Except for Omstein’s tone clusters and Golyshchev’s experiments with sets (discussed in chapter 13) most of the chords employed by Russian composers of the period have a basis in traditional tertiary harmony. In addition to the dominant-based chords of Skriabin and his immediate followers, Russian composers used 7ths of all kinds and higher discords including 13ths. Examples may be found in the charts accompanying Three Compositions by Roslavets (Examples 3-12 and 3-14).

Composers in general did not follow Vladimir Rebikov’s earlier lead, in his Psychological Dramas, by employing extended 4th chords.¹ Vertical arrangements of 4ths and 5ths are usually within a context of tertiary harmony and are more correctly viewed as resulting from a use of nonharmonic notes or from unusual voicing of traditional chords. The double 4ths in bars 61 and 62 of Shostakovich’s Sonata Op. 12 arise from neighboring-tone ornamentation of the C chord and are given greater prominence by syncopation in the right hand (Example 6-1). In Roslavets’s Sonata No. 1 for violin and piano, vertical arrangements of 5ths and 4ths occur in bars 49 and 50 (Example 6-2), but these are dominant-structured chords with the 11th in each case resolving to the major 3rd in a different octave. The minor 3rds of the G-sharp chords, played by the violin, resolve in the piano part. All this takes place in an expanded tonal area of F-sharp minor and in a context consisting largely of such complex dominant-based harmonies. Roslavets writes in this manner at moments of climax in the midst of phrases in order to create tension against the more-traditional voicing used elsewhere.

An arrangement of 4ths or 5ths above and below a major or minor 3rd sometimes occurs in the music of Aleksandr Tcherepnin; for example, in bars 9 and 10 of Pieces Without Title No. 2 and bars 7 and 8 of Op. 5 No. 5 (Examples 10-14 and 7-12). Usually, as here, such formations are part of a linear emphasis on certain pitches. Vertical arrangements of 4ths also arise from the duplicating or filling out of a melodic line, as in bars 68-69 of Mosolov’s Sonata No. 2 (Example 6-3). In this case the device is merely decorative and lies within the area of the underlying chord.

Occasionally the double perfect 4th, used as a harmonic device in its own right, is to be heard in the music of Lourié, for instance, in bars 6-8 of his Syntheses No. 4 (Example 10-19a). A composer who made it a consistent element of his style was Nikolai Lopatnikov (1903-1976). Fourths begin at bar 41 of the first movement of his Sonatina and occur from bar 105 in the last movement (Examples 11-8 and 11-5c). They are used to create areas of instability in contrast to the more tonally oriented main sections. Double 4ths occur freely throughout the work and show varying degrees of dependence on triadic substructures. Bars 6 and 8 of the slow movement are typical (Example 6-4).²

Pattern making, whereby an unorthodox passage is justified by some underlying regularity of texture, is sometimes employed as a method of producing novel combinations of sound. This device seems to have developed from the late works of Rimsky-Korsakov.³ An example, very much in the manner of Rimsky-Korsakov, occurs in bars 39 and 40 of Feinberg’s Sonata No. 5 (Example 6-5), with chromatic movement in the right hand against octaves rising by minor 3rds in the left. Another illustration of pattern making, similar to procedures in Rimsky-Korsakov, is found at the beginning of Aleksandr Tcherepnin’s Dance Op. 2 (Example 6-6). The chromatic steps of the first two lines are modified in bar 17 by transposing the right hand up a minor 3rd and expanding the range of the melody from a 5th to a 6th, while the left hand proceeds by minor 3rds in place of semitones. The resulting harmonic combinations are not particularly unusual, but one feels that they are a product of the pattern; the progressive development of patterns in this way is particularly characteristic of Aleksandr Tcherepnin’s early works.

A more radical use of pattern is found in Lopatnikov’s Ironic Dances No. 2 (Example 6-7). The two-bar phrase in the right hand in bars 18-19 is transposed in bars 20 and 21 by varying intervals against a repeat of the left-hand ostinato. In the following “Agitato” contrary motion between the hands again produces a variety of incidental vertical combinations. Sometimes, as in the more rhapsodic style of Shostakovich, a single chord is sufficient to establish a pattern which then proceeds freely through less-familiar combinations. Instances are the B-flat harmony at the beginning of bar 113 of Sonata Op. 12 and the G 7th in bar 190 (Examples 6-8a and b); in the second case the pattern is followed in alternate bars. The three quarter-note chords of bar 190 follow a logical progression toward resolution and derive from the G 7th chord suggested at the beginning. The structure of the first two chords is employed at random in bars 192, 194, and 196, and they do not reach a triadic resolution again until the last beat of bar 196; set against a rising chromatic bass line they create a variety of incidental arrangements. Bars 229-36 (Example 6-8c) are based on free imitation of a tune first heard in the right hand of bar 1 (Example 6-8d) coupled, apparently at random, with a number of short linear fragments—also possibly derived from bar 1—each of which constitutes a pattern in itself. The tune is filled out in bars 233-34 by quasi-parallel movement of 5ths and tritones; the vertical combinations appear to be fortuitous and justified only by the interest of the linear patterns. In the passage beginning at bar 38 (Example 6-8e) the harmonies are created by combining the left-hand part of bar 1, in canon at the 9th, with repeated notes rising in whole steps (F, G, A, B). The resulting vertical connections are again random and warranted by the pattern.⁴ The technique of pattern making, usually associated with some form of ostinato (as in Example 6-9), also occurs in the music of Prokofiev.

With the predominantly linear character of much of the Russian music of this period, the way in which composers give independence to the bass, other than by rhythmic definition, is important. One method is to place the 7th or 9th of a chord in the bass. This makes it difficult for the ear to relate the note to the root above and gives a measure of independence from the chord; the bass can then be treated freely. A simple example occurs in Deshevov’s Meditations Op. 3 No. 6 (Example 7-11): here the F-flat in bar 9 initiates a passage where the main interest is in the lowest part, which develops a pattern first presented at the opening. A similar case is the first phrase of Prokofiev’s Op. 22 No. 8 (Example 6-10), where the bass half notes are 7ths or 9ths in relation to the harmonies above; this tends to isolate them and emphasize the tonal associations conjured up by the movement of 4ths, at the same time avoiding the banal repetition of V-I harmonies. A second method of isolating the bass occurs in Prokofiev’s Op. 17 No. 5 (Example 6-11); in bar 59 the lowest part is allowed to move against an ostinato in the upper texture. The further the style is removed from traditional practice the easier it is to treat the bass with absolute freedom, as in Roslavets’s Three Compositions. In the middle section of No. 1 the trills and contrary motion are sufficient to characterize the lowest part and differentiate it from the upper voices (Example 3-15a).

An isolated section of bass may be given structural importance if it is made to relate to something outside of the immediate context. In the last piece from Lourie’s Syntheses the very low E’s and G-flats in the bass (Example 6-12) are important as neighboring tones of F, which in various ways has been a central pitch throughout the set.⁵ The G-flats of bars 7, 8, and 12 are accompanied by dominant-structured 7th chords on A to which they do not easily relate aurally, and the E in bar 11 is also isolated from the chords above. More important, however, is the listener’s ability to relate the E’s and G-flats throughout to the tonal structure of the preceding pieces (see Example 5-24).

Another technical feature is the use of compression for harmonic or rhythmic effect. Compression may commonly take the form of the elision of a chord expected because of some traditional association; the sounding together of chords which traditionally would occur in succession; or the progressive shortening of phrases or speeding up of the harmonic rhythm. Examples of these techniques are comparatively rare in Russian Modernist music, and instances of the first two categories can occur only in music where established practices are sufficiently evident to arouse definite expectations.

An example of the first category is found in No. 1 of Shostakovich’s Three Fantastic Dances Op. 5. The composer establishes a traditional bass progression in the first eight bars, approaching the cadence by way of the flattened supertonic (Example 6-13). In the following five bars the music is held firmly in C major by the recurring tonic triad, but the composer creates a mild surprise by jumping directly from the augmented triad on D to a 7th on A-flat (acting here as an augmented 6th) and then back to the tonic, omitting the traditional approach to the cadence employed earlier.

A related passage but without the ironic intent, which illustrates the second category, occurs in bars 36 and 109 of the Sonata of 1911-12 by Aleksei Stanchinsky (1888-1914) (Example 6-14). Again the composer proceeds directly from the minor 6th of the scale to the tonic, this time by bringing forward the F in the bass. This device is related to Skriabin’s occasional practice of holding the dominant chord over the final tonic note, but, by syncopation in the bass, Stanchinsky has intensified the element of compression. The second of Prokofiev’s Sarcasms, at bars 25-28 (Example 6-15), is similar in that it has a series of French 6th chords over notes a 5th below. In this case, because the chords are not functional, the effect of horizontal compression is minimal; instead there is a slight effect of unresolved neighboring tones of the first and second octaves from the bass. Horizontal compression can also occur in linear passages. Seconds like that in bar 48 of Example 5-2a may be read as “knots,” or compressions, in the line.

Deshevov has an unusual example of compression of the third category, used for pictorial effect, in his Rails Op. 16. After the rather static harmonic patterns of the first two pages (Example 5-25), there is a considerable compression of harmonic rhythm from bar 50, with chords changing every beat in the sixteenth-note passages in bars 50 and 53 (Example 6-16). The effect is heightened in bar 54 by the contrary motion and eighth-note movement in the right hand, hinting at even more rapid change. Together with the dynamics, this creates a considerable sense of effort, suggestive of the pull of a locomotive. In contrast, the lengthened metrical stride at bar 55 has the effect of a change of gear as the locomotive accelerates.

An original example of compression, elevating it to a structural level, is found in Dance Op. 1 by Boris Aleksandrov (b. 1905) (Example 11-16). The interval of a 2nd is of importance throughout this piece. At the central climax, in bar 28, the 5ths D/A and E/B are the outcome of two lines proceeding at the interval of a whole step. The lines go back to bar 24—as can be seen by comparing the top and bottom staves of bar 24 and the C and B-flat of bar 26—but it is the only time the two lines sound the major 2nd simultaneously. This climactic device originates ultimately from the alternating 5ths A/E and G/D in the opening bars.

In contrast to compression is the technique of expanding a phrase by insertion. The B chord in Shillinger’s “Heroic Poem” Op. 12 (Example 3-5a) is an insertion into the B-flat cadence with the effect of weakening the tonal drive. Insertions also occur in the last piece, “Grotesque,” of Shillinger’s Op. 12 in a passage which is an expanded cross-reference to the same bar (Example 6-17). From the last chord of bar 2 of “Heroic Poem” to the bass B-flat in the following bar there is the following progression: G chord over C-sharp (the G chord is carried over the bar and followed by a brief reference to C), F chord, B chord, B-flat chord. In “Grotesque,” this harmonic progression reappears, expanded, in bars 31-58 (slightly modified by the E minor triad substituting for G in the right-hand part of bars 31-41), with some additional material (marked with brackets in Example 6-17) inserted at each stage. This reminder of the opening of the work emphasizes the return to E-flat in bar 59, the tonality of the first piece. The insertion at bars 5152 matches the texture of the cross-reference at bars 43-44.

One problem facing avant-garde composers was how to bring a work to a successful conclusion. One possible solution was to avoid the cadence altogether and conclude with an extended triad or pedal. If it was sustained long enough, all momentum would die away and the work could conclude. Skriabin used this method in some of his orchestral works, and Feinberg took it up in his longer compositions. The most extended example in Feinberg is his Sonata No. 5, which ends with two pages of decorative writing over an E pedal (see chapter 7). Boris Liatoshinsky (1887-1968), in his Sonata No. 2, decorates two bars of A pedal with neighboring-tone related chords (Example 6-18) and concludes with a series of major 7th chords (three with augmented 5ths) and a further A pedal in the last three bars.

Another solution was to adapt the V-I cadence to the style of the composition. Anatoly Aleksandrov achieves this at the end of the first movement of his Sonata No. 6 by a linear presentation and neighboring-tone approach to the final chord (Example 6-19). Alternatively, the tonic or the dominant chord could be ornamented in some way. Deshevov, in his Op. 3 No. 4, does this by breaking up the octave C in the last ten bars into a major 3rd sequence in which the bass continuously moves as the alto line is about to resolve (Example 6-20). Boris Aleksandrov, in his Op. 1 No. 2, approaches the final cadence with the bass progression E-A and then proceeds with a colorful filling out of the dominant element in the last five bars (Example 11-17). Aleksandr Krein’s Op. 18 No. 2 has a lengthy insertion between the dominant and tonic chords (Example 6-21). The end of the first movement in Mosolov’s Sonata No. 2 has what is basically a V-I cadence, but it is modified by linear progressions in the upper voices, leading first to subdominant and then to tonic formations at the end of each bar, and by passing through the third of the tonic in the bass at the end (Example 6-22). The conclusion of the exposition of this movement has a giant V-I cadence occupying 23 bars (Examples 6-3 and 5-20). In Nights in Turkestan No. 2, the same composer combines the V-I cadence with a colorful ostinato (Example 6-23). Grigory Krein (1880-1955), at the end of his Sonata Op. 27, has a cadence in which the supertonic, F-sharp, is emphasized by approach from the 4th below in the bass, and the dominant chord is ornamented by its minor 3rd and diminished 5th in quasi-parallel chords above (Example 6-24).

Plagal cadences are subjected to similar dressing up. At the end of his Sonata No. 1, Liatoshinsky surrounds the IV-I chords with neighboring tones (Example 6-25). Anatoly Aleksandrov, at the end of the slow movement of his Sonata No. 6, creates a linear texture by inserting an augmented 6th on the flattened supertonic between positions of the subdominant chord (Example 6-26). A particularly effective cadence is achieved by Vladimir Kriukov at the end of his song Schlaflose Nacht with expressive and imaginative treatment of the final tonic harmony (Example 6-27).

Some composers were successful in devising cadences without relying on V and IV chords. The final cadence in Anatoly Aleksandrov’s Sonata Op. 26 owes a good deal to the preceding tonic pedal and consists only of an augmented triad proceeding to the regular tonic major (Example 6-28). The end of the same composer’s Sonata No. 3 employs a dominant-structured 7th on the flattened dominant with effective linear writing and only a passing reference to the dominant (Example 6-29). The cadence at the end of Miaskovsky’s Sonata No. 3 is also dependent on smooth voice leading, but it is arranged in a chordal style (Example 6-30). In Aleksandr Krein’s Sonata Op. 34, the main functional elements in the final cadence are a tonic triad in the treble and an alto melodic ostinato. These are colored by submediant chords with major 3rds in the bass, the tritone A/D-sharp, and concluding chords in a neighboring-tone relationship to the tonic triad in bars 26265 (Example 6-31). The effective element at the close of Sabaneev’s Sonata of 1915 is the C-sharp minor descent in the left hand shadowed by the 5th above and tritone below (Example 6-32).

Occasionally a particularly ingenious and enigmatic cadence is achieved. The final cadence of Mosolov’s Sonata No. 2, which the composer describes as being in B minor (Example 6-33), follows a lengthy pedal on F-sharp. The chord in the third bar of the example may be interpreted as an ornamented version of the supertonic. The final left-hand figure sounds almost like a half cadence. Mosolov’s Nocturne No. 2 is an impressionistic piece having a certain amount of emphasis on B in the bass. The conclusion is effected by repeating in the bass a figure heard at the beginning, while the treble rises from F to B with a final emphasis on the latter. The harmony appears to be purely atmospheric (Example 6-34). At the end of his Sonata No. 2 Kriukov has an interesting cadence. First the treble closes in on C, having a 5th relationship to the final bass F; then octatonic chords in the treble alternate with the augmented 6th on the flattened supertonic, before ending on a heavily ornamented F chord (Example 6-35).

The stepwise parallel movement of chords occurs throughout the avant-garde and is exploited for a variety of purposes. Triads are usually supplied with some additional friction, as in bars 48-51 of Shostakovich’s Sonata Op. 12 (Example 61). Here they are part of an expansive linear movement between the discord at the beginning of bar 47 and its resolution on the E major triad in bar 52. Identical 7ths, proceeding in parallel motion, are found at bars 23-24 of the first movement of Mosolov’s Sonata No. 2 (Example 10-18). Stepwise movement of varied 7ths, with major and minor 3rds, occurs at the beginning of Prokofiev’s Op. 22 as part of a linear movement between key pitches (Example 4-3). In bars 21 and 22 of Lourié’s Upmann Sketch there is a series of 9th chords with added 6ths, providing a decorative link between two statements of the theme (Example 6-36). Parallel dominant-type 7ths, without added tones, tend not to be found in the Russian avant-garde although they occur in works of other Russian composers, including Aleksandr Grechaninov.⁶

A common root or bass line progression found in Russian music of this period is the tritone with adjacent semitone. It occurred frequently in nineteenth-century Russian music, largely as a result of the use of the flattened supertonic in cadences and modulations.⁷

This underlying harmonic relationship exists in the first subject of Feinberg’s Sonata No. 5 (Example 5-3). In addition to the expanded B chord in bars 1-12, there is a compact dominant-structured 7th on C at the end of bars 8 and 10, which can be read as a traditional augmented 6th on the flattened supertonic, and an F-shatp triad, which occurs when the hands coalesce for a moment on the third eighth note of bars 4 and 6. The effect here is not so much of harmonic progression but of relating three harmonic areas within the general tonal context of B.

A long-term expression of this formula is found in bars 25-26 and 35 of Roslavets’s Poem of 1916. This piece also demonstrates an element of compression because the G and D-flat chords are asserted concurrently in bars 25 and 26. The tension thus created is left in suspense until the resolution on the final C (Example 10-3). Similarly, in Shillinger’s Op. 12 No. 4, the compression of triads on G and F-sharp at bar 1 relates to the cadence in bars 14-15 (Example 6-37); and in Miaskovsky’s Sonata No. 3 there is friction between the D-flat triad in bars 1-6 and the C minor cadence at bars 6-7 (Example 6-38).⁸ As well as defining tonality, this progression can be used to weaken an otherwise too definite tonal cadence; for example, in the case of the B chord in bar 3 of Shillinger’s “Heroic Poem” Op. 12 (Example 3-5a).

The expression of this tritone and adjacent semitone relationship in a single complex is found in the opening bar of Lourié’s Syntheses No. 1 (Example 6-39). Whether this is viewed as an elaboration of the dominant chord whose root appears in the bass or as a compression of the triads of the flat supertonic, dominant, and tonic, it does subtly suggest the tonality of F, which is central to the whole work. A related but much simplified pattern occurs in the last two bars and again points to F as a center.⁹

In compositions which are not tonally structured, and especially in the hands of Roslavets, the progression under consideration continued to be important as a long-range harmonic relationship. It occurs in Roslavets’s Poem No. 1 (1920) between the E/A of bars 16-17 and the E-flat and A of the opening and closing bars. Poem No. 2 opens and closes on C, and the same pitch connection exists between this C and the bass G/F-sharp which mark the central point at bars 1821 (Examples 3-13 and 3-11).

The first of Roslavets’s Three Compositions (1914) is structured entirely on this formula (Example 3-15a). The opening phrase throws emphasis on the notes A-flat, D, and G in the bass of bars 1, 3, and 4. The A-flat and G are related by being quarter notes (in contrast with the more broken texture in between), by the sequential character of the two phrases, and by the melodic rhythm, which at these points differs from the context. The D and G are emphasized by their cadential position. The same relationship underlies the overall form of the piece, as can be heard by relating the prominent bass D of the middle section to the opening Aflat and closing G.

In the last phrase a similar complementary tritone and semitone is heard in the bass—G-sharp, A, E-flat—having A-flat in common with the formation in the opening phrase. In this case A is drawn to our attention by its neighboring tones in bar 8 and emphasized by the leading-tone effect of G-sharp in bars 10 and 11. The E-flat then interposes in place of the expected A in bar 12. An interesting aspect of the piece is the tension between traditional, though localized, tonal functions and nonfunctional pitch relationships. Traditional functions exist in the cadence at bars 3-4 and in the leading-tone effect of the bass G-sharp in the final phrase. However, when the complementary pattern G-sharp, A, E-flat arrives at E-flat in bar 12, there is no functional tie with the A-flat in bar 1 because the E-flat has arrived as a tritone displacement of A and the A-flat has been reinterpreted as G-sharp. Tonal functions are used only to bring local prominence to certain notes.

Typical of the close integration of much of Roslavets’s music is the use in this piece of the same tritone and semitone pattern on a decorative level and in the harmony. Decoratively it occurs (rearranged) in the bass arpeggio in bar 5. The bass of the harmony here is not F-flat but E-flat, and the two notes form part of a descending line from G in bar 4 to D in bar 6. The same pattern of a tritone and adjacent semitone is found in the three groups of treble eighth notes in bars 6, 7, and 8, and in the bass D, G-sharp, A in bars 7-10. An examination of the harmony chart (Example 3-15c) reveals that every chord contains at least one interval of a tritone with a semitone adjacent to one of the tones.

Several ways were adopted of ornamenting a chord which go beyond the traditional use of nonharmonic notes. As the introduced notes have varying degrees of harmonic status they may be described as expanding the harmonic area of the chord.¹⁰ These methods included: free movement by major or minor second steps within the chord; static alternation with a subsidiary chord; the introduction of one or more added notes to make up a secondary chord within the main complex; and stepwise movement into neighboring chords and subsequent stepwise return. The first category is demonstrated in bars 17-24 of Mosolov’s Sonata No. 2 (Example 10-18), where the controlling harmony is F-sharp. In this type of progression, passing chords may emerge according to the degree of local emphasis. The second category is represented in the left hand of bars 177-209 of the last movement of Sonata No. 2 by Prokofiev (Example 6-40). The third category is a favorite with Shebalin and can be seen at work in bars 28-36 of the first movement of his Sonata No. 2 (Example 6-41). In bar 28 the chord is a dominant-structured 7th on C-sharp, but by taking the diminished 5th of the chord along with B and D he creates a subsidiary triad on G, which is given considerable emphasis, especially in bar 31. The fourth category is illustrated in Example 6-42, taken from the beginning of Prokofiev’s Sonata No. 3; in bar 3, notes of the D minor triad assert themselves against the E and G-sharp of the established chord, leading to its displacement in the following bar.¹¹

Harmonic progressions involving the 2nd, the 3rd, and the tritone were discussed in chapter 4, and 5th progressions in the bass were briefly mentioned in chapter 3 in connection with the early works of Roslavets. The perfect 5th, either as a root progression or a linear bass pattern, continued throughout the Modernist period to play a part in structuring harmonic progressions, even in music having a reduced tonal content.

Poem (1916) by Roslavets is a complex work in which traditional harmonic relationships can scarcely be detected much of the time; nevertheless a series of 4ths and 5ths in the lower voice is clearly intended as the basis of a progression. After the thematic material has been exposed in the first two bars, an unbroken chain of falling 4ths leads from F-sharp in bar 3 to F in bar 8 (Examples 6-43a and b). A middle section, having a more polyphonic texture (Example 11-9), commences at bar 11, and the 4ths and 5ths resume from here to bar 15. After the big climax there is a modified return of the opening material commencing at bar 27, this time involving a long-range 5th relationship (G-C, see Example 10-3).

As well as marking harmonic direction within the phrase, 5ths may govern the relationship of one phrase to another. An example is the three phrases which constitute the second subject of Mosolov’s Sonata No. 2 (Examples 6-44a and b). These begin at bars 43, 50, and 59 with second inversion triads of E-flat, Aflat, and E-flat respectively. The E-flat of the first phrase is introduced by the resolution of the E/B-flat tritone in bars 40-42 (Example 5-19d), and the bass line leads back to E-flat at bar 50. The A-flat of the second phrase is introduced by compression of the minor 7th on B-flat in bar 49 and the following eighth-note chord (which respectively suggest supertonic and dominant in A-flat) and by emphasis on the G-sharp trill in bars 48 and 49. The final phrase is a simplified repeat of the first.

In the case of the Roslavets piece the element of traditional tonality is so reduced that one is not aware of any tension between the bass 5ths and the texture above, as one is in the case of Shillinger’s “Heroic Poem” (Example 3-5a), or, in the case of the Mosolov, between the A-flat of the harmonic core and some of the other parts (Example 6-44b).

Another long-range 5th connection is found in the introduction to Sonata Op. 34 by Aleksandr Krein (Examples 3-7 and 3-8). The 9th chord on E in bar 2 and the major 9th on A in bar 16 stand out in their diatonic clarity from the other, more-complex chords, with their frequently octatonic or whole-tone coloring. The former is emphasized in two ways: it provides a resolution to the discord of the first bar, which functions as a kind of upbeat; and it is marked off by a comma from what follows—these two bars constitute an opening gesture. The two chords of bars 2 and 16 form a diatonic framework to the more unusual symmetrical structure developed in between (see the analysis of this passage in chapter 8).

Although 4ths and 5ths were adopted as a basis of structure in Russian music, in the Modernist period they were generally avoided as tonal relationships. The use of tonality by Russian composers and their search for an alternative to tonal structuring is taken up in the following chapters.