Many pieces which possess a harmonic structure predicated on third relations, such as Chopin’s mazurka and some of theWolf songs analyzed by Deborah Stein, undergo a smoothing-out process wherein chromatic mediant relations in early parts of the piece give way to diatonic third and fifth relationships toward the end. Unlike these works, Liszt’s ConsolationNo. 3 in D major begins diatonically and becomes more chromatic as it goes along (Ex. 9.2). The Consolation contains three distinct harmonic

Example 9.2 Liszt, Consolation no. 3, second episode

Figure 9.4 Liszt, Consolation no. 3, first episode

episodes in which tonic D anchors different structures based on third relations. The first episode, mm. 1–18, contains a simple oscillating relative mediant relation. The second episode, mm. 18–43, is more elaborate, incorporating an ascending circle of thirds which entails both diatonic and chromatic mediant relations. The third episode, mm. 43–61, is a coda consisting of an extended plagal cadence whose culmination is enhanced by a striking ascending chromatic-mediant third-divider.
In the first episode (Fig. 9.4), tonic D major is established by a simple cadence over a tonic pedal, after which the music modulates at m. 10 by conventional pivotchord means to F minor, its upper relative or leittonwechsel key. Immediately thereafter, the music becomes sidetracked: a diminished-seventh chord implying a move (as B D F A) to a C minor 6 3 , bass descending, moves instead (as D F A C) to
a peculiar-sounding first-inversion E  major triad while the bass creeps up in the “wrong” direction. In response the texture dissipates upward in a single line as if wondering where it is.2 Eventually lighting on an equally odd-sounding unprepared D major 6
4 (if the way is lost, why not just skip to the conclusion), the music pauses again as if to test if it has found the right spot, and continues on to a tonic cadence. Figure 9.4 depicts the disjunct nature of the low-level stepwise relationships from F to E  toD as binary transformations.3 On the higher level of the phrase, the oscillation between tonic and leittonwechsel defines a reciprocal relative mediant loop, RR.
The second episode (Fig. 9.5) begins exactly as the first, with an identical modulation to F minor. Here, though, Liszt follows the arrival to F minor with two after-cadences, the first at m. 29 reaffirming F minor, but the second at m. 31 suddenly introducing F major. Despite the similarity of these two short cadences, the one to F major sounds more like an arrival to a new tonic than a simple modal
substitution or secondary harmony. This stems in part from the sheer effect of two successive cadences, enhanced by the melody, which jumps an octave to a new register, giving the second cadence a distinctly new color. It is also enhanced by the

Figure 9.5 Liszt, Consolation no. 3, second episode

two measures of F major pedal point which follow. The overall motion from tonic D major to this point is the major-third chromatic mediant relation M−1, with constituents R and P.

Liszt now quickly destabilizes F major witha descending semitone in the bass, sending it by means of another R to A minor. Again there are two after-cadences, the first at m. 35 reaffirming A minor, the second at m. 39 breaking through to A major. This second RP series completes the second stage of an ascending majorthird (M−1) circle. Up to this point, there is a sense of relatively equal alternation
between R and P, eachstep in the circle tonicized yet temporary, yielding two measures later to the next.4 The harmonic relation of the minor and major triads is ambiguous: on one hand, the major triads may figure as pivot chords between minor tonics; on the other, the minor triads figure as intermediary chords in the major-third circle initiated by D major at the beginning of the section. The expected continuation of this process would be another RP alternation, A major–C  minor–D  major, preserving some of the sense of ambiguity as it reaches the tonic. But Liszt intervenes, as it were, in the process. As Figure 9.5 shows, the expected next step is dramatically bypassed as A major gives way directly at m. 41 to a D major cadential 6 4 at m. 43. This M−1 motion between LFM and tonic thereby completes
the major-third circle, resolving much of the structural ambiguity of this section in favor of the major triads, and revealing the deeper, primary structure initiated in m. 18.5 Thus the first section is built on diatonic R, which naturally leads by two applications back to the tonic. The second section relegates R to being a subsidiary element of a structure built on its “beat” level from chromatic M−1, which naturally leads by three applications back to the tonic.

Although the third episode (Fig. 9.6) begins like the previous two with a complete four-measure statement of the first phrase, it devolves into a coda occurring entirely over a tonic pedal point. The consequent phrase leads by m. 53 to an inflection to subdominant G major, its first appearance in the piece. It gives way by minor third, m−1, to B major at m. 55, which yields in turn by major third,M−1, back to tonic D at m. 57. The root of the B  major triad introduces a cross-relation withth e B  found in the G major triad. At the same time this process allows Liszt to revisit the cadential LFM of the previous section. Arriving this time by way of the subdominant
rather than the ascending third-circle, he renders the cadence differently, bypassing 6 4 and dominant and going directly to root-position tonic. There are two ways to interpret the structure of this passage. In the first analysis, shown in Figure 9.6a, G major initiates an upward third-divider whose middle term is B , so that the

Figure 9.6 Liszt Consolation no. 3, third episode: two views

higher-level process becomes a plagal oscillation, D/D −1. By contrast, in the second analysis, shown in Figure 9.6b, the LFM serves as the structural foil to the tonic, with G as an intermediate term, and a chromatic mediant oscillation, M/M−1, as th e higher-level process. Familiar diatonic arguments favor the first analysis: the primacy of the subdominant in the functional hierarchy, and especially the horizontalization of the minor subdominant in the IV–LSM–I progression. The second analysis relies more on context and a freer conception of tonality. As Figure 9.6b shows, the chord introducing the final cadence in all three episodes is a mediant: the URM in the
first, and the LFM in the second and third. This privileges the LFM by analogy with the previous sections. Also, a higher-level chromatic mediant structure is the more natural outgrowth of the mediant-controlled structures of the previous two episodes. In this light, G major represents another path than the third-circle to reach the LFM, which is the musically climactic chord in both the second and third episodes. Finally, the harmonic syntax of the final episode is I–IV–LFM–I. To paraphrase Riemann’s deeply reasoned conclusion, the lower flat mediant possesses the ability to close directly to the tonic and need not be considered inferior to the subdominant.6

Figure 9.7 Basic network diagram for Liszt’s Consolation no. 3

Both analyses have something to offer to the understanding of this passage, but in my mind the second is more in keeping with the details of the piece and with Liszt’s forward-looking approachto harmony.

Hence two processes unfold over the course of the Consolation; bothcan be read from Figure 9.7, which unites the main structural elements of the bass sketches above into a network diagram for the whole piece. The first process provides continual change in the nature of structural third relations, from leittonwechsel oscillation to circle of thirds to chromatic-mediant oscillation. The second, more long-range process supplants the diatonic third relations up to m. 40 with chromatic third relations from m. 41 on. Together they provide for coherence, development, and unity in a piece during whose entirety the dominant and subdominant are never tonicized. One advantage of the holistic approach in this analysis is its ability to express how the high-level diatonic R relation in the first episode is replaced by
M−1, becoming a lower-level element in the ensuing chromatic episode rather than retaining its status in an additive, diatonic RP process. Another advantage is its language, which permits the direct identification of a functional focal point, the LSM, and the description of the way in which it serves to organize the differing structural flows of the second and third episodes. These observations are possible only within a conception of true chromatic tonality, in which chromatic relations are understood to act in concert with diatonic relations rather than being dependent on them.