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Supplement to the Theory of Augmented-Sixth Chords Author(s): Daniel Harrison Source: Spectrum, Vol. 17, No. 2 (Autumn, 1995), pp. 170-195 Published by: University of California Press on behalf of the Society for Music Theory Stable URL: http://www.jstor.org/stable/745870 Accessed: 22/09/2008 11:46

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http://www.jstor.org Supplement to the Theory of Augmented-SixthChords

DanielHarrison

We could take it as a sign of progress that little remains wider range of treatments-specifically, those apparent in theoretically uncertainabout augmented-sixthchords. Or we late nineteenth- and early twentieth-centurymusic. Fittingly, could take it as a sign of complacency. At one time unbroken some of the theoretical methods are similar to those used at by the theorist's whip, these chords are now docile fixtures that time1-although, in some cases, it is the common interest of back-of-the-bookchromatic , content in their ped- in the analytic problems of the repertory and not shared ide- igreed ethnicity and ready for any novice student's four-part ology that is responsible. Another point of contact between exercises. The painstaking (if frequently pedantic) attentions this and earlier efforts is a sympathy for speculative and cre- given them by earlier generations of theorists now seem mis- ative compositional issues-this in addition to the attention guided, or at least unnecessary;few today trouble themselves paid to the usual theoretical and analytical interests. This with issues of derivation, , inversion, classification, and article is interested, in other words, not only in the behaviors the like. Apparently, the augmented-sixthhas been success- of those augmented-sixthchords found in the repertory, but fully domesticated. also in the possible behaviors available to that repertory. We ought to confess, however, that only those augmented- Many were discovered and composed; some, at least to my sixths exhibiting typical eighteenth- and early nineteenth- knowledge, were not. century behaviors have been tamed. Many later nineteenth- One result of this reconfigurationproject is an apparent century behaviors resist the normalizing discipline adminis- lowering of the membership standards for augmented-sixth tered their earlier kin and, as a result, often end up being chord status, giving the three ethnic purebreds an infusion considered unprincipled and licentious. If treated at all in a of new blood for their tight club. To be sure, this influx modern harmony text, it is with unease and little sympathy. diminishesthe theoretical pre-eminence of the ethnic chords, Is it true, then, that we can handle these quintessential chro- as they can no longer pretend to sole proprietorshipof the matic chords only if they are confined to common-practice title "augmented-." This is not to say that the pastures?For those that run free in chromatichabitats-such as some discussed in this article-we seem unable to snare. 'In particular,my work here resembles both in spirit and in substance an This supplement to the theory of augmented-sixths re- 1868 article by Wilhelm Tappert, "Die ibermassigen Sexten-Accorden," configures standard teaching in order to accommodate a Allgemeine musikalische Zeitung 3 (1868): 259-62, 266-68, 275-77. Supplementto the Theory of Augmented-SixthChords 171 ethnic chords lose analytic significance, which they cannot Example 1. Tonal behaviorof a) augmented-sixthinterval; ) simply on account of their abundant manifestations in the diminished-fifthinterval; ) diminished-seventhinterval tonal repertory. But the theoretical understanding of a. augmented-sixthchords needs to be reconstituted if the new- comers are to be integrated well with the charter members. Two benefits accrue from this reconstitution. The first is a more flexible and generous analytic category than we have b. at present. The second is more direct and subtle entry into 9o ,. compositions that feature nonstandard augmented-sixth chords, freeing the analyst from jerry-riggingad hoc expla- C. nations. This benefit is showcased in an analysis of a Brahms part song that concludes this article. 00t 1?

PRELIMINARIES momentarilyknowledge of artful treatments (i.., elided and other and let us also The basic mechanics of chords are well manipulatedresolutions), acknowledge augmented-sixth that what has been asserted about the intervals in known and are in la. Let us mo- question reprised Example ignore is likewise true for the inversions of those which is our of more matters in order intervals, mentarily knowledge complex to that the diminished , the and to focus afresh on one of which is the res- say augmented fourth, elementary ones, the second also resolve in motion olution of the dissonant interval in motion dia- augmented contrary by contrary by . Whenever I refer to one of these intervals in the tonic semitone, which is to that the classes of the say pitch discussion, its inversion is also refer- resolution have a different letter name and scale from following implicitly degree enced. For the sake of convenience, I have chosen the those in the dissonance. This behavior is shared two by only "prime"forms shown in 1 of their inver- other common dissonant intervals in tonal music: Example (instead sions) because they are met with in the root positions of their the diminished and the diminished , whose me- characteristicchords: the augmented-sixthinterval in all three chanics are shown in Examples lb and c.2 Again, let us ignore ethnic varieties of the augmented-sixthchord, the diminished fifth in the major- chord, and the diminished 2Manyintervals are able to fulfill this condition. For example, the doubly seventh in the diminished-seventhchord.3 augmented fourth, occasionally found in German-sixth chords when 3b is respelled as 02 for resolution into -mode cadential 6chord, resolves by diatonic semitone into a . One could go even furtherafield and invite such a study. For present purposes, however, I wish to treat only those cite such curiosities as the (resolves into ) and intervalsthat have some recognizedrole in tonal music, which the augmented doubly augmentedfifth (resolves into ). A study of such interval third, for example, lacks. behavior would, I think, be analyticallyhelpful in twentieth-centurymusics 3Many theorists acknowledge problems in ascribing roots to both the that rely on stepwise for some portion of their structuralco- diminished-seventhchord and the augmented-sixthchords. For example, in herence. The music of Hindemith, for example, or of Britten would seem to Allen Forte's Tonal Harmony in Concept and Practice (3rd ed. [New York: 172 Music Theory Spectrum

Considering these three intervals together is an interesting This point is crucial in understanding the attention many and suggestive exercise on a number of counts. For one thing, nineteenth-century composers paid to augmented-sixth it brings the out of the hinterlands of har- chords, since one of the principal growth areas in nineteenth- mony pedagogy and lets it bask in the same theoretical pres- century harmony was in chords that possessed these powers. tige enjoyed by the other two intervals, indubitably the fun- The diminished-, for example, which contains damental harmonic dissonances of tonal music. There are, of two diminished fifths and a , is a central course, reasons why the augmented sixth does not generally sonority in this repertory. Similarly, the VX9,which grafts a keep such distinguished company, reasons explored below. VII7 onto a S root, is also a characteristic nineteenth-century But the fact that the augmented-sixth dissonance resolves in chord of considerable harmonic horsepower. About the pop- the same way as do the other two intervals indicates that it ularity of the half-diminished seventh and the related V9 little possesses at least some of their powers of tonal propulsion. needs to be said. With this kind of interest at work, chords with augmented sixths naturally stood out as ripe for devel- opment. Their raw tonal energies were identical to those diminished fifths and their had Holt, Rinehart and Winston, 1979], 171-75), any position of a diminished- having sevenths; yet potential seventh chord is analyzed as "?7"because of the enharmonicintervallic equal- been locked up by theorists who, observing the constraints ity of all its inversions. This practiceeffectively denies the diminished-seventh upon augmented-sixth chords in eighteenth-century music, a . I follow here the practice of others in considering VII7 in prescribed particular , positions, and inver- minor the root of the diminished-seventhchord (e.., Edward Al- position sions.4 Unlocking the augmented sixth thus unlocked a rel- dwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. [Orlando, Fla.: Harcourt Brace Jovanovich, 1989], 368-75). The problems with augmented-sixthchords are thornier in that most root-seeking routines yield 4The augmented-sixthchord has been the subject of considerable theo- "unusual"root positions. For example, some analyze the root of both the retical regulation from the eighteenth century onwards. Rameau had par- German and Italian sixths as #IV. Many theorists have submitted to such ticular troubles with it, being unable to explain its origin by any of his usual uncomfortable circumstances. Perhaps the example best known to North- methods; it was hence both rootless and uninvertible. He was reproachedin American theorists is Robert W. Ottman'sAdvanced Harmony, 1st through this matter by 'Alembert, who, however, could provide little more theo- 3rd eds. (Englewood Cliffs, N.J.: Prentice-Hall, 1961, 1972, 1984). In the retical justification. See Jonathan W. Bernard, "The Principle and the El- fourth edition (1992) Ottman switched to the now common ethnic abbrevi- ements: Rameau's Controversywith D'Alembert," Journal of Music Theory ations, although traces of the older notation survive (e.g., p. 249). Others 24 (1980): 53. (See also note 30 in the present article). Among the better have avoided dealing with the idea of root position (Leonard G. Ratner, known attempts to give roots to augmented-sixthchords are those by . W. Harmony:Structure and Style [New York: McGraw Hill, 1962]), have waved Marpurg, who once called them fantastische Accorde and who contructed the reader off from the issue (Aldwell and Schachter, Harmony and Voice them from a diminished fifth split by a major and a Leading, 493-95), or have claimed the chords are rootless (Kostka and Payne, (Historisch-KritischeBeytrage zur Aufnahme der Musik, vol. 5, part 2 [Ber- Tonal Harmony, 383). Although later in this article I will disfranchise the lin, 1761]: 162, 167-68. A similarmethod was practicedby one of Marpurg's augmented-sixth chords as traditional chords-thereby obviating the root antagonists, G. A. Sorge (see Joel Lester, CompositionalTheory in the Eigh- problem-I here subscribeprovisionally to the notion that the most common teenth Century [Cambridge, Mass.: Harvard University Press, 1992], 195). bass positions of the three ethnic augmented-sixthchords function as their One of the most enlighteningviews of theoretical problems with augmented- root positions. Cf. , Harmony, 4th ed., revised and expanded sixth chords comes from an early nineteenth-century source: Gottfried by MarkDeVoto (New York: W. W. Norton, 1978), Kostka and Payne, Tonal Weber's Versucheiner geordneten Theorie der Tonsetzkunst(Mainz: Schott, Harmony, 383, and Roger Sessions, HarmonicPractice (New York: Harcourt 1817-21; 3rd ed. [1830-32] translatedas The Theoryof Brace, 1951), 333-35. by James F. Warner,ed. John Bishop [London:Robert Cocks, 1851]).On pp. Supplementto the Theory of Augmented-SixthChords 173 atively untapped source for new effects that relied upon of the intervals in question-what Schenker called their familiar manners of dissonance resolution. Many of these "univalence"6- within the respective scale structures. This effects will be illustrated in this article. univalence gives them a supremely strong position-finding Another, more speculative, attribute of these three in- role.7 In other words, because each interval only occurs be- tervals might be of interest to votaries of Moritz Hauptmann's tween a single pair of scale degrees, sounding the interval theories; all three resolve to Hauptmann'sfundamental tonal gives away its location within the given key. Univalence and spaces: the diminished fifth to the (major) Third, the dimin- the resultingposition-finding abilities are perhapsthe primary ished seventh to the (perfect) Fifth, and the augmented sixth reasons why the diminishedfifth and diminishedseventh rank to the .5 Thus, it might be said that the three dissonant as fundamental dissonances. intervals deserve their fundamental status by circumscribing, The augmented sixth, on the other hand, is not a creature outlining, or otherwise indicating the basic Hauptmannian of a standard scale system; it cannot be found between any consonant spaces. This point can be developed furtherwhile, scale degrees. It is thus "nonvalent,"if you will, and without at the same time, the augmented sixth can be peeled off from any inherent position-findingpowers. This is the reason why the group so that its distinctive properties can emerge. Schenker, among others, cannot discuss the augmented sixth It is well known that both the diminished fifth and the in the same breath as he does the diminished fifth and di- diminished seventh circumscribenot mere generic thirds and minished seventh; he delays discussion of it until the har- fifths but thirds and fifths between specific scale degrees monic implications of the standard scale systems have been within standard tonal systems. That is, the third defined by explored.8 Because of its nonvalence, the augmented sixth the diminished fifth in major spans 1 and 5, and the fifth has rather different position-finding attributes than its two defined by the diminished seventh in harmonic minor peers, which are explored in the following discussion. spans i and S. This specificity results from the uniqueness

THE AUGMENTEDSIXTH AND ITS POSSIBLEDIATONIC CONTEXTS 215-18 of the Warner-Bishoptranslation, Weber delves into the recent history of and H. C. Koch to task augmented-sixthlore, taking Marpurg over their We to reconcile the sixth treatments of the chord, refusal to admit it into the begin by attempting augmented condemning Marpurg's to standard "churchstyle," and ridiculingKoch's scruples about allowable inversions. It scale systems. Although this attempt will prove is these niggling qualms about the chord that "locked it up," as it were, for to be unsatisfactoryin some crucialrespects, it is not a useless eighteenth- and nineteenth-centurymusicians. For the adventurous,locks can exercise; we will discover that the augmented sixth is quite be of always picked, course; but abiding by the rules was the only course for flexible and able to operate in surprising contexts. the many who wished to work comfortably within the prevailing styles of composition. 5MoritzHauptmann, The Nature of Harmony and Metre, trans. and ed. 6HeinrichSchenker, Harmony,edited and annotatedby OswaldJonas and W. E. Heathcote (London: Swan Sonnenschein and Co., 1888), 5-8. While translatedby Elisabeth Mann Borgese (Chicago: University of Chicago Press, it is true that the inversion of the three intervals would resolve to inversions 1954), 127. of the fundamental tonal spaces, which in themselves are not fundamental, 7See Richmond Browne, "Tonal Implications of the Diatonic Set," In Hauptmann'sconception of interval seems to be more accurately described Theory Only 5, nos. 6-7 (July-August 1981): 3-21. as one of intervalclass, since intervallicand chordal inversion has little effect 8In Harmony Schenker introduces the diminished fifth and diminished on his discussion (e.g., pp. 50-51). seventh on p. 126; the augmented-sixthinterval appears on p. 279. 174 Music Theory Spectrum

The most congenial spots to locate an augmented sixth in Figure 1. Augmentedsixths generatedfrom one semitone pair a standard scale system appear to be at the . That in a tonal system is, the interval can be force-fit with minimum effort onto a scale system by anchoringone of its semitones to a semitone Augmented sixths from major-mode semitones in the system. Figure 1 illustrates. In the left column are the two diatonic semitones of each mode, presented - Descendingsemitone Augmentedsixth above degree format and broken down by direction. Every semitone A- #6-b is matched by another in the same row an augmented sixth 4-3 away. Accidentals attached to a scale degree show if it is raised ($) or lowered (b) a half step compared to the standard Ascending semitone Augmented sixth below form.9 9-8 b2-1 This scheme gives each mode four augmented sixths- b-4 surely an overabundant supply. What is more, the possibil- ities for chords containing augmented sixths are even greater Augmented sixths from minor-mode semitones than what Figure 1 suggests. Because the interval of reso- lution (the octave) is "omnivalent"in all scale systems, the Descendingsemitone Augmentedsixth above scale degree upon which an augmented sixth resolves can be 6-S ?4-S supported in a variety of harmonic formations. Put another 3-2 01-2 way, the scale degree of resolution could be in most cases either the root, third, or fifth of a chord that contains that Ascending semitone Augmentedsixth below scale degree.10 This situation is in marked contrast to, say, S-6 that with the diminished seventh, where the interval of 2-3 bb4-5- resolution-the perfect fifth between 1 and S-is between the root and fifth of a major or minor tonic (or tonicized) triad, In sum, each of the four augmented sixths belonging to a or of some other chord type in which the major or minor triad mode can resolve to one of three chord members, creating is the most characteristicsubset.'l twelve possible classes of resolution. Example 2 sketches the situation for two representative classes: the augmented sixth over 4-3, shown at a, and the one over 8-4, shown at b. The do in other indicate what accidental is attached to the 9They not, words, situation at a shows a of the near note inhabitingthe scale degree. 06, for example, would be an A# in the key straightforwardconsequence of , an Ax in COmajor, an Ah in Cb major, etc. omnivalence (limited by doubling restrictions) of the octave 10Itis reasonable to stipulate that the scale degree of resolution cannot resolution: each of the three triads can freely support the 4- be a seventh, , etc. of a chord since such members cannot, according 3 resolution. Most of the augmented sixths of Figure 1 are to standard teachings, sustain the doubling that augmented-sixthresolution creates. "I am thinking here particularlyof cases such as VII07of V7, where the resolution (V) clearly prevents this . Nonetheless, the sense that VII?7is expected to tonicize the following chord (and hence create a tem- the diminishedseventh at least wants to resolve into a particularperfect fifth porary I and 3). The addition of a minor seventh over the major triad of between either a local or global i and S persists. Supplementto the Theory of Augmented-SixthChords 175

Example 2. Resolutions for two sample augmentedsixths Example 4. Augmented-sixthchord harmonizing35- in minor

a.

J/ t_ -- II I-_- , - S w -0- 4 3 III11 I VI root third fifth l b. 9:".I " -- V |j -----I v.f >/ ~~~0 11IIgI -I_ D a I "Aug. 6th" V3 I 8 7 VII V III root third fifth ? ? Example 3. Augmented-sixthchord harmonizing2-5 in minor sider Example 3, which shows an augmented sixth involving 2-5 in minor resolving upon the third of a tonic triad, an

A n JI I2I 3 action noted with dotted lines in the example. The other notes of the augmented-sixth chord are taken from the German- sixth collection associated with the Db-B interval, which is to say that the augmented sixth under 2-5 has familiar chordal ui 6b------I companions with which to carry out its work in unfamiliar circumstances. Example 4 presents another instance of an I "Aug. 6th" I unusual augmented-sixthchord. In this case, an augmented 4 sixth over 3-2 in minor resolves upon the fifth of a V7 in 3 position. As in the previous example, the other notes of the ilarly unfettered. Example 2b shows a different, more chord are taken from the German-sixthcollection. The har- stricted situation. Standardteaching discouragesdoubling monic effects of Examples 3 and 4 are unusual, but also fresh res- the leading tone in a dominant-functionedentity, so the and attractive;the progressionof parts, entirely convincing.13 olution of the 8-1 augmented sixth into the third of a V chord Similar "undiscovered" progressions can also be mined is illegitimate, and that into the root of a VII chord, dubi- from the raw material of Figure 1. But not all are as inter- ous.12 Thus, doubling conventions put a brake on possibilities esting or useful as Examples 3 and 4; many, in fact, refuse of resolution. to stabilize on their appointed scale degree and instead ask Although our attention will soon be drawn towards the to be heard as being built upon another. For instance, it is more familiar structures represented in Figure 1, it is in- structiveto entertain some of the unfamiliarones, even to the 13Uponhearing these two examples during a public lecture on this topic, point of working out possible progressions. For instance, con- Charles Smith promptly and from memory located compositional manifes- tations. Example 3 is realized as the opening progressionof RichardStrauss's "Befreit," op. 39 no. 4. The progression in Example 4 can be found in the 12The right of VII to behave in a non-dominant way, such as in a concluding measures of Wolf's "Man sagt mir, deine Mutter woll' es nicht," descending-fifthsequence, ought to be reserved. no. 21 from the ItalienischesLiederbuch. 176 Music Theory Spectrum difficultto push the resolution of a 4-3 augmented sixth upon Figure 2. Minor system (above) "stretched"towards its domi- the fifth of a VI chord (shown in Example 2a) and have the nant side (below) chord really sound like a VI; it would much rather be heard as a local tonic. The same is true for the III chord in the same I I informal with the various res- F ab C et G b D example. Indeed, experiments I I I I olutions suggested by Figure 1 indicate that all tend towards having the chord of resolution be either a locally dominant- or a locally tonic-functioned entity.14 Why? ab IC eb G I b D f# I I I

TONAL FUNCTION OF AUGMENTED SIXTHS Moritz Hauptmann's harmonic theories again prove use- The discussionis the fact that the previous predicatedupon ful, this time to explain the relationshipof some non-diatonic sixth is not an interval found in a standard scale augmented scale degrees to standardscale formations. Hauptmann con- and if force-fit into such a one of its system, that, system, ceived key structureas a series of perfect fifths between which semitones will involve a chromatically degree. were embedded thirds. The upper row of 1 illustrates this situation We Figure perfectly. can, however, Figure 2 illustrates this structureusing the key of as treat the altered scale with more if we degrees sensitivity an example.15 Perfect fifths are located between adjacent loosen the strict constraints. For it is clear while none that, upper-case letters, and thirds between any pair of adjacent of these semitones is native to the or in major upper- and lower-case letters. In theory, the fifth-and-third some are more and honored in the question, frequent guests relationships can be extended infinitely in both directions, diatonic household than others. In is an es- particular, #4-S thereby encompassing all possible keys; what Figure 2 shows and chromatic as it creates pecially important popular caller, is a segment from that line delimiting one particular key. of and modulations to the dominant key. b2- Because Hauptmann nominally employed to i is another friendly visitor, responsible for Neapolitan ef- derive scale members, his key structures have remarkable fects. Some of the others are far less encountered frequently "wiggle room"-the ability to be shifted one position along than these. Indeed, b7 in minor (e.g., Gb in A minor) is so the infinite fifth-and-thirdline without loss of the structural is rare as to be mere theoretical fiction. All this by way of integrity of the key. The bottom row of Figure 2 shows such that while the sixth not fit into saying augmented may easily a shift, the structurehaving moved one position to the right the system of a key, it finds more comfortable (towards the dominant side). The between F and in it in accommodation some locations than does others. ab is lost while a between D and f# (H4)is gained. It is in this "stretched"C-minor key system that Hauptmann

140ne can try to repudiate these tendencies with compositionalrhetoric- that is, by putting these progressionsinto real musical contexts. Nonetheless, 15Hauptmann'sminor key is based on the harmonic minor scale. Con- considerablerhetorical effort seems necessaryin order successfullyto stabilize cerning Hauptmann'sderivation of fifths and thirds, especially with respect progressions such as those shown in Example 2a. to minor, see Hauptmann, Harmony and Metre, 14-21. Supplementto the Theory of Augmented-SixthChords 177

Figure3. Key system "stretched"in both directions;after Cyrill of these scale degrees are under the tonic control of C. Two Kistler augmented-sixth intervals are found in this system: one be- tween f# and ab (#4 and b8), and another between db and b (b2 and ? ).19 db F ab C eb G b D f# Figure 3 offers a way to welcome two foreign, chromatic I I scale degrees into a standard scale system, allowing us thereby to privilege those Figure 1 behaviors in which they participate.In addition, it suggests an explanationfor why the found the origin of the augmented sixth-in this example, the augmented sixth tends to bestow tonic or dominant function interval between at and f#.16But this observation is actually upon the of resolution. Both augmented sixths beside the point; the intriguingelement here is the stretched found in Figure 3 are anchoredto functionallysignificant scale key system itself, which Hauptmann conceived as still based degrees within the core, unstretched system. That is, #4 is in the original C-minor system. For Hauptmann, as long as attached to b6, a crucialtransmitter of subdominantfunction, ab was still in the picture, then C minor was still operative. while b2 is attached to #t, the quintessential dominant scale Were the system right-shiftedonce again, so that ab were lost degree. The behaviors of these significant scale degrees de- and A gained, then the C-minor system would have passed termine the tonal function of the augmented sixths attached into a -major system. But a single right-shifted sys- to them. b6, for example, in moving to 5 discharges sub- tem, even though it contains #4, is still under the control of dominant function either upon dominant (as in a Phrygian the original tonic.17 ) or upon tonic (as in a plagal cadence); the aug- For a variety of reasons-none germane to the present mented sixth b6-#4, then, also exhibits these functional undertaking-Hauptmann disallowed shifting behaviors.20The former, dominantizingmotion leads directly in the minor key. Some of his followers, however, ignored to the standard augmented-sixth chords, insofar as the Ital- this prohibition and explored the consequences nonetheless. ian, French, and German sixths all resolve to dominant- Figure 3, for example, shows Cyrill Kistler's doubly stretched functioned chords. The latter, tonicizing motion, although system, which has major-thirdextensions on both sides.18In rare before the mid-nineteenth century, leads to wonderful addition to having f# as #4, this system also has db as b2 as a major-thirdextension towards the subdominant side; both '9It is perhaps not inappropriate, in connection with note 2 above, to observe that Kistler's doubly stretched system contains an augmented third between F# and Dl (t4 and 12). 16Harmonyand Metre, 28-33 and 120-23. 20Iam using the term "subdominant"here to blanket both "pre-dominant" 17Thispoint is discussed in greater detail in Daniel Harrison, Harmonic behavior (e.g., IV6-V) and "pretonic"behavior (e.g., IV-I). This usage is Function in ChromaticMusic (Chicago: University of Chicago Press, 1994), consistent with the Riemannian tradition from which I am drawing. Later, 122-23. taking a cue from William Rothstein ("The True Principles for the Practice '8Cyrill Kistler, Harmonielehrefir Lehrende, Lernende und zum wirk- of Harmony: Or, Schulz, Schenker, and the Stufe," paper read at the Second lichen Selbstunterrichte,2nd ed. (Heilbronn: C. F. Schmidt, 1898), translated International Schenker Symposium at the Mannes College of Music, New as A System of Harmony by Amanda Schreiber (London: Haas and Co., York City, March, 1992), I reserve "subdominant"for plagal, "pretonic" 1899), 74. behavior, using "pre-dominant"for other cases. 178 Music Theory Spectrum

Example 5. Liszt, "Sonetto 123 del Petrarca," mm. 82-84

a. 3 * ? 3 3 ? r lib b ? 8 |; l ; f 1i |l;r jf I ,a| 0:b~bC I 0 rlf jF7~jf -69:0'kc I>|1 x\ I 11 4EI V V V

b.

-.I"Aug. 6th"-- t^.

I "Aug. 6th" I

treatments such as that found in Example 5, the final mea- mented sixth it participates in also takes on dominant func- sures of Liszt's "Sonetto 123 del Petrarca," with the effect in tion. Another example from Liszt's work, the ebb from the question shown at the asterisk. The analysis in Example 5b last rhetorical climax in the symphonic poem Orpheus (Ex- brings out the underlying augmented-sixth structure of the ample 6), is an exemplary illustration. Here, the placement passage, respelling the chord in order to point out the in- of 7-8 in the bass emphasizes the dominant-to-tonic character volvement of t4 and lb, of Ab major in the chord. These scale of the progression. degrees are indicated with open noteheads in the example, The situation in the Orpheus example is, from a purely and their resolution into a tonic-functioned El (S) is high- statistical standpoint, rather rare-so much so that it seems lighted by the dotted lines.21 downright irregular; the idea that augmented-sixth chords The other augmented sixth found in Figure 3 involves progress to dominants and not to tonics is deeply en- t7 and b2. $7 being a dominant-functioned entity, the aug- trenched.22 Yet more than a few theorists have tried to en-

21Aldwelland Schachter(Harmony and Voice Leading, 519) name this the 22Forexamples of how "exceptional"tonic-resolving cases are discussed "common-tone augmented-sixthchord." In light of Charles Smith's citation and even finessed in currenttextbooks, see Aldwell and Schachter, Harmony of Wolf's "Man sagt mir, deine Mutter woll' es nicht" in note 13 above, it and Voice Leading, 496. The authors state matter-of-factlythat such things is appropriateto point out that the common-tone augmented-sixthchord is can happen, but the discussion has none of the depth that marks their in- a principal harmonic motive of that song. troduction to augmented-sixthsas "ChromaticPreparation for V" (the top- Supplementto the Theory of Augmented-SixthChords 179

Example 6. Liszt, Orpheus,mm. 194-206 194 A J 4 _ 4 4.

v I I I I I _ _

^200 de

r o!oi- I- decresc.e rit. A9 A r o rt I i

Aug. 6 (dim. 3) franchise dominant-functioned augmented-sixth chords as augmented-sixth chord in Weber's own notational system. theoretical equals of subdominant-functioned ones. The The firstderivation is from a major-minorseventh with B root most telling attempt is also the first: Gottfried Weber's der- (B7) that functions as V7 of and . The root ivation of the chords from two possible sources, ?II7or V7, is omitted and a minor ninth has been appended, but the in his Versuch einer geordneten Theorie der Tonsetzkunstof crucial feature is the lowering of the chordal fifth from Ftf to 1817.23Example 7 explains the derivation for a particular F~. The augmented-sixth interval created by this lowering is thus between b2 (F) and 01 (D#). This is a dominant- functioned chord. Weber another level heading at the beginning of the chapter on p. 478). Joel Lester, in augmented-sixth provides Harmony in Tonal Music, vol. 2 (New York: Knopf, 1982), 93-94, provides derivation, in which the basic chord is a B half-diminished but one illustrationof a tonic-resolvingaugmented-sixth chord accompanied by two short paragraphsof text. Finally, Kostka and Payne segregate any in ? 89, but later disallowsthe possibilityof VII7in ? 148 #7. (A later reference unusualaugmented-sixth behaviors, includingtonic resolution, into a separate to this disqualificationin ? 202 wrongly refers the reader to ? 38 #7 instead chapter (383-91). While giving the topic more attention, this quarantine is of to ? 148 #7. This error is in all the German and English editions.) Janna nonetheless a subtle and effective abnormalizingtactic. Saslaw summarizesand discusses aspects of Weber's theory pertinent to the 23See Weber, The Theory of Musical Composition, ? 89-94. Weber ini- present discussion in "Gottfried Weber and Multiple Meaning," Theoria 5 tially allows any half-diminishedseventh to parent an augmented-sixthchord (1990-91): 74-103. 180 Music Theory Spectrum

Example 7. Analytic possibilitiesfor German augmented-sixth rules about assigning harmonic meaning to chords skewed chordaccording to GottfriedWeber (from The Theoryof Musical interpretations-perhaps unintentionally-towards the ?II7 Composition, ? 202) analysis. Briefly put, in a typical modulatory situation in- volving root motion by ascendingfifth (tonic to dominant, for example) or root motion between relative keys, a ?II7of some key X would generally be more closely related to the original key than a V7 of some key a fifth higher than X. In concrete B7 terms, consider Example 7 and notice that the tonic of the E: V7 ?II7 analysis (A minor) is a fifth lower than that of the V7 e: V7 analysis (E minor). Say now that this chord is encountered b67 in a C-major context. Weber would invariably identify it as a: ?O17 a ?II in A minor because that key is more closely related to C than is E minor in Weber's structuraltopography.26 Con- seventh functioning as II7 in A minor (?b7). Here again, the ditions under which Weber would analyze an augmented- root is omitted and a ninth added; the alteration in this case sixth chord as V7 are rare, in that they involve direct involves raising the chordal third from D to D t, thereby descending-fifth modulatory motion within the tonal space creatingan augmented sixth between l, (F) and 04 (DO). This (tonic to subdominant, for example), a comparatively un- is the subdominant-functionedaugmented-sixth chord.24 usual procedure. Hence, because of both modulatory habits Despite being given theoretical substance alongside in composition and related concepts of tonal topography in subdominant-functionedaugmented-sixth chords, dominant- theory, the subdominant-functionedaugmented-sixth chord functioned augmented-sixths are extremely rare in Weber's prevailed analytically over the dominant-functionedone in analytic work. He was not, however, prejudicially averse to Weber's theory. This unequal analytic relationship between them.25 Rather, his elaborate but extraordinarily sensitive the two theoretical equals effectively made the V7 analysis non-normative and unusual. 24The functional designation is my own. Weber's derivation of the Looking at this issue from a different perspective, it is augmented-sixthchord from ?II7was widely adopted. See, for example, Simon remarkable, given the aforementioned modulatory habits of Sechter, Die Grundsdtzeder musikalischen Komposition, 3 vols. (Leipzig: eighteenth-centurycomposition, that a dominant-functioned Breitkopf and Hartel, 1853-54), first volume ed. and trans. Carl Christian chord would even be considered as a the- Miller as The CorrectOrder FundamentalHarmonies York: W. A. augmented-sixth of (New oretical its And since Weber Pond, 1871), 148-51; , Theory of Harmony, trans. Roy entity given analytic rarity.27 E. Carter (Berkeley: University of California Press, 1978), 246. 25I have found two examples: Weber'sFigure 1911(p. 356 in the Warner- 26Weberdiscusses this issue, using these very keys as examples, on pp. Bishop edition), an abstract part-writingspecimen; and Weber's Figure 234 343-44. Weber's topography is alluded to in Fred Lerdahl's "Tonal Pitch (pp. 404-9, annotated on pp. 383-87), an analysis of an accompaniedvocal Space," Music Perception5 (1988): 315-49. See especially Figure 17a on p. quartet of his own composition ("Polimeter").Weber spells out his reasoning 332, which reproduces a mirror-imageof Weber's space. Cf. Saslaw, "Got- for choosing the dominant-functionedinterpretation in "Polimeter"on p. 384. tfried Weber and Multiple Meaning," 92. Saslaw ("GottfriedWeber and Multiple Meaning")discusses the "Polimeter" 270ne explanation might be that many early theoretical explanations of passage extensively on pp. 89-91. augmented-sixthchords connected them to the VII , which Supplement to the Theory of Augmented-Sixth Chords 181 provided no justification as to why such a thing could exist, involve augmented-sixths harmonized in the "German" fash- it is impossible to determine his motivation in this matter. ion. The "French" found in the quintet can Nevertheless, it seems no coincidence that prominent exam- lead one away (as it did Piston) from considering the chord 7 ples of dominant-functioned augmented-sixth chords begin to a species of augmented sixth and towards a V, interpretation appear around the time of Weber's treatise. Schubert's works, in which the chord is in 3 position. Although this analysis for instance, abound with them. Well-known examples are clearly points to the dominant origin of the chord, it does not the concluding gestures of the String Quintet, D. 956/IV, the do so in order to connect it to other augmented-sixth chords; A-major Sonata, D. 959/I, and "Der Atlas" from rather, it stresses its seventh-chord structure. The augmented Schwanengesang, D. 957, no. 8.28 Within the body of a move- sixth created between the major third and diminished fifth ment, mm. 722-34 of the C-major Symphony, D. 944/IV, of the chord is an accidental, not a primary quality of the provides another fine illustration. All but the quintet example chord. This point leads us naturally to consider what kind of structures can be labeled augmented-sixth chords. in turn was connected to the V triad. See, for instance, Marpurg,Historisch- Kritische 162. Besides Louis and Thuille also a Beytrdge, Weber, recognize TYPES OF AUGMENTED-SIXTH CHORDS dominant-functionedaugmented-sixth chord; see Richard Isadore Schwartz, "An Annotated English Translationof Harmonielehreof Rudolf Louis and Ludwig Tuille" (Ph.D. diss., WashingtonUniversity, 1982), 286-91. So does Considering the enormous influence Central European H. K. Andrews in The Oxford Harmony (London: Oxford University Press, musicians have had on the development of modern music vol. who follows Alfred in this matter Treatiseon 1950), 2, 57-62, Day (A theory in North America, it is surprising to note the con- Harmony [London: Cramer, Beale, and Co.: 1845], 121-27). One of the tinuing presence in our discourse of an English theoretical earliest satisfactory explanations of the augmented-sixth chord, that by the of three chords Johann Philipp Kirnberger, also awarded it dominant function ("The True quirk: naming augmented-sixth using Principles for the Practice of Harmony," trans. David W. Beach and Jiirgen the "Italian," "French," and "German" ethnic labels. John Thym, Journal of Music Theory23 [1979]: 186-88. Louis and Thuille assert Wall Calcott, in A Musical Grammar (London, 1806), seems that the possibility of both dominant- and subdominant-functioned to have been the first to coin these terms, and for the reasons chords is for the idea that an augmented-sixth responsible augmented-sixth which have ethnic stereo- chord has two roots. One could see how Weber'sderivation of the chord from many long suspected-namely, two different sources could lead to this idea, save that Weber viewed these typing. two sources as one of which was eliminated in the act of potentials, analysis. The Music of France, Italy, and Germany, cannot be illustrated in By contrast, double-root theories seem to imply that the sources are actuals, a smaller compass than by the use of these three Chords. The fee- as if they were fundamentalbasses. Schenker discusses the augmented-sixth bleness of the French sixth, with the of the Ital- chord, for example, as a fusion of elements from ?II7and V7 where the V7 compared elegance and the of the leaves is from a key a fifth higher than the ?II7,as in Weber'sformulation (Harmony, ian, strength German, no doubt of their su- 277-78). Alfred Day also held to a double-root theory involving fusion (A perior excellence. The admirable genius of Graun knew when to Treatise,122). Weber, by contrast, viewed the augmented-sixthchord as de- employ Italian sweetness, and when to change it to German force.29 rived in its entirety from either of the two sources, not as a fusion of both. 28Thequintet example is cited in Piston, Harmony, 426, and Andrews, Oxford Harmony, vol. 2, 61. Aldwell and Schachter, Harmony and Voice 29Callcott,Musical Grammar,1st American ed. (Boston: Manning& Lor- Leading, 496, and Lester, Harmony in Tonal Music, vol. 2, 94, cite the ing, 1810), 239n. Calcott alludes to another reason why the French sixth is A-major sonata. so named; he claims that because it "is only found in the theory of Rameau, 182 Music Theory Spectrum

Along with the ethnic names, current practice has taken Example 8. Louis and Thuille's augmented-sixth chord types the English predilection for recognizing these as the only a. b. c. d. e. f. types of augmented-sixth chords. Continental practice is more flexible in this matter. While the "big three" augmented-sixth chords are invariably discussed (usually Y IIs I 14 I I I t I i is I1 named by their figured-bass signature), other (might we say "cosmopolitan"?) types of augmented-sixth chord also oc- casionally make an appearance. In their Harmonielehre, for correspond to the well-known chords, and d might be styled example, Rudolf Louis and Ludwig Thuille recognize six dis- a defective Italian or incomplete French sixth. But versions tinct types, illustrated in Example 8.30 Versions a, b, and e c and f are novel and have no such easy explanation. No compositional use of version c is cited by Louis and Thuille, but Ebenezer Prout cites a passage from Verdi's , it may be properly termed the French Sixth" (238-39). Although I have not shown in 9, which contains the intervals.31 made an exhaustive search of Rameau's works, this statement appears du- Example requisite To some it is hard to credit this as a substantial bious. The chord is conspicuously absent from the Traite, and Matthew extent, chord Shirlaw (The Theoryof Harmony [London: Novello, 1917], 242, 279) points since it seems to be a by-product of passing motion against out its omission in Rameau's theories in general as well as in Rameau's own a sustained E-major triad, a hearing encouraged by the em- so far as to state that "the German form of the chord compositions, going phasis on passing motion in the bass in the previous measures. . . . must have been for Rameau particularlyembarrassing. It was impossible True, it is not difficult to hear an affinity of the chord in for Rameau to explain this chord and its naturalresolution on the Dominant, to a which has two common either by means of double 'employment'or any other device known to him" question German-sixth, also (242). Although Calcott's ethnic names were used sporadicallyby other En- tones with its chord of resolution (a cadential 6), a relation- glish theorists (e.g., William Crotch, Elements of Musical Composition, 2nd ship that bolsters the pretensions to independence of the ed. it was not until Ebenezer Prout's Har- [London: Longman, 1830], 54), present augmented-sixth. But, whereas the German-sixth is Its and Practice that the names mony: Theory (London: Augener, 1889) rather constrained to to a cadential 6 on account of became firmlyensconced in English theoretical discourse, along with a chau- progress the well-known no such vinistic update of Calcott's stereotyping: parallel-fifth problem, impediment As students are very apt to confuse the names of these three forms of the looms here, the fifth in the version-c chord being augmented, 6 augmented sixth, the following artificial"aid to memory" may be found not perfect. The chord here is thus a choice, not a mandate. three forms to the characterof the music of the useful:--the correspond This choice contributes to the curious lack of "release" upon three countries-Italian music is the simplest; and the "Italian sixth" is resolution of the augmented-sixth to the cadential 6, leading the simplest form of the chord ... French music is the most piquant, and us to the of the version-c so is the "Frenchsixth," with the discord between the upper generator, question structural independence and its seventh . . . Lastly, German music is the richest and fullest in augmented-sixth vis-a-vis its chord of resolution. character;and the "Germansixth" is richer in its effect than either of the Example 8f at first glance seems to have a similar rela- others (203n). tionship to the French sixth that version c has with the Ger- 1907. 4th ed., 1913. See RichardIsadore Schwartz, 30Stuttgart:Grininger, man; that is, the G#t seems to the third of the "An Annotated English Translation,"274-76. An unusually broad concep- anticipate dominant to all other notes to the French tion of augmented-sixthchord types, motivated by issues in contemporary follow, belonging harmony, is also found in Vincent Persichetti, Twentieth-CenturyHarmony: CreativeAspects and Practice (New York: W. W. Norton, 1961), 109-11. 3lProut, Harmony, 208. Supplementto the Theory of Augmented-SixthChords 183

Example 9. Verdi, Requiem; Kyrie, mm. 77-81

TenorSo lo J Ji F I r , r Ky- ri- e e- le- i- son

~C,k'*~ 7 n_J'*jn j F -t i", ^^ ? i J~~~~~~ BU,: BU,: BU,: e~~~~~~~~~~~~~~

sixth. But version f has intervallic properties that connect it Thuille mention the Tristanchord in connection with version strongly to the German sixth. Example 10 demonstrates this f, they nonetheless wave off this interpretation-partly be- close relationship, showing that version f is an inversion of cause of the habit typical of the time to hear the A as struc- a German sixth in terms of its internal intervallicadjacencies. tural and the GI$as passing, but also because they find that No other name suggesting itself easily, I dub version f the version f, by virtue of its two common tones with the dom- "dual" German-sixth chord in recognition of its inversional inant (B and GO),is more easily heard as a dominant sonority intervallic relationship to the German sixth. with two auxiliarytones surroundingthe root (F and DO).33 In contrast to version c, the dual German-sixthchord does They thus want to hear version f more as an enhanced dom- have compositional existence-in one of the most famous inant than as an augmented sixth; since they hear the Tristan passages in nineteenth-century music, in fact (see Example chord as subdominant-functioned,they cannot rationalize an 11). The "Tristan"chord, marked with the asterisk in the explanation that involves the G$ as the chordal tone. example, is identical to the chord shown in Example lOb, the It is true that a textbook resolution of the prototype of the dual German-sixth.32Although Louis and would involve maintainingthe common tones Gl and B, and that such a resolution would support Louis and Thuille's con- tention that the chord is an enhanced dominant. But 32NotaBene: Having now a theoreticallyviable rationale for understand- Wagner's ing the actual spelling of the Tristanchord, we need no longer enharmonically solution is pointedly to disobey the "Law of the Shortest convert the chord into an F half-diminishedseventh chord and then wonder Way" in order to enhance the tension and release from the at its "irregular"resolution. Such conversions have been neces- sitated by the domination of the ethnic-sixth chords and the concomitant exclusion of other chord types. Yet, at the heart of the matter, it is as improper 33Thepresence of two tones in common with the chord of resolution is to call the Tristan chord a half-diminishedseventh chord as it is to call a the same reason it is difficult to hear the augmented-sixthchord leading to German sixth a dominant-seventhchord; its spelling indicates its functional the cadential 6 in the Verdi excerpt (Example 9) as a freestandingharmonic meaning in the same way that the German-sixth spelling does. structure. 184 Music Theory Spectrum

Example 10. Definitionof the "dual"German augmented-sixth augmented-sixthare correct, but scruples about its resolution chord are misplaced. This discussion could continue in this vein for a a. b. while, pointing out the limits of the current ethnically fixed stable A4 _ -- P5 CI __ of augmented-sixth chords and proposing the inclusion of M6 ( M6 such things as the dual German-sixth. It would also seem natural to release augmented-sixth chords from the tradi- :- PPS Co0 A4 C l) -41: 1~~~~~~~~~~~~~~~ tionally strong theoretical restraintsupon inversion by citing many examples from the late nineteenth century that fea- ture diminished-third chords or other manifestations of augmented-sixth inversion. But perhaps the point to be Example 11. Wagner,Prelude to Tristanund Isolde, mm. 1-3 made here is not that we ought to expand the category of augmented-sixthchord in order to include additional chord types, but that we need to reconstitute this category into something more flexible and generous. This program has clearly been suggested from the outset of this article, and is now taken up in earnest.

* PROPOSAL

Tristanchord to the V7. That is, the here-the Under the heading of "augmented-sixthchord" ought to the infamous perpetrator of improper resolution-ensures appear any chord that depends upon the augmented-sixth(or chord's functional independence by avoiding common-tone diminished-third)interval for all or most of its tonal energies. connections.34Thus, intuitions that the Tristan chord is an Where the interval appears within a governing key is im- material, although we can propose that Figure 1 define the 34Anexhaustive summaryof Tristan-chordlore is found in MartinVogel, constraininglimits. In this way, not only are the "big three" Der Tristan-Akkordund die Krise der modernenHarmonielehre (Disseldorf: enfranchised but also those beautiful examples from Liszt Gesellschaftzur Forderungder systematischenMusikwissenschaft, 1962). Vo- shown in Examples 5 and 6, as well as the interesting lab of one that gel documents all manner analytic approaches except recognizes specimens displayed in Examples 3 and 4. The intervallic the Tristanchord as the dual of the German-sixthchord. A dual relationship constitution of chords need not be to the dominant-seventhis augmented-sixth specified enharmonicallyequivalent recognized (107-10), the interval that which association was revived by Benjamin Boretz in "Metavariations:Part or prescribed since it is augmented-sixth IV, Analytic Fallout," Perspectivesof New Music 11 (Fall-Winter, 1972): 162. But this necessitates an enharmonic reinterpretationof the Tristan chord as a half-diminishedseventh, something that Wagner'snotation pointedly dis- with the Tristan chord. But then, impishly, he purposely gets bogged down courages; see note 32 above. Schoenberg, in Theory of Harmony (255-57), in issues of root and derivation, an excuse to demonstrate his fondness for also recognizes the dual German sixth, and even mentions it in connection "vagrantchords," which are to him "most amusing fellows." Supplementto the Theory of Augmented-SixthChords 185

Example 12. RichardStrauss, Till Eulenspiegel,mm. 46-49 become quite recognizable and salient. Consider, for in- stance, the role augmented-sixth chords play in a short se- lustig quence from Franck's Piece heroique shown in Example 13. The chords in question are marked with an asterisk in the score at a; they are re-spelled at b both to highlight (by open noteheads) the propulsive augmented-sixthinterval between b2 and #1 of the local keys and the dual-German intervallic structure. Finally, by keeping an ear on the augmented-sixth * interval, we are able better to understand some of the tonal forces in the opening of Schoenberg's Chamber Symphony, op. 9, cited in Example 14a. The analysis at b out that gives the chord its powers; the remaining notes accompany points two augmented-sixthintervals the chord in m. 3 into the generating interval and provide it with different sonorous propel its resolution in m. 4; one is shown with In this the dual German sixth is welcomed, open noteheads, shadings. way and the other with with other that a be filled. Surely, this is just as much an along any configuration composer might chord as to use. At this we have to be able to augmented-sixth any other that has been discussed tempted point, enough so far. cut away the puzzlement surroundingthe chord marked by the asterisk in 12 and it as an Example analyze augmented- * * * sixth chord, with the interval in question built at the 4-3 semitone in and accompanied by notes that give the The of the last was chord a dual German flavor.35Indeed, under this regime all expository speed paragraph probably sufficient to have raised some with manner of previously unassumingaugmented-sixth behaviors dust, examples racing by like so many billboards on the highway. The result of re- constitution so far is no more than a flood of 35Kostkaand (Tonal also the "Till"chord perhaps newly Payne Harmony, 385) identify enfranchised chords as a type of augmented-sixthchord. Graham H. Phipps, in "The as augmented-sixth accompanied by their Equivalency: A Contextual Perspective for Approaching Schoenberg's Mu- variously unusual tonal functions. But disciplining this now sic," Journal of Musicology 4, (1985): 60, also cites the "Till" chord as an wild herd can be done gently; the recommended method, augmented-sixth,but he calls the resolution to the F-majorchord "deceptive" in light of previous discussions of tonal function, involves and also ignores the Till chord's spelling when describing it as a half- functional attributes. . not a dual German sixth segregation by Although strictly (D, 4 three would have to be a C# in order for the chord to have the requisite interval Figure presents functional types of augmented- structure),the Till chord can still be understood as the dual of a German sixth sixth chords. As the figure denotes, these types are derived with doubly augmented fourth. See Aldwell and Schachter, Harmony and from judgments concerning the harmonic function both of an Voice Leading, 482-83. The similarityof the Till chord and the Tristanchord augmented-sixthchord and of its chord of resolution. has been noted William Music in Strictly by Austin, the TwentiethCentury (New York: it is not the function of an chord W. W. Norton, 140. Robert Gauldin reinforces this connection and as speaking, augmented-sixth 1966), se that is of ultimate well makes a good case for considering Till as a whole to be a satire on Tristan per interest, but its functional context. ("A Concealed Musical Satire: A Possible Till-TristanConnection," unpub- In all the examples cited in this paper, the augmented-sixth lished MS). chord sets up either a tonic- or a dominant-functionedchord 186 Music Theory Spectrum

Example 13. Franck, Piece heroque, mm. 14-18 a.

14 3 * 3 *

^t^FT:"X '^E^ "_ L^O =L

I [^'* Ai >:,^ i A> >12 >;:a >A -

b.:ft( W b^^ | ti}^ i(ii)t

Example 14. Schoenberg,Chamber Symphony, mm. 1-4 a.

I^ u . 1 v 0 ~~~~~~~~~~~~~~~~~~~~~O1 ;

4

- 11ov tl tlo t ~ ~ b.~ ~ ~ ~ ~ -~ 11

0 O00~~~~~~~~~~F

of resolution. If the latter, then the augmented-sixth chord the sense of tonal motion and urge towardsresolution we hear perforce is subdominant in function. A tonic-functioned when augmented-sixthchords resolve. Thus, both tonic and chord cannot sustain the level of dissonance and activity as- dominantfunctions are inappropriateto describe the function sociated with an augmented sixth, and two consecutive of an augmented-sixth chord that resolves to the dominant. dominant-functionedchords in the same key cannot produce The term "subdominant"may be uncomfortable here, for Supplementto the Theory of Augmented-SixthChords 187 although one of the traditional derivations of augmented- Figure 4. Functionaltypes of augmented-sixthchords sixth chords is from subdominantchords (the #IV7of Ottman, et al.),36 one can be hard pressed not to hear the secondary- Augmented-sixth Resolution Functional Type dominant element in an augmented-sixth chord (#4 as I-of- 3) and thus not to hear some type of dominant function as Dominant Tonic Authentic a result.37It is for this reason that Figure 4 calls this functional Subdominant Tonic Plagal Subdominant Dominant Predominant behavior "pre-dominant,"unloading some unneeded freight from "subdominant"and stressingthe dominant setup powers of augmented-sixth chords.38 The b staff highlights these intervals in open noteheads. The How can one tell that a chord of resolution is dominant? operation of the series, which involves continual enharmonic Considerations of local and global key relations are, of reinterpretationscomplicated by elided resolutions of #4, can course, paramount.But there are other means as well. Major- be read from the arrows in the example. Augmented-sixth minor seventh chords, for example, are habitual transmitters chords are shown on the b staff, and their chords of resolution of dominant function, so a motion from augmented sixth to (major-minor sevenths in 4 position) are shown in the left- major-minor seventh naturally is classified as pre-dominant. hand portion of the a staff; the activity of augmented- (This situation is illustrated in the case of one of the "lab sixth resolution is indicated by diagonal arrows. After res- 4 specimens" shown in Example 4.) A cadential 6 also conveys olution, these chords are enharmonically reconfigured as dominant function (or impending dominant function, if one augmented-sixthchords, a process shown by the vertical ar- labels the first part of the cadential motion1 as I); it, too, rows from a to b. Liszt takes advantage of enharmonicequiv- invites analysis as pre-dominant. Insofar as these motions are alence here to dovetail a series of pre-dominant augmented- the typical behaviors of the traditionalethnic sixth chords, we sixth chords with their chords of resolution. need not dwell upon this matter much longer. But an inter- At least two circumstancescan discourage dominant func- esting twist involving the enharmonic equivalence of the tion for the chord of resolution, and hence open up the pos- German-sixth and the major-minor seventh is found in Ex- sibility of dominant function for an augmented-sixthchord. ample 15, and it deserves some comment. Underlying the The first is the unlikelihood that a minor triad can transmit passage is a series of augmented-sixthchords whose essences dominant function. It is for this reason that, as in Franck's are expressed by diminished thirds buried in the sound mass. Piece heroique shown in Example 13, the augmented-sixth chords tonicize their chords of resolution.39What, then, is the function of the chords-dominant or sub- 36Alsoof note here is the traditionallyclose associationof augmented-sixth augmented-sixth chords with IV6 chords in Phrygiancadences. See, for example, Aldwell and dominant? Here we can attend to clues in the voicing and Schachter,Harmony and Voice Leading, 479; Forte, Tonal Harmony in Con- figuration of the chords. Notice in particular the left-hand cept and Practice, 353; Lester, Harmony in Tonal Music, vol. 2, 85. upper part, which contains a conspicuous motion up to and writes that "the of 37JoelLester, for example, majority augmented-sixth ultimatelythrough the leading tone. This motion plainly high- chords used in tonal music are in fact altered dominants of the dominant" the dominant-functioned of the chord, and, to (Harmony in Tonal Music, vol. 2, 93). lights aspect 38Note20 above discussesthe idea of breakingsubdominant function apart in this manner. 39A similar case is found in the "lab specimen" in Example 3. 188 Music Theory Spectrum

Example 15. Liszt, Weinen, Klagen, Sorgen, Zagen, mm. 179-83

a.

- ,^:^bC'' 1: #'>1 >#+t"8Esim. Vte

Xb t l bbbb i/i- 1b11B i1 ? my mind, tips the balance towards hearing the augmented- contents with the tools developed so far. The chord of res- sixth chords as dominant- rather than subdominant- olution is tonic-again, on account of the doubled third pro- functioned, making for an authentic functional type. duced by the action of one of the augmented sixths in the The Till Eulenspiegelcitation in Example 12 illustratesthe preceding chord. The two augmented sixths operating in m. other circumstancediscouraging dominant function. The aug- 3 are creatures of dominant and subdominant functions re- mented sixth resolves into the third of the following major spectively. The Gb-E interval depends on the dominant func- triad. Such a doubling pointedly rejects dominantpossibilities tion of E as 1, while the B -G# augmented sixth is built upon because the doubled third would be, in fact, a doubled lead- 4 as a subdominant element. Dominant function clearly has ing tone. Hence, the F-majorchord is tonic-functioned.Anal- the upper hand in this chord, as the downbeat of m. 3 contains ysis of the augmented-sixth chord is less routine. Consider- the basic elements of a V7 in F: C, E, and Bb. The Gb also able subdominant powers are transmitted by b6 and by the sounding there is in an augmented-sixthrelationship with E, placement of the prominent subdominant element 4 in the which relationship strengthens rather than ambiguates the bass. Yet the first occurrence of the Till motive (rehearsal 2 already established dominant function of the chord. The sec- + 14) interrupts a powerful V7 of F, which the resolution to ond augmented sixth of the chord is only activated on the F in Example 12 can be heard to satisfy. Thus, dominant second of m. 3, and its diatonic member, 4, is buried function can still be heard to persist in the Till chord- at least in the sound mass. Dominant function clearly prevails in this in this incarnation-transmitted by E as S. To my mind at augmented-sixthchord, meaning that it manifests the authen- least, the subdominantelements largely subdue E, leading to tic functional type. a plagal interpretation. Now that the disarraybrought on by the influxof new types Finally, the opening of Schoenberg'sChamber Symphony, of augmented-sixthchords has been reduced by reclassifying op. 9, cited in Example 14 as a kind of marvel among chord types, it is appropriate here to show off what this re- augmented-sixth chord usage, can also yield its functional organized analyticdevice can accomplishby turningattention Supplementto the Theory of Augmented-SixthChords 189 to a composition where the augmented sixth is a conspicuous sense of constrictionand suppressionin the poem. In the text, tonal force, Brahms's part song "Im Herbst," op. 104 no. 5, images of "under," "below," and "beneath" are constantly the score of which appears in Example 16. displayed in the first two verses. (Figure 5 offers the text and translationof the poem.) In the first, leaves fall and the heart BRAHMS:"IM HERBST," OP. 104 NO. 5 sinks; then a journey to the south (below) is likened with one to the grave (six feet under, presumably).In the second verse, Problems with a traditional augmented-sixth chord anal- fog enshrouds the sun and the heart, and existence itself is ysis crop up in the very first measures, as a pre-dominant described as deeply withdrawn. Moreover, the language the German sixth in an unusual 4 position at the end of m. 1 poet uses seems overly terse, as if language itself were re- resolves irregularlyto a cadential 6 in m. 2. It takes but little pressed and enshrouded. The firstsentence of text-all of two effort to uncover a more normal underlying structure; the iambic feet-is remarkablein its sonic economy: Ernst ist der structuralnotes of the bass and top voices could be considered Herbst. The situation eases considerably in the third verse, to be offset, so that the bass line is grounded upon the open- as discussed shortly, but the overall impressionof the firsttwo ing Ab, while the top is fastened to the Ft at the end of the is one of a laconic solemnity that threatens to lapse into an measure. In this interpretation, what appears then in the impassive silence -as if the poet were one with the soundless opening measures is no more than a horizontalized German- bards journeying to the south. sixth chord. Yet the very notion of such a horizontalization Downward tendencies are also quite evident in the destabilizes the idea of the augmented-sixth chord being a -notably, in the diminished-thirdunfolding in the mere passing verticality, as is generally taught. soprano that begins every half verse. Other conspicuous Ironically, this freeing-up of the augmented sixth as a tech- examples are the soprano line in mm. 3-8, which, although nical device serves to repress other types of musical expres- broken by an upward octave transfer at the end of m. 6, is sion. The augmented sixth in this piece is an idee fixe which nonetheless preoccupied (obsessed, even) with descent and seems to preclude other musical thoughts. Each half verse decline. The beginning of the second half-verse in mm. 10-13 (mm. 1, 10, 20, and 30) begins with the same unfolding of seems to promise some alleviation from the downwardspiral. a melodic diminished third as found in m. 1, during which Yet the hopeful ascent in these measures seems only to have some augmented-sixthinterval is sounded harmonically. (In the attainmentof Eb5 in mind since the melody begins there- 4 the German chord at the end of m. 1, a harmonic aug- after another deliberate descent to Ft4, traversing the same mented sixth is formed between the soprano and tenor.) Ut- space as was covered in mm. 7-8.40 terances cannot begin without touching upon the augmented What role, then, does the augmented-sixthchord play in sixth-nor end for that matter, since each verse closes with this story of autumnaldepression? It seems to be at once both an authentic cadence approached through a German sixth. a symptom and a cure, a paradoxicaland intriguingstatus that Before dealing with other augmented-sixth matters, I should enlarge upon what is meant by saying that the aug- mented sixth other musical For the 40Anotherimportant musical aspect of constriction and obsession is the represses expressions. constant and tenor motion in thirds. These voices thus have no obsession with the insofar as it crowds out hence parallel chord, (and freedom of action on their own; they move in lockstep, each is unable to break represses) other possibilities, is a consequence of a pervading free from the constrainingpower of the other. I I

190 Music Theory Spectrum

Example 16. Brahms, "Im Herbst," op. 104 no. 5

P - af - P Soprano & Alto r' J|ib' I Jb_ 'r'r r Ernst ist der Herbst. Und wenn die Blat- ter fal- len, sinkt auch das Herz, sinkt Bleich ist der Tag, und bias- se Ne- bel schlei- ern die Son- ne, die Son- ne

I Tenor J & Bass V- . -^bb rf 1 If f" f'-~ ' I r fy -J

7 ''15,P oI ddolce e

Ir r r r rr rr I: 4 auch das Herz zu tru- bem Weh her- ab. Still ist die Flur, und nach dem Sii- den wal- len die wie die Her- zen, wie die Her- zen ein. Friih kommt die Nacht: denn al- le Krif- te fei- ern, u b-- Ifr r r I-- "- r r- - - r r f

14 -p sempre dolce

1'r tIr ^[r ': I .i I I San- ger stumm, wie nach dem Grab, wie nach dem Grab. Sanft wird der Mensch tief ver- schlos- sen ruht das Sein, ruht das Sein.er Mensch - \J. 8. 51 B : F - I ' If' F' i

22 espress. cresc. f 1J 1 1 siII n- - r r aI, iw- J S

sieht die Son- ne sin- ken, er ahnt, er ahnt, des Le- bens wie des Jah- - res Schluss.

r f :i r r r'If I~- f' ' Supplementto the Theory of Augmented-SixthChords 191

Example 16 [continued].

30 f AT- cresc.

Feucht- wird das Aug, doch in der Tra- ne Blin- ken, doch in der Tra- ne Blin- ken ent-

r r I#-1^ 'i

36 : j rp dolce dim. L I | a a y. Jrf rJ J J I J --___== I ["==.--I-Ito*^ -r

-stromt _ ent- stromt des Her- zens se- lig- ster Er- guss, se- lig- ster Er- guss.

t'|o v- I

explains the attention bestowed upon it. Yes, the sonority Measure 10 finds another treatment of an augmented-sixth pervades the piece-symbolizing the reduced expressive cir- chord. Again, as in mm. 1 and 5, the same pitch material (in cumstances the poet finds himself in. But the treatmentof the both register and voicing) is reassembled, but the augmented sonority, as already suggested, hardly agrees with such re- sixth between Al3 and F#4 now resolves into the third of an duction. Indeed, Brahms explores all manner of possible res- E -major triad, thus placing the interval between scale de- olutions and treatments in seeming attempts to uncover and grees 4 and #2 in Eb major. As Example 17 suggests, the unblock, to find ways out of the constant downward pres- functional type here is plagal. The entrance of Eb major sures. The fact that the German-sixth chord is given its un- seems to augurwell for a solution to the persistent downward usual horizontal arrayin m. 1 is the first telling clue. But other push, since both soprano and bass lines are able to rise gently illustrations abound. Clearly, the V7 of the Neapolitan in m. in its atmosphere.41As already noted, however, once the 5 is an attempt, via the usual enharmonictrickery, to find one soprano reaches Eb5 in m. 14, the text takes a decidedly more way out. Ironically, this attempt abets and enables continued downward this needless to is not re- motion; method, say, 41The reversal of bass motion in m. 10 with respect to m. 1 seems to peated in the remainder of the verse. adumbrate this possibility. 192 Music Theory Spectrum

Figure 5. Karl Groth, "Im Herbst." Translationby the author

Ernst ist der Herbst. Und wenn die blatter fallen, Solemn is the Autumn. And when the leaves fall sinkt auch das Herz zu trubem Weh herab. sinks also the heart to troubled woe. Still ist die Flur, und nach dem Suden wallen Still is the meadow, and towards the south journey die Sanger stumm, wie nach dem Grab. the bards in silence, as if to the grave. Bleich ist der Tag, und blasse Nebel schleiern Pale is the day, and colorless fog enshrouds die Sonne wie die Herzen ein. both sun and hearts. Fruh kommt die Nacht: denn alle Krafte feiern, Early comes the night: for all Powers celebrate und tief verschlossen ruht das Sein. and deeply withdrawn rests the being. Sanft wird der Mensch. Er sieht die Sonne sinken, Soft becomes the man. He sees the sun sink; er ahnt des Lebens wie des Jahres Schluss. he foresees the end of life and of the year. Feucht wird das Aug, doch in der Trane Blinken Moist becomes the eye, yet in the tear-sparkle entstromt des Herzens seligster Erguss. gushes the heart's most blessed outpouring.

depressing turn, forcing the soprano to plod downwardsyet stresses members of the augmented-sixthchord at each down- again, the bass following reluctantly after. Evidently, the beat, as Example 18 indicates with a beam. The return of plagal therapy provided only temporary relief. these opening, pre-dominant augmented-sixth concerns re- The harmonic goal of the descent in m. 17 is the same inforces the sense of constriction and expressive repression German4 sonority met with in m. 1, and the last three pitches at work in the song. of the descent (Ab, G, F#) reprise the opening pitches of m. An apparentlyslight difference between the ending of the 1.42Furthermore, the soprano in these mm. 14-17 pointedly first and second verses makes for a profound difference in one's evaluation of this constriction. In the first verse at m. 17, Brahms the of the "wie 42I have already remarked above on the similaritiesbetween the soprano repeats closing phrase poem, descents in mm. 7-8 and 14-17; i.e., they traverse the same space between nach dem Grab," setting "wie" to a standard German-sixth Eb5 and F#4. But they also share the Ab,-G-F# motive introduced in m. 1, chord and thereby normalizingthe approach to the cadential although in mm. 7-8 it is slightly obscuredby surface elaboration. The desire 6. In the second verse, however, the closing phrase, "ruhtdas to reuse this melodic idea (or the compositional need to restrict vocabulary) thus explains the Neapolitan-sixthin G minor found at the end of m. 7; this chord accommodates Ab as b2. This particularsituation prompts additional tively. The Neapolitan could be regarded in general as one element of a theorizing about the Neapolitan sixth as manifesting augmented-sixthener- horizontalizeddiminished third between bl and #1. This line of thinking is gies, which I will but briefly sketch. The enharmonic relationship of implicit in Schenker's discussion of b2 in Free Composition (trans. and ed. augmented-sixthchord and V7 of the Neapolitan already places them into a Ernst Oster [New York: Longman, 1979], 71 and Fig. 74). The excerpt from special relationship, but the fact that, in normal resolution, b6 supported by Liszt's Orpheusin Example 6, which has an augmented-sixthchord involving a Neapolitan traverses a diminished third to p7 links the two more sugges- b2 and p7 flowing out of a , also supports this hypothesis. Supplementto the Theory of Augmented-SixthChords 193

Example 17. Plagal augmented-sixthchord and then by resolution to a major cadential 6 in m. 21, after which C major blossoms freely. At the moment of acknowledgement-the presentment of b ------$ ,,,i----, Death that Autumn has caused-the obsession with the augmented-sixthchord becomes extreme; mm. 24-26 contain a sequence emphasizingpre-dominant German-sixthchords. pbw,S ------'- I Had this augmented-sixth supersaturation occurred in the Aug. 6th (subdominant) Tonic firsttwo verses, its significancewould have been truly sinister; in the less depressing atmosphere of the C-major third verse, however, this sequence-while still disturbing-seems less threatening. For one thing, the sequence rises, and, more- Sein," contains one less syllable, and brahms consequently over, occurs at a point where the first two verses were forced omits the German-sixth. The German 4 thus progresses di- into continued downward motion. For another, the rectly to the cadential 6 just as it did in mm. 1-2. The con- augmented-sixthchord in m. 24 is, from a pitch standpoint, clusion of the second verse thus makes its affinity to the a new entity. Whereas previous augmented sixths in the piece opening more explicit and pronounced, its message of con- were formed between Ab and Ft, that in m. 24 is between striction and repression more plaintive, and its final empty Bb and Gt. fifth more desolate. The enharmonic equivalence of G# and Ab is something The third verse is quite different from the first two. At- to note here. In the first two verses, a melodic Ab is, with tention is drawn away from the observed world and towards one exception, always obliged to drop to G. This is so even an observing person. Then, the source of the pervasive mel- when an augmented-sixthchord is not involved, as in m. 4. ancholy is identified and acknowledged (identificationof Au- The transformationof Ab into G# in the third verse, how- tumn with Death). And, finally, this acknowledgmentpermits ever, entails a change of directional attribute; G# and its the poet at last to escape the constriction of the first two rising tendency encapsulate the breaking-through that the verses, symbolized by gushing outpouringfrom the previously third verse is about. enshrouded heart. Significantly,the beginning of the second part of the verse The crucial musical difference between the third and the in m. 30, while still structuredaround the melodic diminished- first two verses is mode. It seems trite to point to a change third motive, now has that motive traversingthe new Bbl-G# from minor to major as symbolizing a change in emotional space. As in the previous verses, the final chord of the motive climate for the better, but there is no doubt that the ste- involves a harmonic augmented-sixthinterval, this time be- reotype holds true in this case. What effect does this change tween the tenor and soprano. Yet a change in functional have on the augmented-sixthchord obsession? Initially, only attributeis quite significanthere; for the firsttime in the song, a slight one, as the verse begins with the familiar diminished- the authentic functional type is heard, as Example 19 illus- third unfolding and pre-dominant German-4-to-cadential-6 trates. Here accrues one of the benefits of a reconstituted resolution. The mode shift is signaled subtly by having the augmented-sixthcategory, since the chord in question would 7 passing soprano G4 in m. 20 harmonized by a C-major triad otherwise be analyzed not as an augmented-sixthbut as a V 194 Music Theory Spectrum

Example 18. "Im Herbst," soprano line, mm. 14-17

J. .1 i f IJ- J J. of F. In the context of the song, however, this chord is in- At first glance, the reappearance of the dark, pre- tended to be just as much an augmented-sixth as those met dominant Ab-F# augmented sixth in m. 40 might seem to with earlier-but only by breakingfree from traditionalchord indicate a relapse. But a breakthroughhas occurred, giving taxonomies can one appreciate this.43 this reappearance an aspect of reconciliation. The mode is The opening-up depicted in the third verse receives won- still C major, which guardsagainst relapses of C-minorissues. derful musical support. Both soprano and bass lines engage Alto and tenor pointedly move in a contrary-motion voice in lengthy ascents in mm. 31-37, and the previously bound- exchange, refusing to revert to their C-minor parallel-motion together alto and tenor lines break loose from each other and pathology. Finally, as the soprano prepares to settle down pursue largely independent courses. Most significantly, after upon E4-another gentle coming-to-terms with previous the soprano breaks through her previous ceiling of El 5 and downward obsessions-the alto overlaps her and sings G4. shoots upwardsto G5 in m. 35, she is in m. 37 pushed higher Not to be confused with a symbol of repression (forcing the yet again by the agency of the Bb-GO augmented sixth- soprano down), the alto's overlap is rather a symbol of emer- again exhibiting the liberating authentic functional behavior. gence; from out of the enshrouded interior dawns a previ- We find here no clearer illustrationof the paradoxicalrole of ously repressed voice-perhaps the very "seligsterErguss" of the augmented sixth in this piece; symbolizing the brooding which the poet speaks. repression of the first two verses when behaving pre- dominantly, it is in the third verse an effective therapeutic agent thanks to changes in mode, pitch location, and func- CONCLUSION tional type. The thesis of this article, that we ought to attend primarily to the augmented-sixth interval and its functional context 43Itis appropriateto note here the enharmonicequivalence of the chord and to its harmonization as an re- in 19 with that shown in 8c-that rara avis found so fleet- regard epiphenomenon, Example Example ceives from Brahms's "Im Herbst." Al- ingly in the excerpt from Verdi's Requiem in Example 9. What is more, the eloquent support enharmonic equivalence here is between two types of augmented-sixth though standard-issuepre-dominant Germ n-sixths abound, chords. The differences in spelling between the two indicate differences in there are more than enough nonstandard treatments to call how their respective augmented sixths resolve. That in Example 8c resolves into question the theoretical-and pedagogical-advantages to E. Respelling the chord along the lines of the present case-in other words, of so the three ethnic-sixth chords. the an El -then the interval between focusing intently upon making D# places augmented-sixth C# be in common- and El, meaning a resolution to D. Despite both being augmented-sixth True, they may statistically preponderant chords and despite their enharmonic equivalence, these two chords are practice music and therefore deserve their special names. But functionally quite distinct. when we elevate them to such an extent that we misplace Supplementto the Theory of Augmented-SixthChords 195

Example 19. The authenticaugmented-sixth chord with others that desire flexibility and play, which allow the- orizing about tonal music to be an artisticallycreative act, as Schenker and others have demonstrated. This supplement to the theory of augmented-sixthchords is intended to restore more play into a small component of tonal theory without, it is hoped, sacrificing its integrity. This goal perhaps still involves circling the wagons; but if the area encompassed be Aug. 6th (dominant) Tonic large enough, there will still be enough room for both stan- dard and nonstandardaugmented-sixth chords to run happy and free. other treatments, we lose theoretically and analytically- ABSTRACT theoretically, because we succumb to the temptation to circle Traditionaltonal theory, in its emphasison the threeethnic varieties the wagons of tonal theory in the hopes of closing the system of augmented-sixthchord, proves inefficient in handlingother types and, as a result, leave non-privileged structures and proce- of augmented-sixthchords frequentlyfound in late nineteenth- dures exposed and unprotected; and analytically, because century music. The paper reconstructsthe theory supporting chords more lines so that unusual we are unable to fashion tools and instruments for dealing augmented-sixth along general with whose contents leave them treatmentscan be moreadequately explained and analyzed.Some adequately compositions in this reconstructionis theo- the circle. support givenby nineteenth-century ristssuch as GottfriedWeber and Rudolf Louis and Thuille. It is a truism that tonal lacks the and well- Ludwig theory rigor Excerptsfrom the worksof Liszt,Wagner, Richard Strauss, Franck, defined structure set of, say, pitch-class theory. Certainly, Schoenberg,and Verdi illustrate some of these unusualtreatments. instincts towards making tonal theory more consistent and The paperalso analyzesBrahms's part song "ImHerbst," op. 104 rational ought to be honored, if for no other reason than no. 5, in which unusualtreatments of augmented-sixthchords successful pedagogy requires it. But these instincts conflict abound.