The Progress of a Motive in Brahms’s Intermezzo op. 119, no. 3 ^*

[1] Johannes Brahms’s skill with motivic development is well known. Beginning with Arnold Schoenberg’s famous essay “Brahms the Progressive,”⁽¹⁾ analysts have demonstrated time and time again the masterful ways in which Brahms manipulates his motivic ideas.

[2] Motivic development is especially concentrated in the late piano music op. 116 through 119, written in 1892 and 1893. About op. 118, no. 6, for instance, John Rink (1999, 97) writes that “to characterize [this piece] as a motive in search of a tonic would hardly do justice to the tremendous dramatic impulse generated by Brahms’s incessant reharmonizations of the almost ubiquitous melodic shape.” Notable about many of these pieces is the extreme economy of material: the way in which a single idea is transformed in myriad ways.⁽²⁾

[3] Among the op. 119 pieces, No. 1 has received the most analytic attention.⁽³⁾ Op. 119, no. 2 has also been studied at length, particularly for its re-casting of a six-pitch motto introduced in the A section in the B section.⁽⁴⁾ The literature on Nos. 3 and 4 is relatively scant, however, quite possibly for opposite reasons: whereas No. 4 is the longest, weightiest and most complex in the set, No. 3 is, at least on the surface, the most innocuous. No. 4 is treated in a recent dissertation by Samuel Ng and a paper by Frank Samarotto;⁽⁵⁾ the only relatively comprehensive analysis of No. 3 is in a dissertation by Camilla Cai.⁽⁶⁾ The lighthearted mood of No. 3 masks an underlying sophistication: the piece is remarkable, not only for its economy of material, but also for its use of a double-tonic complex and its serial ordering of chromatic pitch classes, two musical procedures not usually associated with the music of Brahms.⁽⁷⁾ That the motive is exclusively diatonic places the chromaticism into especial relief.

[4] Like many of the late piano pieces (and like the first two in op. 119), the Intermezzo is in ternary form, as shown in Example 1. Section A₁ is in two nearly identical parts, each of which progresses from C major to A major; the B section moves from A major back to C major; and section A₂ is exclusively in C.

[5] In its first appearance, the motive embodies these two keys, which in section A₁ form a double-tonic complex. Before examining the double-tonic complex in more detail, we must first examine the motive itself. It consists of the melodic cell and harmonic progression given in Example 2. The melodic cell, labeled “J”, consists of the interval pattern ascending 3rd, ascending 2nd and descending 2nd. A clef is omitted from the first part of the example because J appears in different scale locations in different parts of the piece. J’s first occurrence begins on $\hat{3}$.

[6] The harmonic component of the motive is dubbed “DOWN-THIRD-UP-FIFTH” after its constituent root motions. In all statements of this harmonic progression, the descending third is diatonic—the quality of the third depending upon the quality of the starting chord—and the ascending fifth is perfect. In this first appearance, the descending third is minor. Moreover, the total pitch-class content of the progression in its first appearance is diatonic.

[7] The melodic cell and harmonic progression—J and DOWN-THIRD-UP-FIFTH— sometimes occur independently, but for the most part interact to create a larger unit. This larger unit, given at the bottom of Example 2, is the motive of my title.⁽⁸⁾ Again, the fact that the motive is exclusively diatonic is significant, because it makes the chromatic pitch classes especially salient.

[8] The opening of the piece animates the motive by repeating and varying the duration of J while arpeggiating the chords of DOWN-THIRD-UP-FIFTH. Example 3 annotates the melody of m. 1 through the downbeat of m. 3, which fuses together three Js.⁽⁹⁾ By fusing together three Js and altering the duration of the final pitch of each J (the durations are , , and , for the three occurrences, respectively), Brahms creates a symmetrical rhythmic structure.⁽¹⁰⁾ The dots below the staff indicate metric position: two dots indicate a strong beat, one dot a weak beat.⁽¹¹⁾ The first J starts on a strong beat and concludes on a weak beat. The third J starts on a weak beat and concludes on a strong beat. The middle J begins and ends on a weak part of two different beats. This rhythmic organization marks the beginning and ending of thrice-J as points of departure and arrival.⁽¹²⁾ Furthermore, mm. 1–3 constitute a single hypermeasure: the sequence beginning in m. 4 retrospectively marks that measure as a hypermetric downbeat, segregating mm. 1–3.

[9] The textural and harmonic context also support hearing mm. 1–3 as a unit. The melody, beginning with thrice-J, is in an inner voice, played by the inside of the pianist’s right hand. The upper voices support the rhythmic structure just discussed, with dotted quarter notes at the conclusion of the first and third instances of J only. Harmonically, the conclusion of thrice-J coincides with the conclusion of the first DOWN-THIRD-UP-FIFTH. In the first two statements of J, the third pitch (A) is not harmonized; rather, it is an upper neighbor to the chordal 5th. But in the third statement of J, when A descends to G it pulls C down to B, and the bass complies: the bass pattern in m. 3 is a transposition up a 3rd of that in mm. 1 and 2. Consequently, the last eighth of m. 2 sounds more like an independent harmony—a bona fide A-minor triad—than the “mere” neighbors in the first two Js. Put another way: while the first two inner-voice As are complete neighbors to the 5th of the tonic triad, the third A bridges two different harmonies, C major and E minor.⁽¹³⁾ In dramatic terms, it is as if the incessant repetition of J induces the harmonic motion across the barline of mm. 2–3. To paraphrase Schoenberg, pitch class A is the “tonal problem” of the piece, creating an imbalance that the rest of the piece serves to rectify.⁽¹⁴⁾

[10] J’s suggestion of an A-minor harmony is played out by the music that follows. The keys of C major and A minor (later inflected to major) “compete” with each other, interacting in a double-tonic complex.⁽¹⁵⁾ In m. 3 (pickup to beat 2), J begins a fourth time but does not complete the neighbor figure; instead, the melody continues upward $\hat{5}$–$\hat{6}$–$\hat{7}$–$\hat{8}$, forcing the upper voices to shift upward. The voice that descended from C to B (on the downbeat of m. 3) has thus returned to C; the right hand plays a C-major triad, seemingly assenting to the C-major tonic and banishing the problem pitch class A. But the bass, instead of returning to C as well, moves to A—belatedly reinforcing the persistent A in the right-hand part of mm. 1–2. The sonority on the downbeat of m. 4 is ACEG, the combination of an A-minor triad and C-major triad.

[11] This “miscommunication” between the hands continues. The left-hand part in mm. 4–5 seemingly tries to establish A minor with the bass line $\hat{1}$–$\hat{6}$–$\hat{4}$–$\hat{5}$, and the right-hand part articulates a sequence that descends by step beginning in m. 4, landing on an A-minor triad in m. 6. But A minor’s leading tone, G♯, is notably absent in the second half of m. 5 (in both parts), and the left hand plays C instead of A on the downbeat of m. 6.⁽¹⁶⁾ Essentially, the two hands have exchanged places here relative to the downbeat of m. 4. Up until this point, the piece contains not a single chromatic pitch class.

[12] Two dovetailed sequences—incorporating significant alterations—occur in mm. 4–12, a passage whose hypermeter is the most complex of the piece. The alterations introduce the first chromatic pitch classes. Example 4 sets the stage for discussing these alterations by providing a 4-measure (and 4-hyperbeat) prototype for mm. 4–12 that ends with a half cadence. The prototype removes the A-vs.-C conflict at the beginning of m. 4 by transposing the circled bass pitches up a 3rd, and cadences on the dominant in m. 7, removing the large phrase expansion in the music while also normalizing the irregular hypermeter of this section.⁽¹⁷⁾ The sequence here continues the rhythmic pattern of the melody of m. 3.

[13] Example 5 approaches the musical score in two stages. In part a. is an unaltered sequence based on the music of mm. 4–5.⁽¹⁸⁾ As shown at b., Brahms alters the sequence by first repeating the chord in m. 6—indicated by the dotted portion of the curved brackets—and by changing E to E♭. E♭, significantly, is the first chromatic pitch class in the piece. The 7th chord expected on beat 2 of m. 6 is thus delayed until beat 1 of m. 7; this chord is chromatically altered as well, with F♯ substituting for the expected F♮. At the same time, this interruption of the first sequence restores the rhythmic pattern of the melody of m. 1.⁽¹⁹⁾ The two chromatic pitch classes tonicize G, V of C, as F♯ alone does in the prototype.⁽²⁰⁾ Despite the G chord’s position, the chord sounds like a tonic due to the cadential figure $\hat{5}$–$\hat{1}$ in the inner-voice melody. For this reason, the prototype in Example 4 places the chord here in position; the melody’s ascending-4th leap (m. 7, b. 2 of the score) is conceptually a bass voice that has been transferred to an inner voice and metrically displaced.

[14] As shown below the staff in part b., part of the previous pattern is absorbed into a new two-measure pattern that participates in an ascending-second sequence; mm. 8–9 may be heard as an internal phrase expansion, repeating the hypermetric “3–4” of mm. 6–7.⁽²¹⁾ Since the second pattern of this new sequence begins with a diminished triad instead of a minor one, there is no room for the chromatic descending line found in the top voice of the first pattern, necessitating an alteration; strikingly, this alteration employs the same two chromatic pitch classes as the earlier one—D♯ and F♯ (one enharmonically reinterpreted)—but serving in a tonicization of V of A minor. Because the second sequence ascends by step, the music of m. 8 has returned to the pitch level of m. 5; the earlier “failed” tonicization of A minor is carried out more successfully here, introducing pitch class G♯. The music of m. 9 is repeated in m. 10, with C♯ replacing C♮. This varied repetition seems to clinch A major’s independence from C major, since C♯ is diatonic only in the former key. The sostenuto marking encourages the pianist to linger for a moment to highlight the arrival of A major. In m. 11, the right-hand part of mm. 9 and 10 is repeated, but the A-major triad is in position this time. The chord is still on a weak beat, however, and its arrival is undermined by a drawn-out 4-3 suspension. The threefold repetition of the pitch material in mm. 9–11 retrospectively causes a reinterpretation of m. 9 as a hypermetric downbeat.⁽²²⁾ Two chromatic pitch classes then revert to their diatonic form: F♯ to F♮, serving contextually to reinforce A major (just as E♭ earlier reinforced V of C), followed by C♯ to C♮. F♮ is reinflected to F♯ to prepare the return of the motive.⁽²³⁾

[15] The chromatic pitch classes introduced in mm. 4–10 act as agents in the double tonic complex. Example 6 collates these pitch classes, listing their location and harmonic function. Witness again the pure diatonicism of mm. 1–6 (b. 1) and the context in which E♭/D♯ and F♯ are introduced, first as agents of C’s dominant, then as agents of A’s dominant. Next to arrive are G♯ and C♯. Only one pitch class—B♭/A♯—remains to be introduced; it arrives in m. 30, a significant harmonic juncture in the B section that I will return to momentarily.

[16] The second half of A₁ is identical in pitches and rhythms to its first half until the last eighth of m. 23.⁽²⁴⁾ This time, the 4–3 suspension resolves within the beat; in place of the earlier line D–C♯–C♮ is C♯–C♮–B, which continues to A at the beginning of the B section. The bass in the second half of m. 24 is changed from A to E relative to m. 12, creating the first cadential in the piece, followed by the first strong cadence, in A major.

[17] After its prominent statement at the opening of each half of A₁, the motive recedes from the foreground until section B; only its harmonic component, untransposed, remains present but not very prominent. The bass motions from A to E in mm. 4–5 (by way of intervening chords) and in mm. 8–9 echo the same motion in mm. 2–3. In the B section, the motive remains closer to the foreground; in particular, DOWN-THIRD-UP-FIFTH is subject to a most remarkable working-out. The route from C major to A major was relatively straightforward; the route back is not so simple.

[18] In m. 25, thrice-J returns, but the lack of accompaniment, low register, and sudden piano undermine A major’s big moment. J begins here on $\hat{1}$ rather than $\hat{3}$, so J and DOWN-THIRD-UP-FIFTH have been transposed by different intervals relative to m. 1: J is transposed down a 5th, while DOWN-THIRD-UP-FIFTH is transposed down a minor 3rd. As shown in Example 7, mm. 25–29 outline a statement of DOWN-THIRD-UP-FIFTH beginning on A major and concluding on C♯ major; unlike the statements of DOWN-THIRD-UP-FIFTH in the A section, the concluding triad here is major rather than minor. This modal change makes the second and third chords of DOWN-THIRD-UP-FIFTH sound like tonic and dominant, respectively, a point I shall return to. Immediately following the completion of thrice-J in m. 27, the music of mm. 23 (b. 2)–24 returns, transposed up a major 3rd and with a thicker texture. In mm. 33–35, DOWN-THIRD-UP-FIFTH appears down a half step relative to mm. 25–29, beginning on A♭ major and ending on C major—again, note the conclusion on a major triad. A small-scale echo of this same transposition occurs in mm. 39–41.

[19] Example 8 illustrates how the music navigates from the DOWN-THIRD-UP-FIFTH on A to the climactic one on A♭. Mm. 29–30 are a transposition of mm. 25–26 up a major 3rd.⁽²⁵⁾ If the music had continued according to this sequence, it would end up traversing the major-3rd cycle A-C♯-F-A and fail to return to C major. The music breaks out of the cycle by pivoting between two different DOWN-THIRD-UP-FIFTHs: m. 30 contains the second chord of a DOWN-THIRD-UP-FIFTH beginning on C♯/D♭ major (Example 7), which serves also as the first chord of a new DOWN-THIRD-UP-FIFTH beginning on B♭ minor (Example 8). This initiation of a new DOWN-THIRD-UP-FIFTH a third lower restores the transpositional relationship between J and DOWN-THIRD-UP-FIFTH from m. 1. Strikingly, this harmonic turning point coincides with the completion of the aggregate by B♭ (Example 6). Measure 30, based on m. 2, is the pattern for a new ascending-3rd sequence that contains three overlapped statements of DOWN-THIRD-UP-FIFTH.⁽²⁶⁾ The last two bass pitches of each measure in this sequence are a 3rd “too low” relative to the pattern in m. 2; by putting the root of the second chord in the bass, this alteration strengthens the harmonic motion of each DOWN-THIRD-UP-FIFTH relative to the opening, where the existence of an independent A-minor triad was only weakly implied.⁽²⁷⁾ The harmonic sequence ends in m. 33, but the pattern of overlapped DOWN-THIRD-UP-FIFTHs continues: the B♭-major triad in m. 33 is the initiating chord of the DOWN-THIRD-UP-FIFTH that concludes the B section, mentioned earlier in connection with Example 7. In this final DOWN-THIRD-UP-FIFTH, J has disappeared; harmony trumps melody here. Relative to the interlocking DOWN-THIRD-UP-FIFTHs in mm. 30–33, this DOWN-THIRD-UP-FIFTH is rhythmically augmented, with each harmony occupying one measure. The exclusive focus on harmony also crowds out any hypermetric ambiguity: mm. 25–40 comprise four 4-beat hypermeasures.

[20] As shown in Example 9, the underlying voice-leading pattern established by the sequence continues beyond the conclusion of the sequence (m. 33), and even beyond the conclusion of the DOWN-THIRD-UP-FIFTH chain (m. 35). The example highlights instances of the Phrygian tetrachord (half-whole-whole).⁽²⁸⁾ The first two tetrachords (on F, then on C) are straightforward reductions of the melody. The thunderous arrival on a C-major triad, the goal of the whole passage, contains a less obvious statement of the next tetrachord in the pattern (beginning on G) embedded within a series of descending 3rds. At the same time, the pitches on successive downbeats—G and F—set up an expectation for E♮ that is realized only in m. 41 when the theme returns, as shown by the bracket above the staff. During the prolongation of the C harmony, a Phrygian tetrachord on C is outlined, the second half of which participates in the small-scale DOWN-THIRD-UP-FIFTH on A♭. Finally, the melody in m. 41 can be heard as initiating a WWH tetrachord beginning on G.⁽²⁹⁾

[21] In the forte DOWN-THIRD-UP-FIFTH statement (mm. 33ff.), F minor sounds like tonic and C major like dominant. Rhetorically, the passage beginning in m. 35 sounds like a retransition. Coinciding with the small-scale echo in mm. 39–41 is a re-introduction of J given in Example 10. When we hear C-E♭-F, we expect the continuation in the top staff of the example. But the music proceeds as given in the bottom staff: the third pitch of J is held for over three beats, and the expected E♭ never arrives. In its place is E♮, which, although unexpected from the standpoint of the J-statement beginning on C, conforms to the statement of DOWN-THIRD-UP-FIFTH within whose echo it is embedded. At the same time, the E♮ initiates another statement of J.⁽³⁰⁾ Reinforcing this E♮ is the E♮ an octave higher, which (as Example 9 showed) participates in a large-scale stepwise descending 3rd spanning mm. 35–41.

[22] The overlap between two forms of J here is only one way in which the music disguises the return of the opening material. Tonally, C major was ushered in as a dominant of F minor (m. 35); but what is initially heard as a dominant is actually the tonic: what first sounds like i to V is really—or rather, becomes—iv to I. Brahms exploits this well-known ambiguity of the tonal system to marvelous effect here.⁽³¹⁾ Rhythmically, the statement of J beginning on E♮ is in augmentation, as shown in Example 11: it is almost as if J has been listening while DOWN-THIRD-UP-FIFTH held center stage. Recall that DOWN-THIRD-UP-FIFTH is augmented from one measure to two measures in mm. 33ff., while J is absent; in mm. 41ff., J is augmented relative to its original statement. (Also, it would have been too abrupt for J to return in its original rhythmic form after the 3 1/3-beat-long F4 in mm. 39–40.) But three statements of thus-augmented J would take too long. Brahms’s solution is ingenious: only two Js are stated, and the second J is shortened to EAG, omitting the first G. In so doing, the music makes an explicit reference to op. 119, no. 2: this shortened form of J in op. 119, no. 3 traces a transposed retrograde of the first four pitches of the six-pitch motto of op. 119, no. 2, as shown in Example 11. The last line of the example transposes the melody of the codetta, which chains together three statements of the abbreviated motto.⁽³²⁾ Since op. 119 no. 2 ends with the abbreviated motto, the motivic relationship between the two pieces can be brought out diachronically if the two pieces are played in sequence.⁽³³⁾ J then returns in its original form in m. 45.⁽³⁴⁾

[23] And speaking of retrogrades, the chromatic pitch classes in section A₂ occur in retrograde order relative to section A₁ plus B. (See again Example 6.) First comes B♭ in m. 46, then C♯ in m. 47, both acting to tonicize D minor, paralleling the use of the same scale degrees to tonicize G major in mm. 6–7. The remainder are tied to an altered recapitulation of mm. 7–8.⁽³⁵⁾

[24] Section A₂ is dominated by a lengthy dominant prolongation (mm. 49–65) that reworks the music of mm. 7ff. As shown in Example 12, m. 49 is a transposition of m. 7 down a perfect 5th, an instance of sonata principle; coincident with this transposition is a reversal of strong and weak hypermetric beats that results from the absolute hypermetric regularity of mm. 25–48.⁽³⁶⁾ Relative to the transposition of m. 7 in m. 49, the music of m. 50 is a whole step too low relative to m. 8; this transposition up a minor 3rd (or down a major 6th) produces pcs A♭ and F♯ that fulfill the retrogression just mentioned, and necessitates the repetition of this material. In m. 50, the lines of m. 8 are re-arranged: the melody line is now on top, and the left-hand part carries both of the chromatic lines from m. 8.⁽³⁷⁾ The new top line in the piano departs from the reigning transposition up by minor 3rd, stating E in place of E♭ (transposition up a diatonic 3rd). Measure 53, constituting the second pattern of a sequence, is the “correct” transposition of m. 8, but again, one voice is inflected: the melodic sequence begun in m. 52 implies a D at the end of m. 53, but D is inflected to D♯, producing a curious ♯$\hat{2}$-to-$\hat{4}$ diminished-3rd across the barline.⁽³⁸⁾ The expected final chromatic pitch class, D♯/E♭, is thus withheld until the “correct” transposition of m. 8. Strikingly, the liquidation here is the opposite of the process in mm. 4–9. In mm. 49–55, a two-measure unit is repeated, then its second measure becomes the pattern for a sequence; in mm. 4–9, a one-measure pattern is lengthened into a two-measure pattern. There is yet another parallel between the two sections having to do with the development of the two figures originally found in mm. 6 and 7: in section A₁, the figure from m. 7 is repeated (in mm. 9–11), producing a hypermetric reinterpretation (in m. 9); in section A₂, the figure from m. 50—which in turn derives from m. 6 via m. 8—is repeated (in mm. 52–54), producing a hypermetric reinterpretation (in m. 52).

[25] After the highly chromatic journey of the B section, pitch class A presents less of a threat than it did in section A₁. The only C♯s in section A₂ (in mm. 47–48 and 54) occur in contexts that reinforce—or at least do not undermine—C major. Though it is clear now that the key of C is primary, pitch class A continues to have a real presence: in mm. 59–61, a melodic A-E occurs twice, followed by C-G in mm. 61–62.⁽³⁹⁾ There are prominent A’s in mm. 63 and 64 as well, but they no longer threaten C major since the “problem” has now worked itself out. In mm. 66–68, thrice-J occurs in its rhythmically augmented form (from m. 41) but without its last note so that it fits within the meter.⁽⁴⁰⁾ By this point, pitch class A has been so thoroughly integrated that we nearly accept the chord CEGA as tonic.⁽⁴¹⁾

[26] Example 13 summarizes the harmonic trajectory of the piece. The boldface pitch classes in part a. constitute a circle of ascending perfect 5ths; here the letter names stand for triads. Conceptually, we can think of this circle of 5ths first being embellished by the chords at the half hours that fill in each 5th with two diatonic 3rds, producing the 24-triad LR-cycle.⁽⁴²⁾ Next, each ascending 3rd is filled in by a DOWN-THIRD-UP-FIFTH, producing a 48-triad cycle that comprises a complete chain of DOWN-THIRD-UP-FIFTHs. The piece traverses only segments of this cycle, as shown by the arcs inside the circle; each arc is labeled with measure numbers. The short cuts across the circle in mm. 26–29 and 34–35 correspond to the two forms of DOWN-THIRD-UP-FIFTH that frame the B section, the two that, unlike all the others, begin and end with major triads.⁽⁴³⁾

[27] Part b. of Example 13 shows how the length of DOWN-THIRD-UP-FIFTH changes throughout the piece: the first two instances—those in the A section—are two measures long measured from downbeat to downbeat. The next two, really one embedded within another, take 2 1/2 and 4 measures. After this lengthening of DOWN-THIRD-UP-FIFTH, it is suddenly contracted: three statements in the span of only three measures. The normative two-measure length of DOWN-THIRD-UP-FIFTH returns at the point at which J disappears, in m. 33.

[28] My own initial impression of the Intermezzo was of blandness: the absolute diatonicism—in C major, no less!—of the opening and the seemingly meandering harmonic progression discouraged me from continuing beyond the first two lines or so. It was only after taking a closer look that I began to marvel at what Brahms has done here: it no longer seemed bland at the beginning, but subtle, with the diatonicism establishing the tonal problem and throwing each chromatic pitch class into especial relief. The densely chromatic B section, with its lengthy DOWN-THIRD-UP-FIFTH chain and regular hypermeter, complements the sparsely chromatic and hypermetrically irregular A₁ section. The strict ordering of the five chromatic pitch classes in the first half of the piece and the reversal of this ordering in the second half is remarkable, and warrants further investigation in the rest of Brahms's oeuvre.

Adam Ricci
UNC at Greensboro School of Music
P.O. Box 26170
Greensboro, NC 27402-6170
adam_ricci@uncg.edu

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Rosen, Charles. 1990. “Brahms the Subversive.” In Brahms Studies: Analytical and Historical Perspectives (Papers delivered at the International Brahms Conference, Washington, DC, 5–8 May 1983), ed. George S. Bozarth, 105–19. Oxford: Clarendon.

Samarotto, Frank. 2004. “Determinism, Prediction, and Inevitability in Brahms’s Rhapsody in E-flat Major, op. 119, no. 4.” Paper presented at the Society for Music Theory conference, Seattle, WA.

Schoenberg, Arnold. 1975. Style and Idea: Selected Writings of Arnold Schoenberg, ed. Leonard Stein with translations by Leo Black. New York: St. Martins.

Schoenberg, Arnold. 1995. The Musical Idea and the Logic, Technique, and Art of Its Presentation, ed. and trans. Patricia Carpenter and Severine Neff. New York: Columbia University.

Smith, Peter H. 1994. “Liquidation, Augmentation, and Brahms’s Recapitulatory Overlaps.” 19th-Century Music 17.3: 237–61.

2006. “You Reap What You Sow: Some Instances of Rhythmic and Harmonic Ambiguity in Brahms.” Music Theory Spectrum 28.1: 57–97.

Straus, Joseph. 1991. “The Progress of a Motive in Stravinsky’s The Rake’s Progress.” The Journal of Musicology 9.2: 165–85.

Ulehla, Ludmila. 1966. Contemporary Harmony: Romanticism Through the Twelve-Tone Row. New York: Free Press.

Webster, James. 1978–79. “Schubert’s Sonata Form and Brahms’s First Maturity.” 19th-Century Music 2.1: 18–35 and 3.1: 52–71.

Footnotes

* My title borrows a phrase from that of Straus 1991. Brent Auerbach, Guy Capuzzo, and the anonymous readers for this journal provided helpful comments on the manuscript. An earlier version of this paper was presented at the 2006 meeting of Music Theory Southeast in Chapel Hill, NC.
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1. Schoenberg 1975, 398–441.
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2. See also Cadwallader 1988.
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3. See, for example, Cadwallader 1983, Clements 1977, Dunsby 1981 (Chapter 5), Jordan and Kafalenos 1989, and Newbould 1977. Two excellent guides to Brahms research are Platt 2003 and Quigley (1990 and 1998).
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4. See, for example, Braus 1994, Frisch 1990,Mainka 1986, and Schenker (unpublished—discussed and translated in Cadwallader and Pastille 1999).
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5. Ng 2005; Samarotto 2004.
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6. Other analyses include Nattiez 1975 and Rosen 1990, both of which focus on the opening 12 measures. An extensive discussion of rhythm in Op. 119, No. 3 can be found in Petersen 1999.
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7. One exception is Jordan and Kafalenos 1989, which asserts the presence of a double-tonic complex involving B minor and D major in op. 119, no. 1. The term “double-tonic complex” originated with Bailey 1985. In an analysis of the Prelude from Richard Wagner’s Tristan und Isolde, Bailey demonstrates that the keys of A (major/minor) and C (major/minor) are inextricably intertwined. That the two keys are intertwined does not preclude the superior position of one key at any given moment. On the structural role of aggregate completion in tonal music, see Baker 1993 and Burnett and O’Donnell 1996. Burnett and O’Donnell additionally argue for the significance of particular orderings of the chromatic aggregate. Clampitt 2004 points out the correspondence between completion of the aggregate and the end of the exposition in the Adagio mesto of Brahms’s Horn Trio in E♭ major, op. 40.
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8. In that it contains multiple components, is an abstraction from the musical surface, and is pervasively present in the piece, it is close in function to Schoenberg’s Grundgestalt; Schoenberg used the term “motive” to designate smaller musical units. Because the precise meaning of Grundgestalt is difficult to discern, I will exclusively use “motive” to refer to the combination of J and DOWN-THIRD-UP-FIFTH. On the conceptual distinctions between motive, Grundgestalt, and related terms in Schoenberg’s writing, see Schoenberg 1995.
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9. A fourth statement of J begins on the last eighth of m. 3, beat 1, but is interrupted when the melody ascends to B instead of descending to G.
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10. Petersen (1999, 151) shows the lengths of the three Js in his Example 9 and mentions in his accompanying text how it does not fit into the notated 6/8 meter.
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11. This notation is employed in Lerdahl and Jackendoff 1983.
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12. Petersen’s (1999) calculus of accents, which takes into account melodic, textural and harmonic factors and is summarized in his Example 12 (p. 153), clearly places the next strong accent following the downbeat of m. 1 on the downbeat of m. 3. (It is questionable, however, whether his methodology of summing all types of accents is valid, because—as he acknowledges (pp. 154–55)—not all of them are performed accents.) Along similar lines, Cai (1986, 304) states “the first two measures, retrospectively, [give] the impression of being upbeats to m. 3 where G, the important motive note, corresponds with the downbeat.” There is another kind of rhythmic symmetry that spans all of mm. 1–3: the durations are retrograde-symmetric about the middle of m. 2 (Cai 1986, 288).
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13. Hook (2002, 142) concurs, saying that the A-minor triad “acquires some significance by the fact that it is the sonority heard immediately preceding the E-minor triad.” In contrast, Nattiez (1975, 323) does not differentiate the verticality on the last eighth of m. 2 from the third eighth of m. 1 and second eighth of m. 2; in his lower-level harmonic analysis, they are all analyzed as VI.
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14. “Every tone which is added to a beginning tone makes the meaning of that tone doubtful...In this manner there is produced a state of unrest or imbalance—The method by which balance is restored seems to me the real idea of the composition” (Schoenberg 1975, 123); “This unrest is expressed almost always already in the motive, but certainly in the gestalt” (Schoenberg 1995, 107). See also Carpenter (1988, 37– 38), which discusses both quotations.
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15. To be sure, the double-tonic complex in this piece is considerably weaker than in the pieces to which Bailey originally applied the term. Nonetheless, it serves as a useful heuristic for understanding the opening measures of the Intermezzo in particular.
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16. This C completes the second pattern of a sequence, however, as I show in Example 5.
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17. Rosen (1990, 115, Ex. 16b) includes a 2-voice, 3-measure prototype that is consonant with mine. His example transposes the left-hand part of m. 4, b. 1 up a 5th instead of a 3rd (representing this voice by a single pitch, E), and stops short of the G-major triad in the fourth measure of my Example 4.
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18. Rosen (1990, 115, Ex. 16a) focuses on the (unaltered) bass line beginning with the second beat of m. 3, interpreting an implied ascending sequence here (E–A, F–B).
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19. Cai (1986, 288) recognizes a “rhythmic reversal” in m. 7 but does not mention that it constitutes a return to the opening.
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20. F♯ tonicizes G in the traditional sense, acting as a(n upward) leading tone; E♭ is, in the dualist sense, a descending leading tone.
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21. Or, as given in parentheses in Example 5, mm. 6–9 may be heard (retrospectively) as a 4-beat hypermeasure. Another, more abstract interpretation might understand mm. 6–7 as an expanded “3” and mm. 8–9 as an expanded “4.”
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22. hat m. 9 constitutes a hypermetric strong beat suggests that the parallel m. 7 might also be interpreted as a strong beat. In this reading, either there is a hypermetric reinterpretation in m. 7, or mm. 4–6 are understood to be a triple hypermeasure (like mm. 1–3). While this reading has some merit, I find it difficult to hear in light of the ascending sequence in mm. 6–9 and for reasons I shall enumerate later.
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23. That F♯ leads back to C major may seem counterintuitive, but it is worth remembering that the first time F was inflected to F♯, it served in a tonicization of V of C. Vestiges of this tonicization can perhaps be heard in the implied voice-leading wedge D (m. 11)–C♯–C♮ (m. 12)–B (m. 15) and E (m. 11)–F–F♯ (m. 12)–G (mm. 13ff.). Cai (p. 296) argues that there is a “much elided cadence” here, with both V-of-V and V chords omitted.
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24. The sostenuto in m. 10 is omitted in m. 22, and a new crescendo appears in m. 23. These two changes propel the music into the B section. Also, the accents in mm. 11–12 are replaced with sfs in mm. 23–24.
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25. The right-hand part in m. 30 is literally a major 6th below that in m. 26; the left-hand part in the first half of the measure is transposed up by major 3rd.
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26. This sequence differs from the one usually indicated by the moniker “ascending 3rd”; the more common ascending-3rd sequence pairs root motions by descending second and descending fifth and alternates diatonic triads and (applied) dominant-7th chords. Jersild (1982) comes close to a label for the sequence based on DOWN-THIRD-UP-FIFTH, calling the sequence that reverses these two root motions “Rising 5th in ascending-3rd progression” (“Opadgående kvintfølger i stigende tertstrappe”). The first part of his label corresponds to “UP-FIFTH” and the second part corresponds to the interval of transposition, the sum of “DOWN-THIRD” and “UP-FIFTH.” A chromatic version of this sequence appears at rehearsal 2 of Bruckner’s motet “Ecce sacerdos.” For more on sequence classification schemes, see Ricci (2002 and 2004).
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27. Rosen (1990, 114) also notes the altered bass pitches in these measures relative to the opening, and points out that each dotted-quarter-note pitch is the root of the harmony beginning the next measure.
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28. This example is inspired by David Lewin’s study of cantus-firmus technique in Brahms’s music (Lewin 1990).
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29. This tetrachord (G-A-B-C) is presented explicitly in mm. 3–4.
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30. The pianist must therefore be careful not to overemphasize the return of J at its original pitch level. To reflect the overlap between these two statements of J, I think it is more appropriate to play the E♮ softly, in which case the listener does not recognize the restatement of J on E♮ until after it has already begun.
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31. Smith 2006 discusses large-scale examples of this type of harmonic ambiguity in Brahms’s G-major String Quintet op. 111 and the B-minor Rhapsody op. 79, no. 1.
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32. This melody also appears at the conclusion of the B section, in mm. 67–71. The absolute durations of the pitches in mm. 41–43 of op. 119, no. 3 are approximately equivalent to those in the B section and codetta of op. 119, no. 2.
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33. Interestingly, the last sounded pitch in op. 119, no. 2 is E4, the first pitch of the melody in op. 119, no. 3.
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34. Rosen calls the return of the opening material “elliptical,” observing that although the rhythm of J returns in m. 45, its pitch pattern in augmentation returns in m. 41. On the sophistication of Brahms’s recapitulatory procedures in sonata forms, see Webster 1978 and Smith 1994.
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35. Brinkmann (1984, 111) observes a parallel between the B♭s and C♯s in A₂ and A₁-B, but does not mention the retrograde relationship and does not continue beyond these two pitch classes.
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36. Thus m. 49 continues a process begun in m. 7: the inner-voice figure first introduced in m. 7 is initially heard as falling on a weak beat, then in m. 9 as falling on a weak beat that is retrospectively interpreted (through its repetitions in mm. 10–11) as strong, and finally in m. 49 as unambiguously strong.
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37. The A♭-A line is doubled in the right-hand part.
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38. All but the upper voice are transposed up by major 2nd in this sequence, but the upper voice’s diatonicism (except for the D♯) seems primary (as in m. 50). Strict transposition up by major 2nd would produce F♯ and D in the second half of m. 53 and F♯ and G♯ in m. 54. Regardless of whether this sequence is heard as a departure from an up-by-major-2nd sequence or an up-by-diatonic-2nd sequence, the D♯ is an anomaly. Also, relative to m. 8, the only alteration is the D♯.
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39. The progression here echoes that of mm. 12–13, the site of the counterintuitive F♯ discussed in note 23. Here both the voice leading and the harmonic progression are normalized: the F♯, in the same octave as before, moves directly to G; the bass remains stationary, resulting in a more normative resolution of the vii°-of-V (over a $\hat{5}$ pedal) to a cadential .
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40. Alternatively, one may hear three complete statements of J in these measures, with overlaps on the downbeats of mm. 67 and 68: the pianist can suggest this interpretation by slightly emphasizing the left-hand Gs through the downbeat of m. 69.
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41. Other examples of this major-mode tonic chord-type occur in the second movement of Schubert’s first A-major piano sonata (D. 664), the Prelude from Wagner’s Tristan und Isolde (see Bailey 1985), and the final movement (Der Abschied) from Mahler’s Das Lied von der Erde—the latter two of which intertwine the same keys as the Brahms Intermezzo. On the use of this tonic chord in twentieth-century music, see Harrison 2002.
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42. Beethoven exhausts 19 of the triads in this 24-triad cycle (proceeding counterclockwise, i.e., an RL-cycle) in mm. 143–76 of the Scherzo from his 9th Symphony. For a study of the properties of this and other neo-Riemannian cycles, see Cohn 1997; a discussion of the Beethoven passage appears on p. 36.
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43. I omit from this example the A-E bass motions in mm. 4-5 and 8-9, which might be interpreted as participating in less well articulated statements of DOWN-THIRD-UP-FIFTH; the statement in mm. 8-9 ends with a major-minor 7th chord, perhaps prefiguring the two short cutting statements in the B section that end with major triads.
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The progression here echoes that of mm. 12–13, the site of the counterintuitive F♯ discussed in note 23. Here both the voice leading and the harmonic progression are normalized: the F♯, in the same octave as before, moves directly to G; the bass remains stationary, resulting in a more normative resolution of the vii°-of-V (over a $\hat{5}$ pedal) to a cadential .

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