Sublimating Sharp $\hat{4}$: An Exercise in Schenkerian Energetics

[1] In the preface to Heinrich Schenker’s early treatise on harmony, published in 1906, one finds the following remarks:

. . . the theory of harmony presents itself to me as a purely spiritual universe, a system of ideally moving forces, born of Nature or of art . . .

I should like to stress in particular the biological factor in the life of tones. We should get used to the idea that tones have lives of their own, more independent of the artist’s pen in their vitality than one would dare to believe.⁽¹⁾

[2] Though originating only about a century ago, these ideas might strike us as belonging to an era far removed from modern-day theory. However, recent years have seen a renewed interest and respect for the intellectual climate within which this thought was cultivated. Spearheaded by the efforts of Lee Rothfarb, the term “energetics” has been resurrected to describe an approach to musical structure and expression that brings together such apparently diverse figures such as Schenker, August Halm, and, most famously, Ernst Kurth. In Rothfarb’s valuable essay on energetics in the new Cambridge History of Western Music Theory, he points to a number of characteristics shared among the theorists who have an energeticist outlook.⁽²⁾ Of these, the first two are of special interest to me here. First, Rothfarb speaks of the metaphor of the thematization of “force,” citing Schenker’s “biology of forces,” Halm’s “drama of forces,” and Kurth’s “interplay of potential and kinetic energies,” as examples. Second, and less obviously, Rothfarb identifies musical logic as an aspect of energetics, by which he means “understanding the succession of events in a piece as unfolding according to properties residing exclusively within the tones, and forces arising from their combinations.”⁽³⁾ In this paper, musical force and musical logic will form a background against which I will examine an unusual special case, in which a very forceful and very logically directed pitch, namely the raised fourth scale degree, is deflected away from its expected course. This particular drama of musical forces is suggestive of hermeneutic interpretation. This is fully in keeping with the energeticist outlook. While tones are the content of music, an “empathetic aural experience,” one which fully embraces music as metaphorically rich, allows us to interpret the activities of those tones as meaningful, even intentional. Rothfarb describes this experience from the energeticist perspective:

Tones, as dynamic symbols, as organisms, as sonic embodiments of psychic energy, attract and repel, strive toward and away from each other.⁽⁴⁾

I will proceed from the notion that the more exact a structural description one can generate for the tones in question the more precisely one can localize its possible fields of meaning. I will return to this issue is my conclusion.

[3] One more preliminary point: My structural description will rely largely on a Schenkerian approach to tonal and temporal structure. A Schenkerian analysis along energeticist lines might strike some as incongruous. Ernst Kurth, the theorist most strongly identified with energetics, was the subject of withering criticism by Schenker and his followers, most notably Oswald Jonas.⁽⁵⁾ Nonetheless, Rothfarb has argued that their underlying attitudes toward the aesthetic understanding of music are cut from the same cloth.⁽⁶⁾ For Jonas, Kurth’s analyses failed to recognize an underlying relationship with species counterpoint that provided music with its structural integrity, and therefore misread its harmonic basis.⁽⁷⁾ I think this is a fair criticism of this aspect of Kurth’s work, but the added specificity of Schenker’s method ought not to conflict with other aspects of energeticist approach. Instead, it should render it more fine-grained, concrete, and ultimately more defensible as a holistic analysis. The following analyses may serve as a test case, presenting an exercise in what one might call Schenkerian energetics.

[4] I began by quoting Schenker on harmony, but, as I have suggested, I want to localize the force of that harmony in a particular step-class, the fourth scale degree in its raised form.⁽⁸⁾ This is apt because one of the most strongly directed motions in tonal music is modulation to the dominant—consider what a dramatic role that motion plays in sonata-form movements, among other types. Of course, the simplest sign that we are modulating to the dominant is the appearance of sharp $\hat{4}$, the unique tone needed to define the goal key, and its leading tone at that. Further, a powerful way the confirm a new key is to arrive clearly on its dominant, for which ♯$\hat{4}$ in that key is a useful ally as an applied leading tone to V.

[5] To see how this works in a typical piece, consult Example 1, which reproduces most of the exposition of the first movement of Mozart’s familiar Piano Sonata in B-flat major, with some annotations. When the elegantly ornamented first phrase is repeated an octave lower, the first difference we notice is that the E flat on which we comfortably rested in measure 2 is replaced in measure 12 by an E natural. (For simplicity’s sake, I will refer throughout to any raised fourth scale degree as sharp ♯$\hat{4}$.) That E natural in measure 12 effects a sudden release of energy; it sets off a ripples of active sixteenth notes that arpeggiate the new dominant back up into the original middle register. We are now effectively in F major, but, absent a full thematic statement, we still feel we have not quite settled in the new key. Mozart strengthens this arrival by introducing ♯$\hat{4}$ of F major in measure 17, followed by five bars of standing on the dominant and a rhetorical pause. Besides the dynamic energy of the modulation, what I also want to point out is how much the fluctuation between natural $\hat{4}$ and sharp $\hat{4}$ pervades this music. Mozart finds opportunities to work it into even the smallest decorative figuration, as in measures 4 and 6, for instance. Later, after ♯$\hat{4}$ of F major is introduced, B flat and B natural are in a near constant play, vying for our attention.

[6] To be sure, this music is the quintessence of Classicism’s lyrical mode, but under this elegant veneer, little sparks of ♯$\hat{4}$ inflame the music with energetic impulses that belie its placidity. Of course, this modulation scheme is a common tactic in sonata forms, and it is just as common to emphasize the subdominant, the natural $\hat{4}$, in the recapitulation, to act as a stabilizing counterbalance to the modulation to the dominant. The commonality of this usage does not diminish its effectiveness; it is the dramatic highlighting of the modulation to the dominant that is in large measure responsible for sonata form’s dynamic vigor. Sonata form aside, ♯$\hat{4}$’s energetic power shows itself in other contexts as well. It can serve very well as an embodiment of heroic triumph, especially when it surmounts the more neutral natural $\hat{4}$.

[7] Example 2a presents the familiar “Eroica” theme, here in its incarnation in the finale of the ballet music from the Creatures of Prometheus, Op. 43. This melody executes a deliberate and steady ascent to scale degree five, as my annotations show, and falls back to the expected half cadence. After the double bar, a faster ascent gets stuck on $\hat{4}$, and all parts stamp their collective feet in frustration. The only way out of this $\hat{4}$ is down: as a chordal seventh, it is obligated to resolve down to the third of the tonic chord. But no: in a heroic effort, this A flat pushes upward through A natural to B flat.⁽⁹⁾ Sharp $\hat{4}$ wins out over natural $\hat{4}$ and the energy of this motion pushes the line past B flat to C.

[8] This results in an odd formal design: one might have expected the closing bars to return to the opening melody, perhaps in the manner shown in Example 2b, which would also satisfy the tendency of the chordal seventh to resolve to G. However, allowing A flat to fall passively back to G would not embody the same exuberant sense of heroic resolve. Recall the two aspects of musical energetics I highlighted in Rothfarb’s account: musical logic, and force as a thematic element. The former is not in play here: notice that ♯$\hat{4}$ is not involved in a modulation to V, so its presence has no logical necessity. Its usurpation of the chordal seventh is a manifestation of pure force; this “non-logical” path is therefore charged with “extramusical” significance. Sharp 4 seems to speak: “So there, I’ll do as I wish!”

[9] To underscore that this move really merits such weight of meaning, I will refer to the passage excerpted in Example 2c, which reproduces the final appearance in the ballet of this celebrated theme, just before the Allegro molto that brings this finale to a rousing close. This last time the insistent stop on natural $\hat{4}$ is abruptly compromised by the bass’s chromatic step into a diminished seventh. Suddenly A natural gets a place of its own, as the third of an F major triad in an apparent modulation to F major.⁽¹⁰⁾ As shown in the sketch in Example 2d, the top voice actually continues to retrace the path it took before, taking the A natural to B flat and then C as it returns to a cadence on E flat major. In keeping with the lighter character of this ballet, ♯$\hat{4}$ is not overly insistent about its moment in the sun: Having shown us that it has the force to derail the course of events whenever it pleases, it can relinquish to the remainder of the finale the celebration of tonic arrival.

[10] As a rule, allowing ♯$\hat{4}$ to satisfy its desire to rise would seem to belong to a general category of positive outcomes: logical consequences ensuing as expected; purposeful, directed motions; the surmounting of obstacles, the satisfaction of desires, and so on. It would stand to reason that denying ♯$\hat{4}$’s inherent impulse would naturally result in a host of negative connotations belonging to some semantic category of denial.⁽¹¹⁾ However, this is not necessarily the case; the myriad nuances of context can do much to enrich the possible meanings we might attribute to tonal structure. I will proceed now to an examination of examples in which an apparent denial of ♯$\hat{4}$’s tendencies can seem to have a decidedly positive cast.

[11] Example 3a provides the opening section of the touching little aria, now attributed to Gottfried Stölzel, that J. S. Bach included in his compilation for Anna Magdalena. Harmonically, the first four bars are a simple statement of E-flat major. The fifth bar begins a modulation to V with as clear a signal as one could want: a ♯$\hat{4}$ in the new key aimed for its dominant through an applied leading tone. (Note that the same passage will recur in the tonic key in measure 14 to bring the piece to its conclusion.) Thus in bar 5 the force of ♯$\hat{4}$ sets the course; bar 6 would seem to lead that E natural to a over F. However, that does not resolve and turns out instead to be a passing chord into bar 7. Here, surprisingly, the diatonic $\hat{4}$ reappears, apparently canceling out the leading tone power of E natural. (Compare the less poignant and more prosaic hypothetical version in Example 3b, which allows the E natural to resolve to V and minimizes the contrast with E flat.)

[12] The effect is a curious dissolution whose meaning may be found in the melody’s disjunct tracings. These are charted in the melodic analysis of the first phrase given in Example 3c. (Note that this is not a hierarchical voice-leading analysis.) The melody’s opening divides into two lines as shown by the separate beaming. In bar 5, the upper line freezes on the curiously dissonant D while the lower line steps deliberately downward to the E flat that is natural 4. That E flat has both momentum and inherent tendency to resolve down to D, but in bar 7 it is abruptly shifted up to rejoin the upper line’s D, effectively joining both melodic strands into a united descent to the cadence. This melody enacts a tonal narrative of the dissonant separation of lines that are brought together into consonant resolution: a realization of the text’s “If you are with me, then I go with joy to death and to my rest.” (Example 3d provides a fuller voice-leading context to supplement this reading.)

[13] The pivotal moment of melodic reunion hangs, of course, on the natural $\hat{4}$ that contradicts the ♯$\hat{4}$ of the bass. Sharp four seems to relinquish its force, not because it is denied, but because it is given up willingly. The modulation to V passes from a state of tensed energy into the condition of passive acceptance embraced by its text. The powerful impulse of ♯$\hat{4}$ is not so much negated or denied as it is redirected, or transmuted into a different state. I can think of no more appropriate characterization than to call this a sublimation.⁽¹²⁾

[14] I will elaborate more on this expressive category presently, but will first consider a more profound counterpart to “Bist du bei mir,” which is found in the final aria of the St. Matthew Passion. Its opening instrumental ritornello is reproduced in Example 4a; a voice-leading sketch is given in Example 4b. The bass is of particular concern to us here; it begins by executing a slow descent while the upper lines weave around each other, the latter a representation of the text’s central conceit of burying Jesus, both literally, and figuratively within the soul of the penitent. It is this sense of achieving a higher state that calls sublimation to mind: “Mache dich, mein Herze rein,” (“Make yourself pure, my heart.”). The bass’s first descent leads to an expected dominant in measure 4; the second descent in measure 6 begins on the IV chord but rapidly plunges to a unexpected E natural, which is of course ♯$\hat{4}$ in this home key of B flat. Again, this powerful harmonic impulse ought to be the force directing us to a cadential dominant. Instead, it passes right through the immediately following V chord, propelled by the agitated interplay in the upper voices, before settling on a low E flat, that is, to the diatonic fourth scale degree. It is this form of $\hat{4}$ that carries through to the closing V-I. The degree to which ♯$\hat{4}$ is a rhythmic crux of the phrase is disguised by its metric freedom: Example 4c shows that the apparent downbeat can be heard to shift to mid-bar, and then even a beat earlier, placing the E natural in a metrically accented position. Again, this sublimation of the harmonic impulse of ♯$\hat{4}$ enacts in tones a willingness, even a desire, to embrace a higher state in which powerful impulses are muted or transformed.

[15] I will now examine more closely the idea of sublimation and how it might apply to music as an expressive category. There are two basic and seemingly quite different meanings, and, oddly, both of them are appropriate here. The first derives from chemistry: the process by which a solid changes into a gaseous state without first becoming a liquid (or the reverse). The second is psychological and particularly identified with Freud: to redirect an impulse of a primitive or visceral nature into one of a more elevated or uplifting kind. The significant element here is that the impulse is not denied but rather transmuted into some other form. Transmutation is, of course, a link between the chemical and psychological meanings; the latter has value-laden connotations of uplift or moral improvement, tied to the archaic sense of sublimation (and to its root meaning of “lifting up”). The aura of moral uplift is easy to connect to the two Bach examples, but this should not mean that the previous two examples imply negative outcomes. In the Mozart sonata, the logic and energy of the modulation is satisfying to experience; in the Eroica, the rise of ♯$\hat{4}$ is invigorating and pleasurable. The rise or fall of ♯$\hat{4}$ is not a matter of diametric opposites but of two different sorts of positives that may arise from the particularities of context. What can make this musical analogy so salient is its ready isomorphism: in the musical structures, scale degree four is still present, but the inflection from raised $\hat{4}$ to diatonic $\hat{4}$ is not its most instinctive path. In psychological sublimation, the impulse is not expunged, but redirected into something more positive. The chemical analogy is even more concrete; its essence is that an expected step, from solid to liquid, is skipped over, just as ♯$\hat{4}$ passes past V to return to natural $\hat{4}$. One is tempted to say that the force of ♯$\hat{4}$ simply evaporates, an image that I think will presently seem quite appropriate.

[16] This lengthy prologue brings me at last to two fuller analyses of pieces where the sublimation of ♯$\hat{4}$ plays a central expressive role in the musical narrative. These two works, composed at virtually the same time by composers one would not normally associate, have markedly different treatments of ♯$\hat{4}$’s energy, resulting in highly individual expressive worlds. It is important to note that although sublimation will be applied to the analysis of both pieces, there is nonetheless a wide divergence in expressive affect and meaning between the two.

[17] The first of these is Debussy’s first Arabesque. Familiar as it is, one detail that always puzzled me: the lack of an A as the first note in the right hand (and the F sharp in the next bar; both occur as expected in later statements). True, omitting the first note suggests the more elegant effect of beginning in the middle. Nonetheless, the missing A seems significant, a clue perhaps; one even feels for it a certain fondness in its absence. It plays a structural role as well. Example 5 shows a voice-leading sketch of this opening music in three of its manifestations. The opening’s easy descent traces out a prolongation of IV⁶, leading to the closely related II⁷. The linear progression from A to E that fills out the IV⁶ is an essential whole, and an important initiator of other descending motions throughout the piece (as the other two sketches labeled b and c in Example 5 show). The opening melody soars back up to that A, now not implied but insistently elongated, just in time for it to become a seventh over V. Its lazy fall in parallel sixths retraces the previous A to E descent, letting the resolution of the seventh to G sharp appear in the lower register and leaving that A ringing as the most prominent tone last heard in that register.

[18] The pitch A is curiously absent in the following bars as the music luxuriates in tonic arrival in measure 6, the pentatonic oscillation between B and C sharp echoing the bass motion C sharp to B that underlay the previous bars. This apparent phrase ending gradually turns into a beginning as the bass rises to F sharp and begins to gather up energy. We are prolonging II, headed for V; as the impulse increases we pick up an A sharp—♯$\hat{4}$!—along the way. By the stringendo in measure 13, things become urgent: the repeated ninth appoggiaturas insist that we must—we will—resolve to a V chord. But, of course, at the last moment we think better of it and release the energy of ♯$\hat{4}$’s harmonic impulse back into natural $\hat{4}$; what appears is nothing other than that pointedly missing A, now at once in the middle of things and an initiator of a new phrase. The force of ♯$\hat{4}$ is sublimated into A natural, a welcome and pleasurable outcome. The desire for V simply evaporates away; the V is skipped as elements of the II continue their prolongation into the related subdominant harmony in measure 17.

[19] I would identify this sublimation of ♯$\hat{4}$ as the central expressive crux of this piece. Its agent of sublimation, natural $\hat{4}$, takes on the character of an independent operator; it seems to need to assert itself, in defiance of the usual tendency for a tonal piece to modulate to, or at least tonicize, the dominant. (This piece never does.) The highlighting of this pitch even plays a role in the work’s elastic phrasing, which is analyzed in Example 6. At the top, 6a sets out a hypothetical model for the opening progression with a more even, normative pacing. Example 6b is a rhythmic reduction of the actual piece. It shows how this progression is expanded to highlight and elongate the arrival of the sounded A. The continuation fills eight bars, with A sharp arriving in that final bar; the subsequent expansion of a single harmony builds tension released only at the sublimating arrival of the next A.

[20] Returning to the voice-leading sketches, the first return of the first phrase is shown in Example 5b. The leisurely descent from A now has a different outcome, a languid arrival back at the IV chord, providing natural $\hat{4}$ with an even fuller prolongation. The piece leans even further toward the subdominant side, before passing to a cadential II-V-I. This cadence is more and more broadly drawn out, a process depicted in Example 6c.

[21] A middle section follows; it begins in A and the subdominant flavor is rich and creamy. Germane to our narrative, there is not a single A sharp in this part of the piece to disturb our enjoyment of A natural.⁽¹³⁾ The return of our opening music is identical for its first sixteen bars; a different course is taken in the music following the sublimation previously described. Example 5c shows that the structural outlines are the same, but beautifully recomposed for a more conclusive close, and in a lower register. Part of that more satisfactory conclusion is the drawn out and deliberate descent of A to the tonic, the same stepwise fourth implied in the first four bars and later repeated; the phrase expansion is shown in Example 6d.

[22] The closing flourish (not shown in these examples) is harmonically odd. It seems that it ought to be a plagal cadence, a IV chord with added sixth decorating the tonic, but the A is omitted leaving G sharp in its place. Having resolved as fully as possible, natural $\hat{4}$ seems content to bow out gracefully.

[23] The sublimation of ♯$\hat{4}$ in Debussy’s Arabesque enacts a marked and deliberate flouting of musical logic, that being the logic of the tonicization of V. It does this not by a kind of denial but by a transmutation of its impulse to a lower level of energy, one that seems to reveal new, and pleasurable possibilities. What grounds this exercise in musical hermeneutics is the specificity of linear and harmonic details brought forth in the analysis, among them, the fact that ♯$\hat{4}$ strongly implies a very definite tonal goal, and allows its evasion to be just as clearly defined. What is equally important is the specificities of context through which a sublimation is actualized and through which its meaning is nuanced.

[24] The expressive circumstances differ vastly in my final example, the third movement of Brahms’s String Quintet, Op. 111. I will deal mainly with the G-minor part, which is a kind of minuet, albeit one with none of poise of a Classical example. Rather, this music is all agitation and nervous energy contained within a forced composure. The two-bar opening is oddly hesitant; lacking the upbeat that joins this idea in the second two bars, the opening barely covers two notes before halting to catch its breath. The halt is significant: it is ♯$\hat{4}$, part of a strikingly dissonant chord. A resolution to V is not forthcoming; fortified by an upbeat, the second pair of bars repeats this figure but deflects ♯$\hat{4}$ back to its natural state. This sublimation is brief, and hesitant, but rich with meaning presently to be revealed. The melody proceeds with a more fluent four-bar span from G to D, but bar 8 once again gets brought up short by the abrupt change of harmony on the second beat. A twisting figure takes us to the cadence, which oddly arrives first in the melody, then again two bars later as the lower voices play catch up. Example 7 renders these events as a voice-leading sketch.⁽¹⁴⁾

[25] I have called this opening a sublimation of ♯$\hat{4}$, though at first it hardly seems worth the attention. How different from the expansive luxuriance of Debussy’s Arabesque: Brahms can hardly touch on ♯$\hat{4}$ before backing away from it, and the natural $\hat{4}$ that sublimates it barely gets its chance to resolve to B flat, which occurs almost incidentally in the following upbeat. The piece seems hesitant to take a stand: Will ♯$\hat{4}$ be willingly sublimated or not? Subsequent events show that the issue is not forgotten. The middle part begins conventionally enough, moving from a previously tonicized D minor to C minor, apparently about to complete this sequence to lead to Bb major. Notice that the top voice has picked up the F-E-D at the cadence before the double bar and is now presenting this third in expanded form, as shown in the sketch in Example 7b. Instead of an arrival on B flat, measure 32 brings a deceptive cadence; the G-flat major chord rings with an eerily hollow texture in which the cello doubles the first violin’s line (and the other parts duplicate its content in other ways). The top voice D flat that replaces the expected D natural is a signal that something is wrong; the music cannot let this go and harps on it again and again, creating a kind of metric expansion with an accelerating rhythm leading to a hemiola. What follows is at once logically expected and strangely bewildering.

[26] The sforzando at measure 43 brings an augmented sixth that leads conventionally to a dominant (with a cadential ). However, the context Brahms has built up invests this moment with three special significances:

1. The D flat on which the music was stuck is now transformed into C sharp, taking on its role as ♯$\hat{4}$ and aggressively resolving to V;
2. Hearing this C-sharp-to-D and the upbeat that follows brings the recognition that we are hearing the reprise of the opening, albeit through an extraordinary recomposition that reverses its harmonic context;
3. With that recognition we become aware that the metric setting is also reversed: where the opening placed D to C sharp in a strong-weak placement, this reprise places C sharp in the stronger and dynamically stressed position.

The cumulative result of these reversals takes us to the far end of the expressive spectrum from that tentatively limned at the opening.

[27] And what of the sublimation of ♯$\hat{4}$? This piece would seem to derive its expressive crux from an inability to embrace its sublimation, from that moment where ♯$\hat{4}$ vigorously reasserts its inherent tonal function.⁽¹⁵⁾ Indeed, the music that follows that climactic turn seems to me to be tinged with a certain regret. Having allowed ♯$\hat{4}$ to resolve to the V chord, that dominant seems unwilling to relinquish its place. Its prolongation underlies the whole reprise, with the resolution to a major tonic appearing only on hemiola offbeats. The G major trio that follows is a comforting balm, both in affect and in the specific reworking of the opening melody. Example 8 shows how the descending third that opens the minuet in such stop-and-start fashion is reworked into a fluid and lyrical song in the trio. (The descending fourth from G to D resonates here also.) The end of the whole movement is shown at letter b. The trio music comes back as a gentle peroration; the final chords include a common-tone diminished seventh sonority that once again allows C sharp to resolve to D (but not to a dominant chord). Sharp $\hat{4}$ has the last say before the melodic D-B third adds the closing benediction.

[28] One might be led to say that this piece is not about sublimation at all, that ♯$\hat{4}$ is simply permitted to do what its syntax demands. However, this would be to miss the subtle narrative premise of its opening and its nearly unique recomposition in the work’s climax. Brahms’s minuet is equally predicated on sublimation, but on the inability to achieve it, or to allow it to stand, just as Debussy’s Arabesque is about its easy enjoyment. One might be tempted to hear in Brahms’s treatment a conservative approach to tonality, and in Debussy’s a progressive flouting of harmonic idioms. This is probably simplistic and in any case secondary to the subtler task of teasing out the expressive particulars of these pieces, wherever they may lead.

[29] I began my study in musical energetics with Schenker in his more idealistic voice: “Tones have lives of their own . . .” My analyses have been structurally specific, but have certainly involved a hermeneutic characterization of musical actions, in the spirit of the energeticist outlook. The chemical sense notwithstanding, “sublimation” has a decidedly human cast; it feels like something that belongs to inner life. At the same time, in ascribing this sort of inner life to tonal structure, I have not attempted to assign a specific narrative content or particular hermeneutic explication to my analyses, nor did the identification with sublimation constrain an analysis to a narrow window of musical meaning. (Even the texted works involve sublimation in only a general sense, delegating more specificity to other aspects of the text.) One advantage of informing a Schenkerian reading with its implicit energeticism is that musical force can be infused with a unique nuance by careful attention and logical explication of the musical structures that surround it. A specific, and well specified musical structure or process can definitely suggest extramusical analogs without needing to be tied to a specific extramusical content.⁽¹⁶⁾ The inference of energetic forces can inform and even clarify one’s understanding of structure, taking us back to the tones themselves, and their inner lives.

Frank Samarotto
Department of Music Theory
Indiana University
fsamarot@indiana.edu

Footnotes

1. Heinrich Schenker, Harmony, ed. Oswald Jonas, trans. Elizabeth Mann Borgese (Chicago: University of Chicago Press, 1954), xxv.
Return to text

2. “Energetics,” in The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge: Cambridge University Press, 2002), 927–55.
Return to text

3. “Energetics,” 927–8.
Return to text

4. “Energetics,” 929.
Return to text

5. Oswald Jonas, Introduction to the Theory of Heinrich Schenker, trans. and ed. John Rothgeb (New York: Longman, 1982), 54–6.
Return to text

6. See, for example, Schenker’s comment about the first movement of Beethoven’s Op. 81a: “Here g-flat² and g² are engaged in a struggle with one another . . . the synthesis of the entire first movement circles around this conflict.” In Free Composition, trans. and ed. by Ernst Oster (New York: Longman, 1979) page 100.
Return to text

7. A similar critique is made Patrick McCreless in “Ernst Kurth and the Analysis of Chromatic Music of the Late Nineteenth Century,” Music Theory Spectrum 5 (1983) pages 56–75.
Return to text

8. This is in keeping with the concept of functional agents described by Daniel Harrison, Harmonic Function in Chromatic Music (Chicago: University of Chicago Press, 1994), esp. pages 49–55, though Harrison does not call special attention to the alteration of the fourth scale degree.
Return to text

9. In his analysis of this theme as it occurs in the final movement of the Third Symphony, Schenker refers to the corresponding ♯$\hat{4}$ and says that it, “embodies the urge of a² to reach b-flat².” Schenker reads the latter b-flat² as the goal of a local Anstieg, though the global Kopfton he takes as $\hat{3}$ (as I do). In “Beethoven’s Third Symphony,” trans. Derrick Puffett and Alfred Clayton, in The Masterwork in Music III (Cambridge: Cambridge University Press, 1997) page 54.
Return to text

10. The effect of an apparent cadence into F is heightened by the octave leap on C as the resolves.
Return to text

11. The semiotic bases of meaning in such situations is explored in Robert Hatten, Musical Meaning in Beethoven (Bloomington, Indiana: Indiana University Press, 1994); Hatten explicitly cites the reversal of the expected resolution of sharp $\hat{4}$ to natural $\hat{4}$ as susceptible to hermeneutic interpretation as a form of denial or negation; see pages 56–63 and especially the analysis of Beethoven’s Op. 7/ii.
Return to text

12. This characterization bears a close relationship to Hatten’s category of abnegation, “a ‘willed’ resignation” that is “actively involved in its reversal of yearning.” (59) Though the spiritual associations that Hatten ascribes to abnegation are very apt for my Examples 3 and 4, other ways in which sublimation is distinct from this category will become elaborated presently.
Return to text

13. The B flat in measure 68 has no trace of an A sharp function.
Return to text

14. Note that that the twisting figure leading to the cadence is concealed in the opening’s D-C sharp-D-C natural-B flat.
Return to text

15. It is this moment that seems to me to be most like Hatten’s category of abnegation, albeit in this context it involves not a reversal of ♯$\hat{4}$’s tendency to resolve but rather its resolution.
Return to text

16. This is arguably the position of Eduard Hanslick; see On the Musically Beautiful, trans. Geoffrey Payzant (Indianapolis: Hackett Publishing Company, 1980).
Return to text

Copyright Statement

Copyright © 2004 by the Society for Music Theory. All rights reserved.

[1] Copyrights for individual items published in Music Theory Online (MTO) are held by their authors. Items appearing in MTO may be saved and stored in electronic or paper form, and may be shared among individuals for purposes of scholarly research or discussion, but may not be republished in any form, electronic or print, without prior, written permission from the author(s), and advance notification of the editors of MTO.

[2] Any redistributed form of items published in MTO must include the following information in a form appropriate to the medium in which the items are to appear:

This item appeared in Music Theory Online in [VOLUME #, ISSUE #] on [DAY/MONTH/YEAR]. It was authored by [FULL NAME, EMAIL ADDRESS], with whose written permission it is reprinted here.

[3] Libraries may archive issues of MTO in electronic or paper form for public access so long as each issue is stored in its entirety, and no access fee is charged. Exceptions to these requirements must be approved in writing by the editors of MTO, who will act in accordance with the decisions of the Society for Music Theory.

This document and all portions thereof are protected by U.S. and international copyright laws. Material contained herein may be copied and/or distributed for research purposes only.