns to G a few bars later.

The first of Shillinger’s Five Pieces Op. 12 has a bichord in bar 6 (Example 10-2). Unlike the harmonies in the above examples, the two elements of this chord have a semitone relationship and, viewed as a single harmonic complex, involve a greater number of added tones.² The left-hand G-sharp triad leads, by 5th progression, to D-flat in the following bar. The right-hand chord is introduced first as a group of added tones, which throughout bar 6 increasingly assert their independent status as a minor 7th chord. This implies a root G and leads, by parallel 5th progression, to a C triad in bar 7. The harmony in bar 7 may be regarded as a bichord (minor 7th on D-flat and triad on C) or as a particular voicing of a minor 7th on D-flat with augmented 4th. This is then transposed through a minor 3rd sequence as far as bar 14. Unlike the example from Aleksandrov, where the bichordal passage marked the preparation for a return to the opening material, the bichord clash here introduces and sets the style of the middle section.

In Roslavets’s Poem of 1916, from bar 23, there is a series of bichords (Example 10-3). The sixteenth notes (G-double sharp, A-sharp, and D-sharp) in bars 23-25 begin to exert themselves as neighboring tones against the diminished 7th harmony on the first beat of each bar. The implied E-flat chord assumes harmonic independence in the middle of bar 25, when the bass moves down to D-flat. The E-flat chord develops into a dominant minor 9th and suggests a striving toward A-flat. The D-flat triad in the bass, however, continues to sound more like a tonic than a subdominant, and the bass C-flats of bar 26 sound like B-naturals completing a focus on C. There is another bichord at the end of bar 25, when the top staves move to the chord of G. The potential exists for the pitch center to move toward A-flat, C, or F. The tension between D-flat and G is taken up again in the bass in bars 28 and 30 and is resolved at the end on C (see further discussion of this passage in chapter 6).

It has been demonstrated in Lourié’s case that it is possible for a single harmonic complex to comprise a trichord. No one used this device more than Nikolai Obukhov. At the beginning of his song Berceuse of a Blessed there is an example of what the composer calls “total harmony” (Example 10-4a).³ These twelve-tone vertical complexes, despite their intricacy and invariant density, are by no means devoid of tonal associations and are in some cases open to explanation as trichords with added tones. In the first five bars of this piece there is a move toward E-flat in the lower staff. In bar 1, reading up, are the tones of the triad of F-sharp and above that its associated dominant 7th on C-sharp. In bar 2 the relationship is reversed: the dominant 9th on B is below, and the associated tonic with its minor 3rd comes above; in this case the third of the dominant is the highest note of all. Thus in bar 1, C (in the bass) is opposed by its tritone F-sharp, and in bar 2 the emerging E-flat tonality is opposed by E. In bar 3 the whole notes carry no separate tonal implications, and some of the notes relate to the bass B-flat as part of a dominant harmony, thus increasing the tonal leading. At the top of bar 1 are three added tones arranged in 4ths. In the following bars such nonharmonic tones penetrate progressively into the lower texture and create an aura of sound, which in this case has a pictorial purpose in representing the heavenly voice and radiance of the Holy Spirit.

Bars 45-47 are related in technique to the beginning and accompany the corresponding portion of the second verse with the Holy Spirit speaking (Example 10-4b). There are 4ths in the middle texture in bar 45 with a tritone juxtaposition of the A chord above and the D-sharp below. Bar 46 has a dominant with its associated tonic below and 4ths again in between. The logic of the passage lies in its linear aspect, over the chromatically descending bass.

From the cases examined so far it is clear that bichords in Russian music are not necessarily related according to their position in the cycle of 5ths, which is the view sometimes expressed when writing about Western music.⁴ Bichords may also be a function of neighboring-tone technique, in which case they are related according to the number of chromatic alterations or neighboring-tone additions that have to be made to the basic complex. The closest relationships are the tritone and the whole tone. The “Petrushka” chord is an example of the first and involves only the addition of a flattened 5th to a dominant-structured minor 9th. The second is illustrated by the chord in bar 12 of Boris Aleksandrov’s Dance Op. 1 (Example 11-16), where a flattened 5th and an added 6th have been introduced into a dominant-structured major 9th. Both these chords would have been very familiar to listeners acquainted with the music of Skriabin. The semitone relationship is a little more remote because it requires the 11th of the basic chord as well as the addition of the augmented 5th, a less-familiar combination. “Heroic Poem” by Shillinger (Example 10-2), bar 6, shows a more remote relationship involving the formation of a subsidiary 7th chord, which required the addition of three chromatic neighboring tones to the basic G-sharp harmony.

The correct recognition and classification of bichords depends on the immediate context. As was demonstrated in chapter 4, tonality may be based either on the cycle of 5ths or on neighboring-tone functions; and even in a context which is predominantly dependent on neighboring-tone technique, traditional dominant functions may also exist locally. In Lourié’s Syntheses No. 1 (Example 10-1) the chord in bar 2 may be described as tonic + subdominant because there is a pitch center of F and the relationship of F to B-flat is clear in the layout. In bar 5 the two elements of the bichord form a remote association, not only in terms of the cycle of 5ths but also in terms of neighboring-tone technique because they do not easily relate to a single root.⁵ In this connection it is important to draw a distinction between the relationships governing neighboring-tone simultaneities and neighboring-tone progressions (as discussed in chapter 4). As a progression the two chords of bar 5 would be closely related. Prokofiev’s Op. 22 No. 5 (Example 105) is a hybrid form. Although the passage from bar 12 on may be regarded as bichordal and bitonal, the harsher clashes are avoided; and it may also be argued that the F-sharp triad is merely decorating the right-hand progression.

Bltonallty and Polymodality

Sustained over a longer span, such bichords may create a measure of bitonality, provided the term is understood in the more general sense of “tonal” proposed in chapter 7. Bitonality may mean the prolonged and simultaneous emphasis on two pitches involving the use of bichords. It can also indicate an alternation of pitch centers rapid enough to prevent either from becoming fully established. The two forms are exemplified in Prokofiev’s Op. 22 No. 5, where tritones are first exchanged melodically at bars 2-3 and 4-5, and then, from bar 12, primary triads in C major in the right hand are juxtaposed with the F-sharp triad in the left (Example 10-5).

Compared with Western experiments in bitonality, there is a large area of pitch experiment in Russian music which may more aptly be described as poly-modal.⁶ It consists most frequently of a dual or triple pitch emphasis within a single flexible scale and owes its origin to the variable modes of folk music discussed in chapter 7. It is a logical extension of the modal variability of nineteenth-century Russian Classical music. In the twentieth century Russian composers found new ways of reducing and controlling tonal functions and were therefore better able to maintain a nice balance of emphasis between two or more pitches over an extended period of time.⁷ With their naturally linear way of writing and polyphonic techniques they were able to develop new forms of polymodality in addition to that based on the minor 3rd.

In considering the folk-music background of polymodal structures in the Modernist period, it is instructive to examine some of the folk-song settings of Saminsky and the effect that the form of the song has on his choice of harmony.⁸ “Song of Solomon,” as sung by the Georgian Jews, makes use of C as a recitation note and cadences on A-flat (Example 10-6). This is reflected in the harmony, which swings between the major triad on A-flat and the chord of C minor. The simple structure of the Cossack song “Ah, This Misting Day,” from Terek in the northern Caucasus (Example 10-7) is perhaps the commonest of all folk-song forms in Russia. It is based on two modal points related by a 4th (F-sharp and B) with their respective triads. The move to the lower neighbor, E, with its slightly delayed resolution, is a common idiom; and the cadence is formed by moving from one modal point to the other. As with a great many songs of this construction, a suggestion of 5/3 and 6/4 formations on the lower modal point (F-sharp), points up the D as the third most important pitch. All this is faithfully reflected in Saminsky’s setting, with its prominent use of the F-sharp, B, and D triads and the lower auxiliary E in the bass of bar 5.

The Armenian song “Deli Yaman” represents another great body of folk melody, one based on the symmetrical 0,3,7,10 chord (see also Example 8-30). Again the structure of the tune is reflected in the emphasis on the chords B-flat, D, and G in Saminsky’s setting. Saminsky adds a final cadence to bring the music back to B-flat (Example 10-8), but the actual verse of the song is modally variable at the minor 3rd (B-flat/G).

The examples considered above illustrate the fact that the common idioms of folk music considered in chapter 7—major and minor 3rd modal variability and triadically related pitches—are also reflected in harmonic settings. Russian composers will sometimes introduce a familiar folk idiom into a setting even when it is not expressly stated in the song. August Eichhom, who did some important groundwork in collecting folk music of Uzbekistan, has left a setting of the Uzbek song “The Poor One” (Example 10-9). Here he introduced an element of modal variability at the minor 3rd, which is not implicit in the song, by forming the final cadence on G. This also has the effect of incorporating a triadically based melody into an 0, 3, 7, 10 structured setting and adding a third pitch to the B-flat and D emphasized in the melody.⁹ Saminsky’s setting of “Song of Solomon,” mentioned above, makes considerable use of the F chord with similar effect—introducing three triadically related principal chords (F, A-flat, and C) and suggesting an 0,3,7,10 setting for a triadically based melody. In “On the Distant Ridge” (Example 1010), a Bashkir tune from the Ural region based on the modal points A and D, Saminsky introduces an element of modal variability at the minor 3rd by ending on B where the tune cadences on D. This procedure does not occur in the song (though the idea for it may have been taken from the melodic shape in bars 4 and 6 of the tune) but is wholly in keeping with the folk-song idiom.

It is precisely the harmonic relationships suggested by the triadically related pitches and by the modal variability at the major and minor 3rd in the above examples which form the basis of the polymodality that is the subject of the final section of this chapter. Chapter 7 contains examples of modal variability involving the minor and major 3rd and of three pitches related in the form of a triad. It is possible for pitches related in these ways to be combined simultaneously in different linear strands or to be balanced in such a manner that a piece may be said to be based on them collectively.

A simple but effective example of dual modality at the minor 3rd is Sunny Day (Example 10-11), composed by Aleksandr Tcherepnin in 1915, when he was 16. Like much of his music, it should be heard in linear terms. The right hand presents alternations between C major and A minor while the left responds with reciprocal oscillations in reverse order. The result is a nice balance between the two modes until the cadence on C in bar 8. The initial move to F in bar 10 is sufficiently striking to effect a modal shift so that up to this point there are three modes of the scale related in the form of a triad (F, A, C). Subsequently the music becomes more definitely C major and ends in that key.

Prokofiev’s Op. 22 No. 20 (Example 10-12), composed in the following year, is in some respects similar, though it is more complex; it maintains a balance between C and A till the end. Again the right hand has linear alternations between A and C, and these are the two principal pitch centers of the piece. The work begins with a hint of E and a suggestion of A-flat in bar 5, but after this the frequent Cs in the right hand sound less and less like the 3rd of A-flat, and the C/A oscillations commence in bar 8. The low Gs in bars 10 and 14 and the low E in bar 12 all have a slight dominant sound, and so does the bass G in bar 15, in conflict now with F-sharp in the treble. After an intimation of D major in the middle of bar 20, the bass notes D-flat and G, together with the treble C, suggest a possible cadence on C (see chapter 6 for a discussion of this cadential figure). However, the bass (E-A) at the beginning of bars 23 and 24 is equally indicative of an A minor conclusion. The piece ends poised between the two. The numerous chromatic inflections in this composition are largely decorative, but they also play an important part in controlling and balancing the two centers of A and C.

Tcherepnin’s Pieces Without Title No. 1 (Example 10-13) also has a bimodal emphasis on the minor 3rd throughout the first section, this time G and B-flat. The harmonic background, as demonstrated in bar 1, is a symmetrical construction centering on G, but the following right-hand melody hovers between G and B-flat. This duality is maintained as far as bar 12. The next piece in the set (Example 10-14) is based on the same two pitches but inverted to form a major 6th. Here the left hand suggests incomplete chords in B-flat while the right-hand tune centers modally on G. The initial range of a 5th and the retaining of A and F in a neighboring-tone relationship with G in the first four bars is typical of folk-song structures, and so is the rise to the 4th (C) and the following descent to D. In folk songs these and the high F would be felt to be secondary modal centers, but this is not easily heard here because of the harmonic formations below. Notes on the two staves have different functions in relation to the two pitch centers. For example, in the bass, the Fs are heard as dominants of B-flat, but in the treble as the flattened 7th of G. This lends a particular charm to the whole passage. Bars 9 and 10 should not be interpreted as chords but as parallel lines which relate to the principal centers of pitch; their sometimes symmetrical vertical relationships help to maintain a tonally neutral background. Because of this linearity and the ambiguity of the Fs, the G in the last bar carries considerably more weight than would normally be associated with an added 6th.

Prokofiev’s Op. 22 contains several examples of the major 3rd dual pitch center. In No. 10 (Example 10-15) a balance is maintained between G-flat and B-flat. The G-flats could be neighbors of F in a B-flat setting, or the G and F may be neighbors of G-flat. In bars 13-16 the melodic formations suggest B-flat while the left hand continues with the triad of G-flat. Only at the very end does the music cadence on the former. In No. 13 (Example 10-16) there is a melodic emphasis on E at the beginning, with G-sharp heard in the bass in bars 1 and 4; the same procedure occurs at the end. In the body of the piece E appears as a bass pedal while melodic formations constantly move in the direction of G-sharp, which is also emphasized by the trill (A-flat). The technique here differs from that in Tcherepnin’s Pieces Without Title No. 2, discussed above, in that it is largely modal and linear throughout with a minimum of tonal harmony.

Prokofiev’s Op. 22 No. 16 (Example 10-17) is one of the most successful examples of a balance between three modes, or centers of pitch, related in the form of a triad and maintained over an extended period. The piece begins and ends over an E pedal, but in the middle of bars 3 and 7 it cadences on A while the melody continues to rise to C and E in bars 4, 5, and 8. This threefold relationship is taken up in the following bars. From bar 9 the music is never far from C because of the dominant 7th on G in the middle texture. This, however, is juxtaposed alternately against the triad of E and a 5th on A, while A and E alternate in both treble and bass. At the end the complete texture of the three opening bars is reinterpreted over three double pedals—5ths on A, C, and E in turn. The last step has a slightly Phrygian sound, and the final bass E has a suggestion of dominant, but this fades before the end.

Having dealt with the principles of bimodal and polymodal writing in a number of small pieces, we now examine two larger works from different periods in the Modernist era: the first subject of Mosolov’s massive Sonata No. 2, composed in 1923 and 1924, when the composer was at the peak of his career; and Lourié’s Syntheses No. 4, composed toward the beginning of the Modernist period in 1914, a time of intense experimentation, when Lourié was in the lead of the avant-garde.

Mosolov called his Op. 4 “Sonata in B minor” but a glance at the beginning and ending of the first movement is enough to reveal that this is no traditional minor key (Examples 10-18 and 6-22). The main pitch centers, which are clearly expressed in the first subject, are B and D. The radical sound of the opening is due to the clashes in the right-hand ostinato and the tonal pull between the bass line and the internal chords. The structure is more linear than is at first apparent. The ostinato is based on the 5th A/D, ornamented by the simultaneous sounding of its neighbors, B-flat and E. The middle texture consists of chords in the key of D major, and a third strand is the descending bass line, which strongly suggests a tonal center of B, though it is not clearly defined as major or minor.

Certain notes play a double and others an ambiguous role. The B-flat of the ostinato, for example, leads into the D major area, through association with its dominant, A; while the A-sharp in the left hand functions as a leading tone, partly because it occurs in alternation with B and partly because of its powerful harmonic position in the bass. In contrast, the inner E-sharp has little harmonic authority and gravitates strongly toward F-sharp.

In bars 4 and 5 D-sharp saves the bass from being drawn into the D tonal area. Even the D-natural, in the bass at the end of bar 5, continues to relate strongly to B, partly because of the preceding D-sharp and partly because of its metrical placing, which emphasizes its passing character. There is the ambiguity of a passing D in the bass, which relates to B as its center, and a harmonic D in the ostinato functioning as a rival tonic. In this context the B and D of the inner chord at the end of bar 5 assume a neutral position, as do the C-sharp and E of the chord following. The modal C-natural in bar 6 serves to maintain a level of discord at this point consistent with the context. The bass F-sharps in bars 7 and 8 are heard as dominants and keep the tonality of B alive until the lower line is restored in bar 8.

When the opening is repeated, from the end of bar 8, the E-sharp is given a greater harmonic weight by separating it from the chord and allowing it to stand as an accented sixteenth note on the first beat. This, together with the C-sharp in the bass three bars earlier and the latter’s persistence through bars 12 and 13, has the effect of shifting the tonal center toward F-sharp. At the same time (from bar 9) the ostinato is simplified to allow the D and E to sound separately, a move which helps to clarify the centrality of the D. In bar 14 the emphasis on E-sharp is increased still further, as it moves to the bass, and the pitch-center conflict is now between D and F-sharp. This move from D and B toward D and F-sharp introduces the transition passage of bars 17-32, which is based on F-sharp as far as bar 24 and leads eventually to a repeat of the first subject at bar 34 (for further discussion of this movement, see chapter 12). The main pitch centers of the first subject are the triadically related B, D, and F-sharp; the second subject does not enter until bar 43, after the first subject has been repeated.

A glance through the score and music reduction of Lourié’s Syntheses No. 4 (Examples 10-19a and b) reveals a periodic emphasis in the bass on D-flat, reinforced at the beginning by its 5th, A-flat—notated here as C-sharp and G-sharp. This bass D-flat is twice interrupted by an A, once at bar 13 and again at bar 23, and also by an E at bar 7. The top beam in the reduction indicates the presence of a recurrent F, supported in bars 2 and 22 by a high A and in bar 18 by C, the whole forming the F triad. The bass C, in bars 18 and 21, also relates to F, and so this too is attached to the top beam in the music reduction.

The right-hand part of bar 1 consists of a dominant-structured chord on F, with B-flat as a passing tone, while the left hand is built around the minor triad of B-flat (with a reference to its tritone, E). The bass continuation, however, prevents this from being a simple B-flat minor arrangement because the strong D-flat of the bass is emphasized by its 5th in the next two bars. There is here a dual pitch center of B-flat/D-flat, and the notation of the bass line in sharps at the beginning is no doubt a visual means of drawing attention to this dichotomy.

The function of the tones A and E, which were mentioned above, now becomes clear. The E is the tritone of B-flat and exercises a control on that pitch, while the A has a similar role in relation to D-flat, since it subverts the 5th relationship of A-flat and its leading effect tends to favor B-flat. The vertical arrangement of 4ths, as in bars 6, 7, 8, and 11, assists in maintaining a tonally neutral background.¹⁰

The prominent F in the treble is a common ground, as it is to be found in the triads of both B-flat and D-flat and it completes a triadic formation. Together with its supporting triad, it favors B-flat because of the 5th relationship, but this is offset by the harmonically more favorable position of D-flat throughout in the bass. F is also central to the set as a whole.¹¹

After the first bar there is a chromatic descent from A to E—written in the score as a series of ascending major 7ths—which gives prominent attention to the two control pitches. Next, starting at the end of bar 3 and extending into bar 6, is a descending treble line giving prominence to D-flat and terminating with a leap to its control note, A. At the same time, in bars 4-6 a line rises to B-flat and passes through its tritone, E. In bars 7 and 8 another tritone, F/B, appears in the upper line, but this does not seem to be structurally important because there is a marked tendency to go on to B-flat. It is this 5th relationship, F to B-flat, that is noted in the reduction. In bars 6 and 8 the approach to B-flat and D-flat in the bass, from a semitone above, is a further example of the care to maintain a balance between these joint central pitches. There follows a modified repeat of bars 4-6.

The D-flat in the bass at bar 12 does seem to throw considerable emphasis on that pitch, but after a rather complex bar (12) and a change of texture, the A in the bass in bar 13 firmly stamps out the D-flat ascendancy. There are allusions to bars 1 and 6 in bars 15-21, and bar 22 is similar to bar 12 with some slight but interesting adjustments in the dynamics. The low C in the left hand of bar 18 is marked to be played loudly, perhaps because of its connection with the A-flat chord in the right hand (to strengthen the effect of the D-flat potentially moving to C). The high F-sharp of bar 22, with its implied resolution to G, is noted in the reduction.

In the coda, which begins in bar 24, Lourié has a surprise in store which throws new light on pitch associations throughout the work. By a series of 4ths in bars 24 and 25, he focuses attention on F-sharp in the bass and A-flat in the treble (see reduction). The A-flat is already familiar as a 5th to D-flat and for its tendency to weaken B-flat by eliminating its leading tone A. The F-sharp bears the same subversive relationship to B-flat as the A has had to D-flat. This passage may therefore be heard as a last determined effort to establish the ascendancy of the latter. Bar 26 reshuffles the events of the previous two bars and, by means of the low C, emphasizes the pattern of tritone with internal adjacent semitone in the bass line—a further emphasis on D-flat.

Bars 27 and 28 dwell hesitatingly on the figure from bars 6, 8, 11, and 18, as though searching unsuccessfully for a solution. Clearly the choice between A and A-flat is crucial to the outcome of the piece. The final enigmatic D under G-sharp not only contradicts the anticipated D-flat but is part of an overall tonal plan for the set (discussed in chapter 11).

The techniques used to achieve a balance between two or more pitch centers, as demonstrated in this last section of the present chapter, may be summarized as follows:

(1) Provision of a tonally neutral or tonally weakened background by the use of such devices as double 4ths, augmented triads, or other symmetrical formations (Examples 10-12, 10-13 and 10-19).

(2) The straight juxtaposition of two chords (Example 10-11).

(3) The successive statement of two cadences or implied cadences in different modes (Example 10-12, end; see also Example 5-33).

(4) The use of neighboring-tone technique to create an ambiguous situation (Example 10-15).

(5) Emphasis on a single tone in the bass in opposition to a tonic stated or implied elsewhere (Example 5-3).

(6) Combination of tonally suggestive harmony in one part with modal or scalar emphasis on another pitch in a different layer (Examples 10-14 and 10-18).

(7) Combination of voice-leading emphasis with a pedal (Examples 10-16 and 1017).

(8) Substitution of an unexpected chord in place of an anticipated one to create a new emphasis (Example 10-17, bars 10-12). The use of the mediant in place of the tonic, as on the first beat of these bars, is a fairly common procedure and also occurs in Prokofiev’s Rondo Op. 52, bars 23-24 (Example 4-36), and his Op. 22 No. 11, bars 8-9 (Example 11-14).

(9) The use of control pitches to effect a balance between two rival pitch centers (Example 10-19). Such devices can in certain circumstances bring the music to the verge of atonality. Music which does not use tonality in some measure as a basis of structure is rare in Russian works of this period, but in chapter 13 consideration will be given to some nontonal techniques. Meanwhile, chapters 11 and 12 deal with larger structural issues, including sonata forms.