Augmented sixth chord

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The interval of an augmented sixth normally resolves outwards by semitone to an octave. About this sound Play 
The 3 most common augmented sixth chords in the tonalities of C major and C minor: Italian 6th, French 6th, and German 6th.

In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance,[1] further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.[2] The three more common types of augmented sixth chords as usually called Italian 6th, French 6th, and German 6th.

Resolution and chord construction[edit]

The augmented sixth interval is typically between the sixth degree of the minor scale (henceforth 6) and the raised fourth degree (henceforth 4). With standard voice leading, the chord is followed directly or indirectly by some form of the dominant chord, in which both 6 and 4 have resolved to the fifth scale degree (henceforth 5). This tendency to resolve outwards to 5 is why the interval is spelled as an augmented sixth, rather than enharmonically as a minor seventh (6 and 5). Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by borrowing 6 of the parallel minor scale.[3]

Double-diminished triad[edit]

In music theory, the double-diminished triad is an archaic concept and term referring to a triad, or three note chord, which, already being minor, has its root raised a semitone, making it doubly diminished. However, this may be used as the derivation of the augmented sixth chord.[4]

For example, F-A-C is a minor triad. F-A-C is a doubly diminished triad. Note that it is enharmonically equivalent to G-A-C (incomplete dominant seventh [missing E] or "backdoor" dominant-seventh substitute VII). A-C-F is an Italian augmented sixth chord.

Types[edit]

There are three main types of augmented sixth chords, commonly known as Italian 6th, French 6th, and German 6th. Though each is named after a European nationality, theorists disagree on their precise origins and have struggled for centuries to define their roots, and fit them into conventional harmonic theory.[3][5][6]

Italian sixth[edit]

The Italian sixth moving to V. About this sound Play 

The Italian sixth (It^{+6} or It^6) is derived from iv^6_{} with an altered fourth scale degree, 4: 614; A—C—F in C major and C minor. This is the only augmented sixth chord comprising just three distinct notes; in four-part writing, the tonic pitch is doubled.

The second movement of Beethoven's piano sonata in F-sharp major, op. 78, begins with an Italian sixth chord. About this sound Play 

The Italian 6th is enharmonically equivalent to an incomplete dominant seventh.[7]

French sixth[edit]

The French sixth chord; the distinguishing tone is highlighted in blue. About this sound Play 

The French sixth (Fr^{+6}_{} or Fr_3^4) is similar to the Italian, but with an additional tone, 2: 6124; A—C—D—F in C major and C minor. The notes of the French sixth chord are all contained within the same whole tone scale, lending a sonority common to French music in the 19th century (especially associated with Impressionist music).[8]

German sixth[edit]

The German sixth (Gr^{+6}_{} or Ger_5^6) is also like the Italian, but with an added tone 3: 6134; A—C—E—F in C major and C minor. In Classical music, however, it appears in much the same places as the other variants, though perhaps less used because of the contrapuntal difficulties outlined below. It appears frequently in the works of Beethoven.[9] The German sixth chord contains the same notes as a dominant seventh chord, though it functions differently.

It is more difficult to avoid parallel fifths when resolving a German sixth chord to the dominant, V. These parallel fifths, referred to as Mozart fifths, were occasionally accepted by common practice composers. There are two ways they can be avoided:

  1. The 3 can move to either 1 or 2, thereby generating an Italian or French sixth, respectively, and eliminating the perfect fifth between 6 and 3.[10]
  2. The chord can resolve to a "six-four" chord, functionally either as a cadential six-four intensification of V, or as the second inversion of I; the cadential six-four, in turn, resolves to a root-position V. This progression ensures that, in its voice leading, each pair of voices moves either by oblique motion or contrary motion and avoids parallel motion altogether. In minor modes, both 1 and 3 do not move during the resolution of the German sixth to the cadential six-four. In major modes, 3 can be enharmonically respelled as 2 if it resolves upwards to 3, similar in voice leading to the resolution of French sixth to the cadential six-four. This respelled chord is sometimes referred to as the English, Swiss or Alsatian sixth chord,[citation needed] or as a "'doubly augmented sixth chord"', as it contains two augmented intervals. However, other sources describe it as a German sixth.[11]
The German sixth; the distinguishing tone is highlighted in blue. About this sound Play 
The German sixth is typically followed by a I_4^6 chord to avoid parallel fifths. About this sound Play 
German sixth chord respelled with doubly augmented fourth (highlighted in blue) for voice-leading purposes. Also referred to as English, Swiss or Alsatian.
A German sixth chord from Michael Haydn's Requiem in C minor, first movement. (Loudspeaker.svg Listen)

Other variants[edit]

Other variants of augmented sixth chords are sometimes found in the repertoire, and are sometimes given whimsical geographical names. For example: 4672; (F—A—B—D) is called by one source an Australian sixth.[12] Such anomalies usually have alternative interpretations.

Standard harmonic function[edit]

From the Baroque to the Romantic period, augmented sixth chords have had the same harmonic function: as a chromatically altered predominant chord (typically, an alteration of ii_3^4, IV_5^6, vi7 or their parallel equivalents in the minor mode) leading to a dominant chord. This movement to the dominant is heightened by the semitonal resolution of both 6 to 5 and 4 to 5; essentially, these two notes act as leading-tones. This characteristic has led many analysts[13] to compare the voice leading of augmented sixth chords to the secondary dominant V of V because of the presence of 4, the leading-tone of V, in both chords. In the major mode, the chromatic voice leading is more pronounced because of the presence of two chromatically altered notes, 6, as well as 4, rather than just 4 in the minor mode.

The most solid and obvious view of an augmented sixth chord is a subdominant borrowed from the parallel key.

"A German sixth in the key of C contains the notes Ab C Eb F#. This would entail the minor parallel, being C minor, having the minor 3rd (Eb) and the minor 6th (Ab) and then the augmented 4th being F# which is the augmented 6th of the Ab upon which the chord is built. So a IV chord of the parallel prodominant Eb, which is the subdominant, leading into the dominant chord of C major being G, thus containing the F# as a leading tone. This is actually using the minor parallel keys submediant VI (the prodominant major key subdominant) to set up the dominant. The subdominant of the parallel prodominant."

"German Sixth in C major Ab C Eb F# C major (C D E F G A B) to parallel C minor (C D Eb F G Ab Bb) Ab being the VI chord submediant then to prodominant Eb major (Eb F G Ab Bb C D) Ab being the IV chord subdominant. The subdominant of Eb is Ab major (Ab C Eb) the sixth of which is F. Augmenting the sixth to F# gives us Ab C Eb F# a German sixth. F# is a leading tone to the root of the Dominant of C which is G major or the augmented fourth leading to the fifth of C major which is G. F is the fourth of C and is Augmented. From Ab in Eb we have Lydian being that it is the IV chord and the augmented fourth is D. Since the parallel keys major subdominant is used for the predominant the #4 is also translated and the French sixth is formed Ab C D F#.

So the function of an Augmented sixth chord is the subdominant of the parallel prodominant major setting up the dominant chord in the original key."<Allen 2014, 42>

Root position and inversion of augmented sixth chords[edit]

Augmented sixth chords are occasionally used with a different chord member in the bass. Since there is no consensus among theorists that they are in root position in their normal form, the word "inversion" isn't necessarily accurate, but is found in some textbooks, nonetheless. Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.

Rousseau considered that the chord could not be inverted.[14] 17th century instances of the augmented sixth with the sharp note in the bass are generally limited to German sources.[15]

Excerpt from Bach's Mass in B minor. At the end of the second measure, the augmented sixth is inverted to create a diminished third or tenth between the bass and the soprano (C—E); these two voices resolve inward to an octaveAbout this sound Play 
Root positions of the augmented 6th chords in the tonality of C, according to Simon Sechter.[16]

Simon Sechter explains the chord of the French Sixth as being a chromatically altered version of a seventh chord on the second degree of the scale. The German Sixth is explained as a chromatically altered ninth chord on the same root, but with the root omitted.[16]

The tendency of the interval of the augmented sixth to resolve outwards is therefore explained by the fact that the A, being a dissonant note, a diminished fifth above the root (D), and flatted, must fall, whilst the F - being chromatically raised - must rise.

Extended functions[edit]

In the late Romantic period and other musical traditions, especially jazz, other harmonic possibilities of augmented sixth variants and sonorities outside its function as a predominant were explored, exploiting their particular properties. An example of this is through the "reinterpretation" of the harmonic function of a chord: Since a chord could simultaneously have more than one enharmonic spelling with different functions (i.e., both predominant as a German sixth and dominant as a dominant seventh), its function could be reinterpreted mid-phrase. This heightens both chromaticism by making possible the tonicization of remote keys, and possible dissonances with the juxtaposition of remotely related keys.

Augmented sixth chords as altered dominant chords with flattened 2nd degree[edit]

The augmented sixth chord may be built on notes other than 6.

Tchaikovsky considered the augmented sixth chords as being altered dominants.[17] He described the augmented sixth chords as inversions of the diminished triad and of dominant and diminished seventh chords with the second degree chromatically lowered, and accordingly resolving into the tonic. He notes that, "some theorists insist upon [augmented sixth chord's] resolution not into the tonic but into the dominant triad, and regard them as being erected not on the altered 2-nd degree, but on the altered 6-th degree in major and on the natural 6-th degree in minor", yet calls this view, "fallacious", insisting that a, "chord of the augmented sixth on the 6-th degree is nothing else than a modulatory degression into the key of the dominant".[18]

Augmented sixths as dominants in the tonality of C, according to Tchaikovsky. Notice the early resolution of an inner voice to avoid parallel fifths in the last example.[18]
An Italian sixth chord built on scale degree 2. Here the Italian sixth chord functions as a substitute for the dominant, with which it shares the third and seventh. Schubert's A major sonata, D. 959. About this sound Play 

Classical harmonic theory would notate the "tritone substitute" as an augmented sixth chord on 2. The Augmented sixth chord can either be the It+6 enharmonic to a dominant 7th chord without the 5th, Gr+6, enharmonically equivalent to a dominant 7th chord with the 5th, or Fr+6 enharmonically equivalent to the Lydian dominant without the 5th, all of which serve in a classical context as a substitute for the secondary dominant of V.[19][20]

Original dominant 7th-tonic progression About this sound Play , tritone substitution (V7/V-I) About this sound Play , augmented sixth chord (It6-I) About this sound Play .

Enharmonicity to other chords[edit]

Enharmonic equivalency of the French sixth[edit]

The French sixth has two characteristics in common with the diminished seventh chord:

  1. Both chords are constructed of two superimposed tritones; in the French sixth, between 62 (A—D) and 14 (C—F). Thus, both have inversional symmetry;
  2. Both are enharmonically equivalent at the tritone; i.e., both chords transposed up or down a tritone will result in the same pitches as the original.

As with the diminished seventh chord, the latter property allows the chord to be used in modulating to very remote keys. For instance: 6124; (A—C—D—F in C), could be interpreted identically in F if reordered and respelled as D—F—G—B, i.e., the French sixth of the IV key area, displaced an interval of a tritone relative to the tonic key, I.

Dominant functions[edit]

German sixth, A-C-D-F, and equivalent dominant seventh, A-C-E-G[21] About this sound Play 
Irregular resolution through augmented sixth equivalence About this sound Play .[22]

All variants of augmented sixth chords are closely related to the applied dominant V7 of II; both Italian and German variants are enharmonically identical to dominant seventh chords. For example, in the key of C (I), the German sixth chord, A—C—E—F, could be reinterpreted as A—C—E—G, the applied dominant of D (V/D).

Function[edit]

In most occasions, the augmented 6th chords precede either the dominant, or the tonic in second inversion.[7]

The augmented sixths can be treated as chromatically altered passing chords.[7]

Tristan chord[edit]

Richard Wagner's Tristan chord (indicated below with Tr) from the opening of his opera, Tristan und Isolde, can be interpreted as a French sixth in the key of A minor (F-A-B-D) with an upwardly resolving long appoggiatura in the upper voice (G to A). Note that the D resolves downwards to D instead of E:

Tristanchord.png

See also[edit]

References[edit]

  1. ^ Andrews, Herbert Kennedy (1950). The Oxford Harmony 2 (1 ed.). London: Oxford University Press. pp. 45–46. OCLC 223256512. 
  2. ^ Andrews 1950, pp. 46–52
  3. ^ a b Aldwell, Edward; Carl Schachter (1989). Harmony and Voice Leading (2 ed.). San Diego, Toronto: Harcourt Brace Jovanovich. pp. 478–483. ISBN 0-15-531519-6. OCLC 19029983. 
  4. ^ Ernst Friedrich Richter (1912). Manual of Harmony, p.94. Theodore Baker.
  5. ^ Gauldin, Robert (1997). Harmonic Practice in Tonal Music (1 ed.). New York: W.W. Norton. pp. 422–438. ISBN 0-393-97074-4. OCLC 34966355. 
  6. ^ Christ, William (1973). Materials and Structure of Music 2 (2 ed.). Englewood Cliffs, NJ: Prentice Hall. pp. 141–171. ISBN 0-13-560342-0. OCLC 257117.  Offers a detailed explanation of augmented sixth chords as well as Neapolitan sixth chords.
  7. ^ a b c Rimsky, p. 121.
  8. ^ Blatter, Alfred (2007). Revisiting Music Theory: a Guide to the Practice, p.144. ISBN 978-0-415-97440-0. "One may note that the French sixth contains the elements of a whole tone scale commonly associated with French impressionistic composers."
  9. ^ Notable examples include the themes of the slow movements (both in variation form) of the opp. 57 ("Appassionata") and 109 piano sonatas.
  10. ^ Benjamin, Thomas; Michael Horvit & Robert Nelson (2008). Techniques and Materials of Music: From the Common Practice Period Through the Twentieth Century (7 ed.). Belmont, CA: Thomson & Schirmer. p. 165. ISBN 978-0-495-18977-0. OCLC 145143714.  Beethoven frequently moves from one form of the chord to another in such a way, sometimes passing through all three.
  11. ^ Drabkin, William. Augmented sixth chord. Grove Music Online (subscription needed). Accessed March 2012.
  12. ^ Burnard, Alex (1950). Harmony and Composition: For the Student and the Potential Composer. Melbourne: Allans Music (Australia). pp. 94–95. OCLC 220305086. 
  13. ^ Piston, Walter; Mark DeVoto (1987). Harmony (5 ed.). New York: W. W. Norton & Company, Inc. p. 419. ISBN 0-393-95480-3. 
  14. ^ Rousseau, Jean Jaques. Dictionnaire de Musique. 
  15. ^ Ellis, Mark (2010). A Chord in Time: The Evolution of the Augmented Sixth from Monteverdi to Mahler, pp. 92-94. Farnham: Ashgate. ISBN 978-0-7546-6385-0.
  16. ^ a b Sechter, Simon (1853). Die Grundsätze der musicalischen Komposition (in German). Leipzig: Breitkopf und Härtel. 
  17. ^ Roberts, Peter Deane (1993). Modernism in Russian Piano Music: Skriabin, Prokofiev, and Their Russian Contemporaries, p.136. ISBN 0-253-34992-3.
  18. ^ a b Tschaikovsky, Peter (1900). "XXVII". In Translated from the German version by Emil Krall and James Liebling. Guide to the Practica Study of Harmony (English translation ed.). Leipzig: P. Jurgenson. pp. 106, 108. 
  19. ^ Satyendra, Ramon. "Analyzing the Unity within Contrast: Chick Corea's Starlight", p.55. Cited in Stein.
  20. ^ Stein, Deborah (2005). Engaging Music: Essays in Music Analysis. New York: Oxford University Press. ISBN 0-19-517010-5.
  21. ^ Benward & Saker (2008). Music in Theory and Practice, Vol. II, p.222. ISBN 978-0-07-310188-0.
  22. ^ Owen, Harold (2000). Music Theory Resource Book, p.132. ISBN 0-19-511539-2.

Books[edit]

  • Rimsky-Korsakov, Nikolai (1886). Practical Treatise on Harmony (13th - 1924 ed.). St. Petersburg: A. Büttner. 
  • Piston, Walter (1941). Harmony (co-author Mark DeVoto 5th - 1987 ed.). New York and London: W. W. Norton & Company.