Augmented Sixth Chords: An Examination of the Pedagogical Methods Used byThree Harmony Textbooks

In searching for manifestations of Hegelian unity in music (as theorists andphilosophers so frequently do), one need not look further than the augmented sixth chord.Defined by its linear melodic outline, it functions as a vertical, harmonic construct;innately chromatic, it impetuously proclaims a tonal center; distinct in its individualcharacter, it is consummated only in concurrence with its fellow harmonies; indeed, theaugmented sixth chord is an exemplary juxtaposition of antithetical concepts. How canone even begin to explain so complex an entity? How can one account for its copiouspossibilities and implications? Theorists and pedagogues have taken many differentapproaches to the teaching of augmented sixth chords. In the following paragraphs, threesuch approaches will be examined and discussed as put forth by three different textbooks:Harmony and Voice Leading (Aldwell and Schachter), Harmony (Piston), and Harmony(Schoenberg).

Intended for students of varying theoretical backgrounds, both the Piston andAldwell/Schachter texts provide an organized, methodical explanation of augmentedsixth chords and their uses. (Schoenberg, writing for a different audience perhaps, differswildly in his approach and consequently will be discussed separately.) Discussion ofthese chords in both textbooks begins with a description of the interval of the augmentedsixth and its title role in augmented sixth chords: Piston provides a brief, detailed, verbalaccount, while Aldwell and Schachter introduce the interval with an excerpt from aMozart sonata before proceeding to a verbal description. They then make several generalstatements to be elaborated upon later and point out that these chords are unique as theydo not belong to the key of their resolution. The description is clearly communicatedthrough use of letter note-names and written notes, while Pistons description is slightlyabstruse in its reliance on scale degrees. Having introduced augmented sixth chords, bothbooks then explain contrapuntal origins and present the four, multi-national varieties:Italian, French 4-3, German 6-5, and German 4-3. Piston lists the four chords andadequately explains their construction. He then appends his Definitions section with aResolutions section that makes use of the same esoteric jargon as his introduction of

the augmented sixth. Several interesting comments on the intuitive and logicalassociations of the different chords with either major or minor modes provide somecompensation for the sections deficiencies; nonetheless, Pistons commentary pales incomparison to Aldwell and Schachters exhaustive accounts of each chord that includecharacteristic qualities, frequent uses, resolutions, and examples from widely-knownrepertoire. It is interesting to observe the paradigm shift from Pistons definitions, whichassign each chord to a somewhat contorted version of a Roman numeral, to those ofAldwell and Schachter who, having already dismissed augmented sixth chords as keylessentities, absolve themselves of any such diatonic responsibility.

After expounding on the intricacies of these chords, Aldwell and Schachterdiscuss various means of approaching augmented sixth chords. Any student who thoughtthe previous description were lackadaisical will certainly take recompense in reading thissection: Aldwell and Schachter thoroughly chronicle the methods of arriving ataugmented sixth chords via chromaticized, altered, or just plain simple forms of I, II, IV,and VI. Though they have abstained from relating augmented sixths to any diatonicharmony thus far, the authors can not entirely escape pedagogical tradition, and so theydo correlate these chords to II and IV. Aldwell and Schachter then explain the use ofaugmented sixth chords as agents of modulation to V and discuss other miscellanea thatPiston only briefly touches upon. Both textbooks proceed to mention the use of thesechords in inversion, resulting in diminished thirds; this is fairly self-explanatory and neednot be elaborated upon. Finally, both texts arrive at descriptions of perhaps the mostinteresting and empowering quality of augmented sixth chords: their ability toenharmonically double as dominant seventh chords and thus create a portal to distant andunrelated keys. It is unfortunate that this elucidation is relegated to the very end of thechapter at which point the student may be overwhelmed by the complexity of the topic as this aspect of augmented sixth chords provides easy access to a wide spectrum ofinteresting possibilities that were previously unattainable.

Before moving on to Schoenbergs textbook, it is necessary to take note of theproblem of parallel fifths that arises when the German augmented sixth chord resolves toV. The problem lies not in the parallel fifths themselves as these can be easily avoidedby inserting a 6-4 chord but rather in the fact that this strictly forbidden interval

progression is actually quite innocuous and often occurs in compositions of the greatmasters. Both the Piston and Aldwell/Schachter texts dutifully warn the student of thedanger of parallel fifths and discuss ways of avoiding them within this particularresolution, but they all too grudgingly admit that, were this sacred doctrine violated, thesacrilegious composer would not necessarily be smitten to the ground by a lightning boltfrom the heavens.

In stark contrast to both the aforementioned textbooks, Schoenbergs Harmony isnot intended for the average student. As the author delves into a profound philosophicalinvestigation of augmented sixth chords without actually explaining what they are, itbecomes quite apparent that the reader must be endowed with both previous knowledgeof the topic as well as saintly patience. The contents of the chapter seem better suited tothe composer struggling to find interesting creative outlets within the tonal idiom than tothe musician seeking a clarification of harmonic theory.

Rather than explaining augmented sixth chords as a whole and then specifying thecharacteristics of the four different types, Schoenberg accounts for each chordindividually. He begins with augmented 6-5 chord, but is almost immediately distractedby the issue of parallel fifths in this chords resolution. After stating that these fifths arenot so bad after all since they were used by Mozart, he declares that anything written bythe masters should be permitted. This statement sends him on yet another tangent, and hebegins to consider the differences between practical and aesthetic theory, only toconclude that the student should not write parallel fifths whenever it is possible to avoidthem. Such digressions are characteristic of Schoenbergs writing style in this book; thereader must accept them and grow accustomed to them in order to benefit from theauthors wisdom. Returning to his original subject, the augmented 6-5 chord, Schoenbergpresents a very interesting approach to its derivation: bound to the notion that the chordmust belong to a diatonic scale degree yet seeking consistency, Schoenberg classifies theaugmented 6-5 as an incomplete ninth chord on II, where the root (scale degree 2) is notactually realized. Any other derivation, he maintains, would define the chord as a variantof either II, IV, or VI depending on its context, and this disparity may be confusing (!).Schoenberg uses this very argument later in the chapter to dismiss the idea that the chord

could belong to any particular key, and having thus liberated augmented sixth chords, heimmediately associates them with diatonic harmonies yet again. Now that the augmented6-5 chord has been explained to the authors satisfaction, he accounts for the otheraugmented sixth chords as inversions of the 6-5. Since he views the chord as a ninthchord, four inversions must exist; thus Schoenberg invents a new species of thisaugmented sixth chord. The next few pages are devoted to the anthropomorphization ofvarious scale degrees and to unnecessarily complicated analysis of enharmonicallyequivalent spellings. Finally, Schoenberg states the significance of the chords doublefunction as augmented sixth chords and dominant seventh chords. Of the three textbooksexplored thus far, only Schoenbergs Harmony fully addresses the possibilities andimplications of this duality.

The remainder of the chapter is of greater compositional interest than it is oftheoretical significance. Schoenberg, recognizing that the student may be timid in writingchords of such distinguished, chromatic, character, urges him or her to make frequent useof these chords in order to consistently and distinctly color a composition. The studentneed not fear that the overall sense of tonality will be lost, since it can always bereinforced through proper resolution of the augmented sixth chord to V and then I.Schoenberg presents the idea of constructing augmented sixth chords on each diatonicscale degree (the scale degree itself acts as the silent root of the ninth chord, of course)and suggests that all these chords may be used, even if vigorous means are sometimesneeded to restore the key. (252). Later in the chapter, two new varieties of chords areintroduced: the first is an inverted, French, diminished third chord in which the third issurrounded by the minor seventh formed by the remaining two tones; the second is thesame as the first, but here, the upper leading tone is lowered by a half step so that it is nolonger a leading tone (in essence, this is a half diminished seventh chord). In both thesechords, the outer voices that form a minor seventh resolve outward to an octave, just asan augmented sixth would. Schoenberg points out that these chords are not particularlycomplicated and do not require lengthy discussion, but then proceeds to discuss them forthe next several pages. The unexpected outward resolution of a minor seventh, however,is a useful and interesting compositional device. Towards the end of the chapter,Schoenberg suggests that the student practice connecting augmented sixth chords with

diminished seventh chords, augmented triads, Neapolitan sixth chords, and otheraugmented sixth chords, and explains the benefits of each of these relationships. Thisonce again presents the student with many interesting options.

Schoenberg concludes with some remarks about the necessity of proper voiceleading in composition and the possibility that extended chromaticism will someday be asprominent in vocal music as it is in instrumental music. Maintaining the logical andrhetorical style of the rest of the chapter, the author leads to his final coda by writing: Inconclusion, yet other possibilities for resolving the diminished seventh chord should beadded here. To reward the brave reader for surviving up to this point, Schoenberg offersextremely insightful and useful commentary in the penultimate paragraph: pitches areflexible. Each pitch even combinations of two or three pitches contains a myriad ofpossibilities. Alterations as simple as moving a single pitch up or down a semitone canresult in entirely new contexts, while still maintaining some tonal relevance. Havingthoroughly confused the reader, Schoenberg vehemently urges him or her to go forth andexplore. Keeping this imperative in mind, even some of the authors more far-fetchedadvice is invaluable to the composer.

The pedagogical methods used by Piston and Aldwell and Schachter arethoroughly organized and fairly clear, which accounts for their popularity and widespreaduse. Though Pistons explanations tend to be obscure, they are quite adequate, and thoughAldwell and Schachters explanations tend to be gratuitously detailed, they are thoroughand they demonstrate the significance of augmented sixth chords within a greater musicalframework. Schoenbergs book, though not for the faint of heart, is perhaps the mostinteresting, most compositionally useful, and at least as unique in character as the chordthat it describes. Though these three textbooks competently clarify augmented sixthchords, the intricate and somewhat mysterious nature of these harmonies is never trulyelucidated. A teacher can, at best, combine the three didactic approaches by describingthe more tangible qualities of augmented sixth chords, familiarizing the student withcommon uses of these chords, and sending the student off to discover for him or herselfthe plethora of possibilities that exist in the uncharted waters of the chromatic world.

I. the interval of the augmented sixtha. why an A6 and not a m7?b. Inherent chromaticism of the double leading tonec. Outward resolution to a P8 (play examples; compare to examples of resolution

of a m7)II. augmented sixth chords

a. chord construction (play each chord)1. Italian2. French 4-33. German 6-54. German 4-3

b. Common resolution of each chord (play each resolution)1. mention parallel 5ths formed by German A6, show that they are not

strongly heard, suggest that proper voice leading be followed forpedagogical purposes

c. approaching A6 chords (play each approach)1. from II and IV

a. chromaticized voice exchange2. from VI3. from I4. contrapuntally

a. through chromatically descending bassb. with b6 as neighbor note to 5

d. common uses and characteristics of each chord1. play and discuss examples from the repertoire

III. diminished third chordsa. inversion of A6 chordb. proper voice leading

Separate Lesson

IV. A6 chords in modulationA. modulation to V

1. discuss role as secondary dominant2. play and discuss examples from repertoire

B. modulation by half step1. discuss double function as dom7

a. function as V7/bIIb. typical usesc. play and discuss examples

C. other possible modulations

1. discuss the possibilities created by constructing A6 chords on differentscale steps and reinterpreting them as dom7 chords

2. play and discuss examples

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