On the Imagination of Tone in Schubert's Liedesend (D473), Trost (D523), and Gretchens Bitte (D564)
Abstract and Keywords
This article examines figures 1 and 2 in Riemann's 1914–1915 article. First, it examines the different aspect of Riemann's conception of tone: his notion of Klangvertretung, that any tone may project or assume meaning as one of the three elements of a major or minor triad. Second, it explores Riemann's notion of Klangvertretung as outlined in his “Ideen zu einer ‘Lehre on den Tonvorstellungen’”. Third, the article demonstrates the analytical utility of the concept, exploring how attention to the changing triadic-functional identities of tones in three Schubert Lieder offers an enriched view of structural and chromatic third relations in the works.
If we plunge straight to the heart of neo-Riemannian theory, it takes us to figure 3 in an article that Riemann wrote in 1914–1915 called “Ideen zu einer ‘Lehre von den Tonvorstellungen.’ ”1 This figure, reproduced as example 10.1, consists of three pairs of triads: C major and C minor on the left, C major and A minor in the middle, and C major and E minor on the right. These correspond respectively to the PRL transformations, as construed by neo-Riemannian theorists.2 I shall rehearse what these transformations are in a minute, but first I shall discuss what Riemann intended to portray through example 10.1.
By the time Riemann wrote his article in the mid-1910s, he had rejected the physical and physiological foundation for music theory, which had so famously led him to believing in the existence of the undertone series. He now confessed that finding a physical foundation for music theory was a mistaken pursuit. Its replacement would be a theory of the imagination of tone (a “Lehre von den Tonvorstellungen”), an idea he claims he had first postulated but lost sight of in 1873.3 This was to be a theory of the “ ‘logical activity’ of musical hearing.” This new discipline would be akin to the painter who “in advance, gazes inwardly upon a picture that he wishes to paint;” that is, the painter visualizes mentally before (p. 295) painting. Similarly, Riemann argued “a composer hear[s] inwardly and in advance all that he notates afterwards.”4
The key to Riemann's theory of the imagination of tone is “hearing ahead.” But it is not only composers who hear ahead: Riemann argues that performers, score readers, and even page turners should do this too. He adapts the relationship between hearing and notation depending on the agent: where the composer “hears inwardly” or “imagines” and then notates, others start from the notation and then “imagine” the music before sound takes place. That is to say, the performer sees a tone in the notation and imagines it before playing it; the score reader (who in Riemann's discussion is attending a concert) “is always some distance ahead with his eyes.” Similarly, the page turner, as Riemann emphatically puts it, does not so much “read along” as “read ahead” of the performed piece.
Riemann argues that a similar sense of anticipation is also possessed by yet another category of musician, namely the trained listener, who, if already familiar with a piece, will also imagine a tone before hearing it and according to Riemann will measure mistakes or out-of-tune pitches against his or her expectations. Although such listeners are without notation, there is still a visual aspect to their activity. Brian Hyer has explained this phenomenon in “Reimag(in)ing Riemann.” The listener sees the tone through a visual representation of tonal space, such as the image of the Tonnetz.5
So, in other words, the set of triads in example 10.1 arose in a brief pedagogical section of Riemann's article, in which he explores how students can hone their skills in the art of hearing ahead. One of the first things Riemann had to do, however, was to put a limit on his theoretical materials—or to put a limit on what the student might hear. He therefore secured a strictly triadic context for his theory of imagination: “today we hear individual tones and intervals always as representations of triads (major or minor ones) according to available possibilities.”6
Example 10.1 relates to his idea of hearing individual intervals. Riemann observes that the imagination of any perfect fifth or major or minor third may only ever be heard as representing two triads: one major, one minor. Imagining the interval of a perfect fifth yields only one possible major and minor pairing, namely the major/minor tonic, as shown in example 10.1; imagining a major third yields another unique major-minor pairing, namely the relative major and minor; finally, the right-hand pair C major and E minor in example 10.1 shows the unique major/minor pairing when a minor third is imagined.7 Neo-Riemannian theorists have (p. 296) used these observations about the nature of the two common tones and the single displaced tone to distinguish these three sets of triads: P, meaning “parallel,” is the transformation involving the common tones of the perfect fifth (C, G), with a semitone displacement (E to E♭, or vice versa); R, meaning “relative,” is the transformation with the common tones of the major third (C, E) and a displacement of a full tone (G to A, or vice versa); L, meaning “Leittonwechsel,” is the transformation with the common tones of the minor third (E, G) and a semitone displacement (C to B, or vice versa).8 Nowadays, these are generally taken to be the core transformations in neo-Riemannian theory—a point to which I shall return.
In this essay I wish to take a step back and scrutinize figures 1 and 2 in Riemann's 1914–1915 article (reproduced here as examples 10.2a and 10.2b). These relate to his theory of the imagination of a single tone—an aspect of Riemann's writings that has so far received no attention from neo-Riemannian theorists. Thus, in the rest of this essay, I shall first rehearse what Riemann understood by examples 10.2a and b, and then second, I shall investigate some of their theoretical implications for neo-Riemannian theory, and finally, I will explore their analytical potential in two songs by Schubert by comparing my Riemannian analysis with a Schenkerian approach.
So, first of all, what did Riemann intend by the material in example 10.2? Again, it is crucial to note that the examples comprise only major and minor triads. We have already covered the reason for this, and it is worth repeating Riemann's statement that “today we hear individual tones and intervals always as representations of triads (major or minor ones).” As can be seen in examples 10.2a and 10.2b, the pitch A is treated as 1̂, 5̂, 3̂ (in that order) in major and then minor triads, yielding six possible triads.9 Riemann has the following to say about example 10.2a: “One of the first, most basic exercises of the faculties of the musical imagination would have to be to imagine specifically each individual note in its six possibilities for the representation of a tonal complex.”10 Regarding example 10.2b, by contrast, Riemann says that “a single assigned note will be filled out, into a triad by the student by adding the two other notes.”11 So both of these are pedagogical exercises and serve as two sides of the same coin. In one case, the student extracts the common tone from the series of triads (example 10.2a); (p. 297) in the other, he or she starts with the common tone and provides the triads around it (example 10.2b). Note that the student is encouraged to see these triads as a “representation of a tonal complex.” I shall return to this observation later.
After presenting these exercises, Riemann went on to muse on the increased musical appreciation and aural dexterity a student would gain from doing them. If hearing a piece for the first time, a listener would know that the sound of a single tone is open to six possibilities, though Riemann suspects that the most likely possibility to come to mind will be the root of a major chord—an interesting conclusion considering Riemann's propensity for dualism. But if in possession of a score, Riemann points to some visual clues that limit the possible triads down from six—the most obvious being the key signature, which enables the student to narrow down the choice of triads to those suited to the major or minor key denoted by the signature.12 Riemann also points out that a tone in the middle of a piece can be exploited as a kind of riddle, especially if it is “strongly foreign” to the previous harmony; then, he argues, the possibilities are wide open all over again and the “solution” is only found in the composer's continuation. In such cases, the Riemannian student who is well versed in these exercises will be able (presumably at lightning speed) to relish in the riddle of possibilities, in the uncertainty of the continuation, and in the pleasure of the actual continuation. Significantly, the kind of hearing that Riemann advocates is very much “in the moment”—a point to which I shall also return when I compare Riemann's theory of tone to Schenker's theory of the Urlinie.
Earlier I noted that Riemann understood these six triads as a “representation of a tonal complex.” What are the theoretical ramifications of Riemann's claim? The tonal complex can be mapped onto the Tonnetz, which also features in his 1914–1915 article (see example 10.3a). In keeping with Riemann's theory of dualism, the six triads would feature in the Tonnetz as shown in example 10.3b. By contrast, a neo-Riemannian (or fundamental bass) reading places the same triads on the lattice as shown in example 10.3c. Riemann's configuration is naturally symmetrical because there are three major and three minor triads, and the former are labeled from the bottom while the latter are labeled from the top. In other words, when A serves as a 1̂, it generates the triad above and below it; when it serves as a 5̂, the “roots” of the triads are a fifth below and above it; and when it serves as a 3̂, the “roots” of the triads are also below and above it (this also means that 3̂ is always a major third away from the “root”). By contrast, in the fundamental bass system, all triads are labeled from the roots at the bottom of the triad and therefore the symmetry of how the pitch sits within the triads is not reflected in the labels. Given that theorists are generally drawn to patterns, they are far more likely to respond positively to the look of example 10.3b than example 10.3c. This may account for the general lack of interest in this collection of triads until neo-Riemannian theorists fashioned them into the PLR cycle, as in Riemann's own configuration in example 10.2a they do not at first sight seem theoretically or analytically useful.13
Even in terms of classic harmonic thinking (that is to say, dispensing with the Tonnetz for the moment and focusing on Roman numerals), they also seem a pretty useless set of triads. Taking A major as tonic, they form the following chords: I, IV, ♭VI, iv, i, vi (as annotated in example 10.2a). Note that in this scenario there is no (p. 298) dominant. Of course, it would be possible to create a dominant by instead interpreting the first triad as a dominant, as follows: V, I, ♭III, i, v, iii (also shown in example 10.2a). In the case of the former set of functions, the tone that generates the system is fundamentally a 1̂, whereas in the case of the latter, it is a 5̂. This need not be problematic from a theoretical perspective, but it at least predicts that if a piece of music were constructed entirely around a single pitch and if it were to establish its (major or minor) key around that pitch as 1̂ rather than 5̂, then our (imaginary) piece would lack a dominant. Or, to put this the other way around: if we want to gain the dominant, then A can be interpreted only as 5̂.14 Rather than lament the fact that gaining a dominant severely limits how the common tone can be interpreted, I shall instead explore the joys of how this common-tone theory can throw off the shackles of this apparently fundamental harmony. In other words, without resorting to Riemann's dualism, I shall argue that this complex of triads is theoretically and analytically useful. However, before getting to some analysis, I have two more points to make.
First, in the context of this chapter, the important point to remember about Riemann's two examples is that, in the case of example 10.2a, the student is expected to extract a single common tone from a complex of given harmonies, whereas in (p. 299) example 10.2b he or she generates the complex of harmonies from a single common tone. Translated into analytical terms, then, Riemann's two examples are useful for demonstrating how a single common tone may be extracted from the fabric of the music (example 10.2a) or, as a kind of opposite, a single common tone may be exposed in the texture in such a way as to suggest that the harmonies turn around it or emanate from it (example 10.2b). This chapter therefore explores further an idea I proposed in an earlier study about Schubert's treatment of pitch in Ganymed (D544), albeit from a Schenkerian perspective. There I suggested that Schubert's treatment of pitch enabled him to expand his harmonic horizons, and I argued that, in Ganymed, the reconstrual of pitch drives the unfolding of the harmonic structure instead of classic progressions or indeed the composing out from an Ursatz. As I demonstrated, Schubert generates harmonic stations by allowing a pitch to serve as a 1̂, 3̂, or 5̂ within a triad, and would also sometimes allow it to serve as a 7̂ in a dominant seventh. Similarly, the pitches in (foreground) voice-leadings that are suggestive of a particular harmonic move, such as 7̂–8̂ or a fifth in the bass, may be reinterpreted to deliver something other than the expected tonic and dominant harmonies.15
Others have also explored Schubert's use of common tones, notably David Kopp, whose transformation system is predicated, as examined further below, on common tones. Kopp has therefore also talked about the change of identity of pitches in Schubert's harmonic unfoldings, and he—rather nicely—includes their use in a greater array of dissonances than I did.16 Other scholars, Diether de la Motte and John Gingerich, have both observed the almost obsessive presence of the pitch G in the cello's melody of the secondary theme in Schubert's Quintet in C Major (D956). During the course of the theme, G serves as 3̂ of E♭, 5̂ of C major and 1̂ of G major.17
These studies (including my own) have tended to focus on common tones when they are obvious in the texture, usually serving as a distinctive melodic feature. As de la Motte observes, the pitch G is present in the melody for 56 quarter-note beats in 24 measures; this adds up to 14 measures worth of G, or more than half the melody.18 Indeed, as Riemann might put it, the listener “knowing the key of this piece” is likely to expect a high presence of G in the secondary area of a C-major movement. Schubert, however, translates the expected key into a tone, and his “imagination of tone” places it first as 3̂ of E♭ major—a key not strictly diatonic to C major—then as 5̂ of C major before locating it as 1̂ within G major. Even then, G major appears in a subsidiary harmonic position; the 1̂ in G major is only assertively stated on the arrival of the closing section of the exposition in measure 100.
This study will delve further into cases where Schubert's harmonies turn around a single pitch that is showcased melodically or texturally, as suggested by example 10.2b. But taking my cue from Riemann, I will also scrutinize cases where common tones are hidden and therefore need to be extracted from the harmonic fabric, as suggested by example 10.2a. Additionally, and again following Riemann's cue, I shall look to the key signatures and the harmonic contexts they imply in order to detect how Schubert plays with the imagination of tone. My case studies are Trost (D523), Liedesend (D473), and Gretchens Bitte (D564), all songs written during Schubert's phase of greatest harmonic adventure around the years 1816–1817.
(p. 300) The second theoretical point I wish to make before getting to my analyses of these songs has to do with what is arguably the chief debate in neo-Riemannian theory, namely which transformations should constitute the core ones. There are three opinions on this, represented mainly by Brian Hyer, Richard Cohn, and David Kopp. In his article “Reimag(in)ing Riemann,” Brian Hyer argued that in order to navigate the Tonnetz (in example 10.3a), four transformations are required: PLR + D. Subsequently, Richard Cohn appealed to “the law of the shortest way” and notions of “efficacy” and “parsimony” to argue that the fewest possible variables should be sought to navigate the Tonnetz. For him, only PLR are necessary. That is to say, Hyer's D transformation, which covers the horizontal axis of the Tonnetz, can be gained by combining LR (to go in the dominant direction) and RL (to go in the subdominant direction). So, for example, an authentic cadence, according to Roman numerals, is V–I; according to Hyer, it is D, and according to Cohn, it is RL. In 2002, David Kopp argued against Cohn's use of combinations of R and L to express the dominant, as it gives the false impression that one of the most common harmonic moves is a compound transformation. Although he agreed with Hyer's sentiment for a larger set of transformations, Kopp went further still and developed a common-tone theory for every possible direct transformation. He ended up with I, D, D−1, F, F−1, M, M−1, m, m−1, R, r, P, and S.19 So, how did he arrive at all these? He wrote out all of the possible triads that share one, two, or all three common tones with C major.20 As it turns out, no neo-Riemannian—other than Kopp himself—has used Kopp's all-inclusive theory of transformations; indeed, the fact that it is all-inclusive is seen as the argument against its usefulness. However, as shown in example 10.4, Riemann's set of six triads based on a single common tone offers a solution here: all of Kopp's transformations (except for I: identity) may be found in Riemann's tonal complex. It could be argued that deriving Kopp's transformations from a single common tone, rather than all three pitches of the triad, is more parsimonious, which is a crucial criterion for Cohn and others who have followed suit.21 Moreover, the collection of triads can also be formulated into a cycle, using only the core transformations, as in A+, F♯ –, D+, D–, F+, A–, A+ of example 10.2, using RLPRLP, respectively.22 To my mind, a particularly attractive aspect of Kopp's system of transformations—especially for the purposes of my analyses—is precisely the fact that it expresses direct relations among all possible transformations within the collection of six triads, and is not seemly confined to articulating an ordered set of maximum common-tone relations. And unlike classic neo-Riemannian theory, which favors fewer transformation types, there are no compound transformational expressions.23 Indeed, the system put forward here—as a revision (of the derivation) of Kopp's transformations—is one that is distinctly Riemannian: as Riemann's career progressed, he was interested in providing a full inventory of Klang relations.24 In this light, I propose that any of Riemann's six triads may be considered to relate to any other one at least on a theoretical level. How and why they relate as they do in compositional practice is another matter, and it is to some musical analysis that I now turn.
Let's begin by following Riemann's advice on how to imagine a tone. The key signature of Trost (D523) has four sharps and the first pitch encountered by the singer is a G♯ (see example 10.5). In this context, the singer, thinking only of the (p. 301) vocal line, is most likely to imagine the pitch as either 3̂ of E major or 5̂ of C♯ minor. The first surprise, then, is that it in fact serves as a 1̂ of G♯ minor. Pressing onward, we see that Schubert visits B major, then G major, and finally E major in this short 17-measure strophic song.
This song has already caught the attention of three scholars, namely Michael Siciliano, Harald Krebs, and Thomas A. Denny, the latter two of whom sought to theorize Schubert's harmonic schemes for songs that begin and end in different keys. Siciliano elegantly shows that all but the final transformations in Trost make their way consistently around the RPL cycle, and he argues that the cycle created by neo-Riemannian relations replaces the lack of a single tonic known to diatonic theory.25 Although Krebs argues a strong case for double tonics as an alternative to monotonality, he analyzes Trost in a single key (example 10.6). In part, the song is short enough to be contained in this way, but he also observes that it does not venture to any keys that are not easily reckoned within an overall E-major Ursatz. The only potentially awkward key is G major, but he shows this to be very much a low middle-ground event. Occurring as it does between two statements of the dominant, he concludes that G major is an “oscillatory progression” between the B major harmonies in measures 6 and 11.26 As Krebs summarizes in a subsequent study, all the conditions are met for the harmonies in Trost to be read as a logical progression in E major: there is a large-scale V–I, whereby iii and ♭III serve to embellish the dominant, and the Kopfton 5̂ (B) spans almost the whole song. Interestingly (given Riemann's comments on key signatures), Krebs additionally argues that the key signature clinches his argument that the song should indeed be regarded as monotonal, in E major.27
Thomas A. Denny responded to Krebs's analysis in his own attempt to theorize Schubert's key relations in songs that begin and end in different keys.28 His approach was starkly different. Instead of looking to voice leading, he looked for patterns in Schubert's harmonic stations themselves. He came up with three models. The model relevant to Trost is given in example 10.7. Denny explains the concept behind the model as follows: Ia and Ib are two separate but equal-ranking tonics, and the two Xs stand for other keys. Denny noted that generally the Xs tend to be a third away from their respective tonics, and moreover that a rising third relation often incurs a falling one in the second half of such structures. Indeed, Trost is Denny's showcase piece for this model: as the annotations show in example 10.7, the first part of the song rises a third from G♯ (p. 302) (p. 303) minor to B major and the second part descends from G major to E major; as it turns out, the relationship between the two Xs is also a third, though Denny's structural break deemphasizes this feature. In Denny's defense, this structural break is supported by the surface of the music in Trost. The shift from B to G major is the most aurally disjunct in the song, aided by the chromatic path (D♯ to D♮) taken by the vocal line.
There is an aspect of Schubert's choice of keys that is drawn out by Krebs's use of Schenker that is not explicitly obvious in Denny's method of analysis, namely that the tone B is common to all harmonies in this song. As shown in example 10.8, it serves as 3̂ in G♯ minor, 1̂ in B major, 1̂ of B minor, 3̂ in G major, 1̂ in B major, and 5̂ in E major. Although Krebs's graph shows the Kopfton B as starting in measure 3, the tone is clearly present in the harmony from the beginning of the song. What purpose, then, might a Riemannian reading of this tone serve? To answer this question, we must compare Schenker's imagination of tone with Riemann's.
An important distinction can be drawn between a Schenkerian and Riemannian conception of the imagination of tone. Both theorists sought to train the ear, but to do radically different things. Schenker argues the case for a long-term hearing of the Kopfton, in which the pitch is retained mentally as an 8̂ (1̂ ), 5̂, or 3̂ of the triad of the Ursatz. Such graphs in Free Composition as figures 15/1b, 2b–c, 3b–3c2–3, and 5a are helpful in demonstrating that how the primary tone is retained as 3̂ or 5̂ even as it is supported in the middle ground by a new harmony. Or—to pick a graph of a work more or less at random—the phenomenon of the mental retention of a pitch is illustrated by figure 130/4b, where the 3̂ is specified above a common tone E even when it belongs to A minor (vi) in the I–vi–I prolongation in C major.29 In other words, Schenker's conception of the imagination of a tone aspires to a background hearing that requires the mental retention of an 8̂, 5̂, or 3̂ despite harmonic changes underneath. Or, to demonstrate this through Trost, the primary tone 5̂ is mentally retained (or imagined) as 5̂ of E major, despite the (iii-)V–♮III–V motion that supports it until it begins its descent to 1̂. In a Riemannian conception, the pitch B in Trost should be traced as transforming its identity as each new harmony enters. The point is precisely to grasp the shifts from B̂ as (3̂, −) to (1̂, +) to (1̂, −) to (3̂, +) to (1̂, +) and finally (5̂, +), as illustrated in example 10.8.30
(p. 304) A few practical observations may be made about Schubert's presentation of harmony in relation to the theoretical derivation of what might be termed Riemann's “single common-tone group” of example 10.2. First, Schubert uses five of the six “aesthetic possibilities,” and clearly construed the available triads around B̂ in order to gain a dominant-tonic relationship.31 Second, the tone must be extracted from the surface texture in certain places and is placed in the ear by the melody in others. Although the vocal line does not include a B̂ in the first phrase (hence it does not feature in Krebs's graph until measure 3), the second phrase enters early on B̂, as if to anticipate the next new harmony. Meanwhile, the piano has had B̂ in its upper voice all along. As noted earlier, the new key, B major, is stated as V–I in measures 4–6, but the 64 53 formula serves to bring in the B̂ as (1̂, +) immediately, while providing harmonic motion underneath. The vocal line fractures any sense of continuity between B major and the G major of the next phrase because it moves chromatically in measure 6 (these correspond to Denny's Xa || Xb harmonic stations). By contrast, the piano retains the B̂ in the same voice, albeit an inner voice, in this passage; it shifts from (1̂, +) to (1̂, –) to (3̂, +). The exit from G major back to B major is altogether smoother, as the voice performs the task of repeating the B̂—again entering early, undoubtedly for effect, as the singer sings “nimmer lange weil’ ich hier.” Indeed, during this passage, the voice remains on B̂, changing from (3̂, +) to (1̂, +) to (5̂, +). The piano postlude brings out the B̂ once more, entering early in measure 14 and articulating a downbeat, marked with Schubert's characteristic double emphasis of fp and 〉. At any rate, there is no doubt that the common tone is a hallmark of this song, and that the harmonies in the song turn on that pitch.
Liedesend is one of two songs that George Grove criticized for carrying modulation to an “exaggerated degree” in his dictionary entry on Schubert. In an otherwise sympathetic defense of Schubert's modulatory strategy in the songs (he argues that the key changes are an important means of expressing the text), Grove saw no real justification for the keys in this song:
[I]n the short song Liedesend of Mayhofer (Sept 1816), he begins in C minor, and then goes quickly through E♭ into C♭ major. The signature then changes, and we are at once in D major; then C major. Then the signature again changes to that of A♭, in which we remain for fifteen bars. From A♭ it is an easy transition to F minor, but a very sudden one from that again to A minor. Then for the breaking of the harp we are forced into D♭, and immediately, with a further change of signature, into F♯. Then for the King's song, with a fifth change of signature, into B major; and lastly, for the concluding words…a sixth change, with eight bars in E minor, thus ending the song a third higher than it began.32
It seems Grove may simply have been objecting to the number of times Schubert modulates and possibly to what appears to be a large variety of keys: he lists no fewer than twelve, requiring six key signature changes. According to Grove, the song includes: C minor, E♭, C♭, D, C, A♭, F minor, A minor, D♭, F♯, B and E minor. What is there to observe about common tones in this set of keys? If the keys are taken at face value and represented by their tonic triads, then a search for common tones produces the groupings in example 10.9 (accidentals apply to individual triads). Each group of four triads (p. 305) is separated by a noncommon tone pair of triads: D and C majors, and A minor and D♭ major, respectively. As shown in the example, the first three triads share Ê♭ and the last pair of the group shares Ĝ♭/F̂♯. The next four all revolve around Ĉ. The final group is a series of fifth relations or D transformations, and thus in each case the 1̂ becomes the 5̂ of the next triad.
It will be recalled that Grove generally saw the motivation for key change in the words. In this case, it is almost too easy to offer a cogent explanation for Schubert's key changes: a new key is forged as the narrator depicts, in turn, the king on his throne, the bard playing his harp, the sweet tune he plays, the bard's inability to appease the king, his frustration at his lack of success (the bard breaks his harp), and finally the calm of the king, whose direct speech is then set to the cycle of fifths. Nevertheless, in the passage cited above, the only suggestion Grove makes regarding a hermeneutic motivation for Schubert's choice of harmony is the “breaking of the harp,” which “forces” a new key. Indeed in light of the common-tone links observed in example 10.9 between adjacent harmonies, it seems tempting to say that when the bard breaks his harp, the entry of D♭ “breaks” the common-tone pattern. However, Grove is not drawn to make any specific comment on the concomitant passage, namely the entry of C major after D major. The main gist of his commentary is to measure how quickly the keys go by and how closely related they are. Therefore he writes that after C minor, Schubert “goes quickly” through E♭ and C♭ major; A♭ “remains” for 15 measures; and, judging from Grove's language, we are as suddenly in D major, as the entry to D♭ is forced. Note also that he draws a distinction between the “easy transition” from A♭ major to F minor and the “very sudden one” from A♭ major to A minor. To be sure, in classic harmonic terms, A♭ major to F minor seems close because F minor is the relative minor of A♭ major, while F minor to A minor seems a distant move because they relate as i–♯iii. However, in common tonality, a move from F minor to A minor is achieved relatively easily through two semitone displacements around the common tone C. Such a conception still preserves the distinction in the degree of distance observed in the classical model because A♭ major and F minor have two tones in common, while F minor and A minor have only one.
Nevertheless, on closer inspection of Schubert's score something is amiss with Grove's analysis, and indeed it has to do with a misreading that emanates from taking in a visual clue (key signature) and narrowing down the imagination of tone (p. 306) to fit the signature. As noted above, Grove comments on each change of signature. However, after the signature change to no sharps or flats in measure 52, the singer sings an Â and Grove imagines it as 1̂ of A minor (example 10.10). This is a perfectly natural impulse. It even fits Riemann's advice on how to imagine a tone in the context of a given signature: one's first port of call should be to construe it as a tonic. An A, appearing after a signature of no sharps or flats, is obviously not going to be part of a C major triad. But Riemann also intended his listeners and score readers to be ready for surprises or “riddles.” Schubert's Â is harmonized by an F♯ minor triad. Grove would have done well to observe more carefully that the pitch needs to be imagined in the more unlikely scenario of a (3̂, –). Indeed, it forms part of the cadential pattern ii6–V64 53–I in E major. What effect does this correction have on the common tones found in example 10.9?
(p. 307) (p. 308) (p. 309) (p. 310) (p. 311) In substituting E major for Grove's misreading of A minor, the Riemannian student—versed in the extraction of tone, as cultivated by example 10.2a—will immediately observe that the single tone that unites the harmonies around it is Â♭/Ĝ♯, as illustrated in example 10.9. Indeed, the noncommon tone relationship in Grove's list of keys for the “breaking of the harp” is smoothed over as the Ĝ♯ of E major becomes Â♭ of D♭ major.33
If we now turn to the music (that is to say, to how these harmonies are composed out), we see that Schubert has done little to make the common tones we have been analyzing audible. Despite the common tones, Grove's perception that this song comprises one contrasting key after another, with the occasional smooth modulation, is accurate. The two first stanzas begin with arpeggiations in their respective home keys (C minor and D major), but in the approach to D major from C♭, the Ĝ♭/F̂♯ common tone is not exploited in any way. The move from C to A♭ majors does at least emphasize the common Ĉ in both the voice and piano. The entry of the fourth stanza is the smoothest in the song, as Grove observed: the move from A♭ major to F minor involves two common tones. Although we saw earlier how the breaking of the harp was less sudden than Grove observed, the exit from D♭ major to F♯ major is not presented as an enharmonic fifth relation on the surface because the F♯ section does not enter on its tonic. Instead, the pitch F̂♯, which appears in the voice and prominently in the accompaniment, is interpreted not as 1̂ but as 5̂ of F♯'s subdominant. The next main keys (B major and E minor) roll through in dominant-tonic relationships, although during the B major section there is a brief turn to D major; again, nothing is made of the common tone. By and large, then, the keys unfold, but little emphasis is placed on the common tone material in the succession of keys. The Riemannian student, carrying out an (aural) common-tone analysis of this song, will necessary rely on the training from example 10.2a to extract tones. Indeed, without the common-tone thread of the keys being emphasized aurally, the keys jar more. This may be one of the aural effects that Grove was responding to when arguing that the modulation was carried out to an exaggerated degree in this song.
In my final example, Gretchens Bitte (example 10.11), the common tone is aurally very striking from the very beginning of the song. It is placed in the most salient positions in the vocal line, articulating as it does the beginnings, midpoints, and endings of phrases. Indeed, it governs the harmonic maneuvers for some 33 measures of the song. In short, Gretchens Bitte seems to be a compositional incarnation of Riemann's singing exercise in example 10.2b.
As we know by now, Riemann advises the singer to begin by contextualizing a pitch in light of its key signature. The imagination of tone in the case of the vocal line's first D̂♭ is a relatively straightforward affair. Given the six flats in the signature, it is most likely to be either 1̂ of D♭ major or 3̂ of B♭ minor. It turns out to be the latter. The voice enters with a D̂♭ that occupies both the up- and downbeat.
The first vocal utterance spans the end of measure 14 to the beginning of measure 51, as the harmony traverses tonic to relative major. The vocal line both begins and ends with the D̂♭. The pitch thus starts out as (3̂, –) and becomes a (1̂, +). It also appears at the midpoint of the passage on the downbeat in measure 4. Here, it is 1̂ of its triad, accompanied as it is by the mediant major. After a brief piano interlude (p. 312) in measures 5–6, the next vocal section opens again with D̂♭ on the downbeat of measure 7, this time prepared by a larger leap than before, namely from an F below. The harmony has returned to the original key of B♭ minor and hence D̂♭ is again (3̂, –). The pitch changes identity as the phrase ensues, ending on yet another D̂♭, which is now (1̂, −).
Within these ten measures, as example 10.12 shows, Schubert's common tone has appeared in three of Riemann's six triads, namely as 3̂ of B♭ minor, 1̂ of D♭ major, (p. 313) (p. 314) (p. 315) and 1̂ of D♭ minor. Each of these harmonies is tonicized, even if only briefly. One might easily imagine that Schubert could venture next to G♭ major, one of his favorite harmonic spaces (though he prefers to use the key in a tonic-major context). However, his next harmonic turn is to the most unlikely of the remaining candidates among Riemann's six triads; he ventures to A major. The common tone is again placed in the vocal line, although this time as an upbeat to the descending A major triad that starts on the following downbeat (see measures 12–13). Ĉ♯ now serves as (3̂, +). A major is tonicized, and in this case remains active for an extended period of time (measures 124–26).
The remaining two triads G♭/F♯ major and minor, which would complete the full complement of triads united by D̂♭/Ĉ♯, are sounded in the next section of the song. It also begins with a double iteration of Ĉ♯, both as upbeat and downbeat for “Wohin.” The immediate context in which the pitch appears is a quick shift from A major to F♯ minor harmonies. F♯ minor is strongly implied but never explicitly arrived at measures 284–33, and then an F♯ major chord sounds, as Schubert leads us to B minor in measure 33. The C♯, thus, is first 5̂ of a minor dominant before asserting itself as 5̂ of the major dominant for an authentic cadence in B minor, as shown in example 10.12.
The singer of Schubert's song has, in a certain sense, completed the exercise set out by Riemann in example 10.2b. Not all of the triads serve as a tonic, but Riemann never said they had to. As shown in example 10.12, our singer has sung the triads in a different order. She starts always from the same pitch and sings B♭ minor, D♭ major, D♭ minor, A major, F♯ minor, and F♯ major. Her Riemannian task is done, but the song is not. Indeed, the fleeting presence of the last two triads, as well as their nontonic function, brings about a new harmonic space for the next portion of the song.
Before pressing on to examine the rest of the song, it is worth scrutinizing further the order of presentation of the harmonies around D̂♭/Ĉ♯. As can be seen in example 10.12, in addition to the common tone that has been the focus of our aural attention in the vocal line, there is always another common tone between adjacent harmonies. They unfold therefore in the smoothest possible order, producing the following transformations respectively: R, P, L, R, and P. Note also that they are not construed to produce a dominant anywhere; instead—and undoubtedly because the song sets out in a minor key—the natural tendency is to construe the triads around the common tone in such a way that generates a i–III relationship. But Schubert had options in this respect: if F♯ minor were his tonic, then he could have had both III and V. However, in opening up the song with D̂♭ as (3̂, –), and thereafter construing the harmonic motion around this pitch in the melody, Schubert both (p. 316) expanded his tonal palette and eschewed the most fundamental of harmonies, namely the dominant.
In this light, the passage in measures 33–35 is interesting. Given the shape of the vocal line, our Riemannian student is liable to assume (especially on looking ahead) that the harmony is likely to be G major, for an authentic cadence into C major. Schubert has something else in mind: he interprets the B̂ and D̂ and 5̂ and 7̂ of an E major harmony, without however treating it like a dominant seventh. Indeed, the music to the words “ich bin, ich bin alleine” does seem to stand alone—or at least apart—from the shape of the harmonies underneath it: the singer seems to be singing a line most suited to G major, while the accompaniment is working to E major. Her subsequent cries, “Ich wein,’ ich wein,’ ich weine,” also sound “alone.” While she repeats her words emphatically, the accompaniment wanders off: it neither underscores her apparent 7̂–8̂ in C major (it provides E major to C major) nor does the accompaniment comply with her simple descending line at the end of the phrase (it provides an interrupted cadence). That said, while the interrupted cadence is but a gentle departure from the expectations of the vocal line, it does bring about a Ĉ♯, which has been in our ear so prominently from earlier in the song. The piano asserts an accented diminished chord, with Ĉ♯ at the top as again the operative pitch pressing things to D minor. This gesture is, however, an upbeat to another snippet of melody in C major, where the Ĉ is clearly staked out by the voice (measures 38–39). With things apparently settled on C major, the reiteration of measures 354–39 is identical, save for the Ĉ (instead of B̂) upbeat at the end of measure 39.
At this point in the song, the voice and piano seem to be fighting each other, rather than, as it were, being in perfect harmony. Indeed, the passages in measures 36–37 and 40–41 where the interrupted cadence is found recall a much earlier passage in the song (measure 26) when Gretchen sang a descent from 5̂–1̂ in A major to the near-rhyming word “allein.” There—to the words “weisst nur du allein”—the voice and piano resolve the key together. The accompaniment, “knowing” where she is going harmonically, portrays a common understanding in this passage, but later it emphasizes her loneliness.
One might be easily tempted to make a grand hermeneutic gesture about the fact that the manuscript breaks off at this point; the song is incomplete—or so it at first seems. It ends with a change of key signature in measure 44, introducing four flats. John Reed argued that Schubert lost his way harmonically at this point and concluded that Schubert therefore abandoned the composition.34 Any poignant conclusions about Schubert's compositional fragment breaking off like the fragments of Gretchen's heart are quickly deflated if one takes into account more recent suspicions that the rest of this song was lost rather than never composed.35 However, on a more pragmatic note, we can turn to Riemann once more, but this time to “hear ahead” of the notation: if he taught us to hear a tone in light of a key signature, perhaps we can at least use the signature to imagine what the next pitch—and even the next harmony—might have been in the missing portion of this song. In calling upon the exercises in example 10.2, and knowing as we do that the focal pitch of measures 36–43 has been Ĉ, we can imagine the next pitch in the vocal line could (p. 317) also be a Ĉ. From the key signature, it is likely to be either 3̂ of A♭ major or 5̂ of F minor. I vote for a move to A♭ major. Benjamin Britten in his completion of Gretchens Bitte did the same, while N. C. Gatty introduced F minor (with a number of harmonic turns around Ĉ), although he altered the signature to six flats to expedite the return to the opening B♭ minor key.36
There is a difference between the choices Riemann and Schenker would make if they were imagining the likely harmonic context of this tone. Riemann would entertain either possibility, though given Schubert's predilection for ♭VI, he might vote for A♭ major (that is, Ĉ as (3̂, +)). Schenker, however, would be desperate by now to have a dominant for his bass arpeggiation—not least because after the motley of foreground keys so far in the song, the entry of Ĉ in measure 43 comfortably begins to look like part of an Urlinie descent from D♭. But it needs proper support: the F major harmonies in measures 37–41 do not qualify because they are not (foreground) tonics. So, an arrival of F minor after the key signature would begin to put things right for the bassline. Schenker could even argue that the minor dominant is common in minor-key pieces, and once reached, it invariably seeks the leading note to incur the structural interruption. This would nicely set up a return to the original key of B♭ minor—and moreover would restore order (I have characterized this hypothetical ending in example 10.13). Of course, there is no guarantee that Schubert would have returned to the opening key, as Schenker would undoubtedly prefer him to. By contrast, a Riemannian imagination of the rest of this song could be far more adventurous, allowing the fate of the harmony to lie, as it were, in the hands of the pitch Ĉ.
Whatever we might imagine the lost portion of this song to have sounded like, one thing is for certain: a Riemannian and Schenkerian understanding of Schubert's pitch material and choice of keys opens up vastly different possibilities not only for how the music might have continued, but also for how we should hear the music we do have. As we have seen, Riemann's idea of emphasizing the change in identity of a (p. 318) common tone contrasts starkly with the Schenkerian notion of structural common tones, particularly those that belong to the Urlinie and even more particularly, the Kopfton itself. Riemann's and Schenker's theories represent two different aspirations of hearing: Riemann's theory privileges the moment, where surface key—or even surface triad—is the focus of attention. Schenker's is a large-scale hearing, based in monotonality. The two theorists therefore also represent different conceptions of large-scale tonal structure: Riemann's system allows for a single pitch to anchor a harmonic complex, such that a song or section of a song is not so much “in a key” as “around a pitch”; for Schenker, a single pitch may indeed be prolonged for a long time but it must ultimately move to something else; it must generate counterpoint. For Schenker, the presence of a structural tonic and dominant in the Ursatz is paramount, while in Riemann's conception the need for a large-scale tonic and dominant can easily be obviated. In short, what Riemann hit on in his theory of the “imagination of tone” is not only a means to engage listeners, performers, score readers, and page turners but also a means by which composers expanded tonal space and went beyond the confines of thinking in terms of root motion.
(1.) Hugo Riemann, “Ideen zu einer ‘Lehre von den Tonvorstellungen,’ ” Jahrbuch der Musikbibliothek Peters 21/22 (1914–1915): 1–26. References in this chapter will be to the English translation: Hugo Riemann, “Ideas for a Study ‘On the Imagination of Tone,’ ” trans. Robert W. Wason and Elizabeth West Marvin, Journal of Music Theory 36 (1992): 81–117.
(2.) The neo-Riemannian designation for P is different from Riemann's. Riemann uses “Parallele” for our relative relationship; our parallel relationship is Riemann's “Variante.”
(3.) Riemann, “On the Imagination of Tone,” 82–83. To be sure, Riemann's main theoretical preoccupation lay in musical hearing (“musikalisches Hören”), although it manifested itself in different ways throughout his career. Riemann's doctoral dissertation was entitled “Ueber das musikalische Hören” (University of Göttingen, 1873).
(4.) Riemann, “On the Imagination of Tone,” 83.
(5.) Brian Hyer's article, “Reimag(in)ing Riemann,” Journal of Music Theory 39 (1995): 101–138, has been seminal to the development of neo-Riemannian theory, especially with regard to such technical aspects as the mapping of major and minor triads on the Tonnetz and their reconceptualization in a nondualistic, equal tempered space. At the beginning of his article, he scrutinizes the various Riemannian concepts that are obscured by the necessarily more narrow translation of nuanced German terms into the English “imagination.” As he explains, one important aspect that is lost in translation is Riemann's emphasis on the visual aspect of reading ahead; in this context, Riemann uses the word “Tonphantasie,” which stems from “phantazein” or “to render visible,” rather than “Tonvorstellung” (p. 103). For an assessment of the importance of Hyer's article to the technical aspects of neo-Riemannian theory, see Richard Cohn, “Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective,” Journal of Music Theory 42 (1998): 167–180.
(6.) Riemann, “On the Imagination of Tone,” 87–88 (my emphasis).
(7.) Riemann indicates these intervals using Arabic and Roman numerals for the pitches of major and minor triads respectively, and the triads are reckoned according to his theory of dualism. Hence in example 10.1, 1 and 5 refers to C and G respectively in the major triad, while I and V refers to G and C respectively in the minor triad; similarly 1 and 3 refers to C and E, while I and III refers to E and C; 3 and 5 refers to E and G, while III and V refers to G and E. Throughout this chapter, I shall refer to the pitches using nondualist designations of the scale degrees, borrowing the Schenkerian caret symbol. The implications of Riemann's conception will, however, be considered at the end of this chapter (see also n. 30 below).
(8.) Strictly speaking, Riemann's own explanation of these relationships was based solely on the common tones. See the explanation offered by Brian Hyer and Alexander Rehding, “Riemann, (Karl Wilhelm Julius) Hugo,” The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie, 2nd ed. (London: Macmillan, 2001), 363.
(9.) Riemann's dualistic conception is further evident in examples 10.2a and 10.2b as he proceeds in order of decreasing strength of the tone from generating tone to fifth to third, which in the case of the minor therefore yields (in our terms) D minor, A minor, then F♯ minor; if Riemann were thinking in terms of the fundamental bass and the strength of the common tone according to the overtone series, he would have ordered the minor triads as A minor, F♯ minor, and D minor.
(10.) Riemann, “On the Imagination of Tone,” 86 (emphasis in original).
(13.) The collection was systematized, although not derived from example 10.2a, by Jack Douthett and Peter Steinbach, “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations and Modes of Limited Transposition,” Journal of Music Theory 42.2 (1998): 246–249, and developed in the context of Schubert by Michael Siciliano, “Neo-Riemannian Transformations and the Harmony of Franz Schubert” (Ph.D. diss., University of Chicago, 2002).
(14.) Note that with this interpretation, we also gain a III and V for the minor key and that this is the only interpretation in which a dominant is gained for the minor key. The issue of whether or not it is problematic from a theoretical perspective to take the common tone in the tonal complex as 5̂ in order to gain the dominant finds a comfortable solution in a neo-Riemannian context: it helps to support Lewin's claim that the D (or DOM) transformation is reckoned as a descending fifth, an idea adopted by both Hyer in “Reimag(in)ing Riemann,” as explained on p. 108, and David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002), 169–170.
(15.) See my “Schubert, Theory and Analysis,” Music Analysis 21 (2002): 209–243.
(16.) The only reason I included just the dominant seventh was that my observations were driven by the harmonies that appeared in Schubert's Ganymed. Kopp has been criticized by Richard Bass for poor reasoning over his choice of which dissonances to include or exclude. As Bass points out, the augmented and diminished triads are out, but the dominant seventh and German augmented sixth are in (the latter because it as the same pitch content as V7). Bass has a point that some dissonances that are proximate to those included are inexplicably excluded. However, the elegance of Kopp's analysis of, for example, Schubert's Sonata in B♭ Major (D960) lies in the manner in which he exposes the pitch B♭ as the thread that unites not only the harmonic stations of the ABA´ sections of the first thematic statement but also the dissonant harmonies that bring about the return of B♭ major between sections B and A´; one would hope that—had one of the dissonances been, say, a diminished seventh—it would have featured in the system. See Bass, “Review of David Kopp, Chromatic Transformations in Nineteenth-Century Music,” Music Theory Online, 10:1 (2004), par. 7.
(17.) Diether de la Motte, A Study of Harmony: An Historical Perspective, trans. Jeffrey L. Prater (Dubuque: W. C. Brown, 1991), 218–219, and John M. Gingerich, “Remembrance and Consciousness in Schubert's C-Major Quintet, D 956,” Musical Quarterly 84 (2000): 619–634, here p. 620.
(19.) Kopp's labels attached to the transformations are explained in Chromatic Transformations, 165–176.
(20.) Kopp produces a table of how these transformations arise from common tone relations with the C major triad in Chromatic Transformations, 2.
(21.) The importance of parsimony as a criterion for a persuasive theory has been stated on numerous occasions by Richard Cohn. See especially his “Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations,” Journal of Music Theory 41 (1997): 1–66, and “Music Theory's New Pedagogability,” Music Theory Online 4.2 (1998), par. 13. The logical outcome of the principle is Cohn's hexatonic systems, which are outlined in “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late Romantic Triadic Progressions,” Music Analysis 15 (1996): 9–40.
(22.) See n. 13.
(23.) See especially Cohn, “Introduction to Neo-Riemannian Theory.” Cohn argues that the Tonnetz is a “canonical geometry for modelling triadic transformations” (172) and that the D transformation which Hyer added to the basic PLR group is “redundant” because it can be formed through the combination of R and L (172).
(24.) For a synopsis of this progression in Riemann's thought, see Henry Klumpenhouwer, “Dualist Tonal Space and Transformation in Nineteenth-Century Musical Thought,” The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge: Cambridge University Press, 2002), 466.
(25.) Michael Siciliano, “Two Neo-Riemannian Analyses,” College Music Symposium 45 (2005): 92, 101, and 105.
(26.) Harald Krebs, “Third Relation and Dominant in Late 18th- and 19th-Century Music” (Ph.D. diss., Yale University, 1980), 154; Krebs's graph is in this study as figure III.14, vol. 2, 70.
(27.) Krebs, “Alternatives to Monotonality in Early Nineteenth-Century Music,” Journal of Music Theory 25 (1981): 1–16, here, 2–3. The model for Krebs's analysis may be found in Heinrich Schenker, Free Composition (Der freie Satz): Volume III of New Musical Theories and Fantasies, trans. and ed. Ernst Oster (New York and London: Longman, 1979), sections 244–245 and fig. 110 (d).
(28.) Thomas A. Denny, “Directional Tonality in Schubert's Lieder,” in Franz Schubert—Der Fortschrittliche? Analysen—Perspectiven—Fakten, ed. Erich Wolfgang Partsch (Tutzing: Hans Schneider, 1989), 37–53.
(29.) Schenker, Free Composition, Figures as cited in the main text above.
(30.) A word on my notation: as was mentioned earlier (n. 7), the Arabic and Roman numeral annotations in Riemann's examples common tones distinguish between the same pitch in the context of a major and minor triad. The effect of this is most noticeable in example 10.1. Note how each of the two common tones is labeled differently depending on whether they form part of a major or minor triad, as we saw in n. 7. Although, for instance, the C and G ostensibly remain constant between C major and C minor, Riemann seems to suggest they transform from 15 to VI. It is worth exploring whether this is just a product of Riemann's dualism or whether there is some substance to the notion that a tone changes quality and that this could do with being expressed in its label. For Riemann, as is evident from examples 10.1 and 10.2, a single pitch in all its six triadic possibilities can be assigned a different label, thanks indeed to his dualistic conception. From a purely practical (or analytical) perspective, this has a certain advantage: one can write, for instance, that the pitch A is III and this simultaneously reveals the triad it belongs to ˚c♯. From the perspective of perception, it seems right to express that a pitch does change its quality depending on its context.
David Kopp has observed this, but turned to Hauptmann to explain how the multiple appearances of F in Schubert's Die junge Nonne (D828) are “not all the same F” (see Kopp, Chromatic Transformations, 261). He suggests it is advantageous to think of Hauptmann's dialectic labels for components in the triad, and he illustrates how the change in “meaning” of pitches comes about thanks to Hauptmann's dualistic conception of major and minor triads (Kopp, Chromatic Transformations, 58–60). In his dialectical system, I is root (or “unity”), II is fifth (or “opposition”), and III is mediant (or “synthesis”; therefore III is always a major third from the root). Thus, to take one example of how pitches change meaning when common tones exist between triads, in the case of the Leittonwechsel transformation, C major is C = I, G = II and E = III, while E minor is B = I, E = II and G = III. The common tones E and G are III and II in one triad but II and III in the other.
In this chapter I seek to specify the quality of the common tone in each triad of Riemann's tonal complex by adapting neo-Riemannian nomenclature familiar from the treatment of triads: (1̂, +) (1̂, –) (3̂, +) (3̂, –) (5̂, +) (5̂, –). Thus, (1̂, +) denotes the root in a major triad and (1̂, –) denotes the root in a minor triad; (3̂, +) denotes the third in a major triad and (3̂, –) the third in a minor triad; (5̂, +) denotes the fifth in a major triad and (5̂, –) denotes the fifth in a minor triad. I also introduce the symbol B̂ in order to denote a pitch, as opposed to a triad or key.
(31.) Neo-Riemannian cycles—whether LPR, LP (hexatonic), or RP (octatonic)—are intended to show how transformations bypass the traditional tonic-dominant diatonic relation. Whereas Siciliano emphasizes that Trost follows an almost perfect path through the LPR cycle, thereby lending order to the harmonic structure, I prefer to argue that in this case (unlike the case of Gretchens Bitte that we will examine shortly), Schubert chose the only two tonics from among the six triads that provide a diatonic framework for the song: G♯ minor has its relative major, and E major has its dominant.
(32.) George Grove, Grove's Dictionary of Music and Musicians, ed. J. A. Fuller Maitland (London: Macmillan, 1908), 329.
(33.) Richard Cohn has noticed that the series of keys (as they are established, rather than as they are identified by Grove) in Liedesend produce a kind of palindromic effect, with third substitutions, around the || mark: C–, C♭+, D+, A+, C+, A♭+ || F–, E+, D♭+, F♯+, B+, E–. After a colloquium that I delivered at Yale University (January 2007), Cohn pointed out to me how these keys turn back on themselves; I am grateful to him for sharing this observation with me.
(34.) As John Reed puts it, “The song, what survives of it, is of fine quality, and it is tempting to speculate about the reasons for Schubert's failing to finish it. The operative quality of his unfinished Faust pieces suggests that he may have cherished an ambition to write an opera based on the drama; but he was not ready for that in 1817, and in the final (C major) cadences one can almost sense the feeling of uncertainty about what happens next.” See Reed, The Schubert Song Companion (New York: Universe Books, 1985), 252. See also Maurice J. E. Brown, who also thought it was unfinished, in Schubert: A Critical Biography (London: Macmillan, 1958), 76.
(35.) Walther Dürr (ed.), Neue Schubert-Ausgabe: Lieder, Band 11 (Kassel: Bärenreiter, 1999), 292.
(36.) The completion by Benjamin Britten was published under the title Gretchens Bitte: Szene aus Goethes Faust (London: Faber Music, 1998), and N. C. Gatty's completion was published (without commentary or attached article) in Music and Letters 9 (1928): 386–388.