Augmented sixth chord

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Augmented sixth chord
A German sixth chord on the last beat of m. 96 in Scott Joplin's "Binks' Waltz" (1905). [1]

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, [2] was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods. [3]

Contents

Conventionally used with a predominant function (resolving to the dominant), the three more common types of augmented sixth chords are usually called the Italian sixth, the French sixth, and the German sixth.

Augmented sixth interval

Augmented sixth chord
The interval of the augmented sixth normally resolves outwards by semitone to an octave.

The augmented sixth interval is typically between the sixth degree of the minor scale, Scale deg 6.svg , and the raised fourth degree, Scale deg 4.svg . With standard voice leading, the chord is followed directly or indirectly by some form of the dominant chord, in which both Scale deg 6.svg and Scale deg 4.svg have resolved to the fifth scale degree, Scale deg 5.svg . This tendency to resolve outwards to Scale deg 5.svg is why the interval is spelled as an augmented sixth, rather than enharmonically as a minor seventh ( Scale deg 6.svg and Scale deg 5.svg ).

Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by borrowing Scale deg 6.svg of the parallel minor scale. [4]

Types

There are three main types of augmented sixth chords, commonly known as the Italian sixth, the French sixth, and the German sixth.

Augmented sixth chord

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. [4] [5] [6] According to Kostka and Payne, the other two terms are similar to the Italian sixth, which, "has no historical authenticity-[being] simply a convenient and traditional label." [7]

Italian sixth

Augmented sixth chord
The second movement of Beethoven's Piano Sonata in F major, Op. 78, begins with an Italian sixth chord.

The Italian sixth (It+6 or It6 or iv6) is derived from iv6 with an altered fourth scale degree, Scale deg 4.svg . This is the only augmented sixth chord comprising just three distinct notes; in four-part writing, the tonic pitch is doubled.

Augmented sixth chord

The Italian sixth is enharmonically equivalent to an incomplete dominant seventh. [8] VI7=V7: A, C, (E,) G.

French sixth

A French sixth chord in Schubert's Die schone Mullerin, #5: "Am Feierabend" Play (help*info) French sixth chord in Schubert's Am Feirabend.png
A French sixth chord in Schubert's Die schöne Müllerin , #5: "Am Feierabend" Loudspeaker.svg Play  

The French sixth (Fr+6 or Fr4
3
) is similar to the Italian, but with an additional tone, Scale deg 2.svg . 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). [10]

Augmented sixth chord

This chord has the same notes as a dominant seventh flat five chord and is in fact the second inversion of II75.

German sixth

The German sixth (Ger+6 or Ger6
5
) is also like the Italian, but with an added tone, Scale deg 3.svg .

Augmented sixth chord

In Classical music, however, it appears in much the same places as the other variants, though perhaps less often because of the contrapuntal difficulties outlined below. It appears frequently in the works of Beethoven, [lower-alpha 1] and in ragtime music. [1] The German sixth chord is enharmonically equivalent to a dominant seventh chord though it functions differently.

Avoiding parallel fifths

It is more difficult to avoid parallel fifths when resolving a German sixth chord to the dominant chord. 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 Scale deg 3.svg can move to either Scale deg 1.svg or Scale deg 2.svg , thereby generating an Italian or French sixth, respectively, and eliminating the perfect fifth between 6 and Scale deg 3.svg . [11]
    Augmented sixth chord
  2. The chord can resolve to a 6
    4
    chord
    , functionally either as a cadential 6
    4
    intensification of V, or as the second inversion of I. The cadential 6
    4
    , 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 Scale deg 1.svg and Scale deg 3.svg do not move during the resolution of the German sixth to the cadential 6
    4
    .
    Augmented sixth chord

    In major modes, 3 can be enharmonically respelled as Scale deg 2.svg , allowing it to resolve upwards to Scale deg 3.svg . This is may be called a doubly-augmented sixth, although in reality it is the fourth that is doubly augmented. [12] :99

    Augmented sixth chord

Other types

Other variants of augmented sixth chords can be found in the repertoire, and are sometimes given whimsical geographical names. For example: 4–6–7–2; (F–A–B–D) is called by one source an Australian sixth, and 7–1–3–5 (B–C–E–G#), sometimes called the Japanese sixth [13] [14] Such anomalies usually have alternative interpretations.

Function

Standard function

From the Baroque to the Romantic periods, augmented sixth chords had the same harmonic function: as a chromatically altered predominant chord (typically, an alteration of ii4
3
, IV6
5
, 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 to Scale deg 5.svg from above and below (from Scale deg 6.svg and Scale deg 4.svg ); [15] essentially, these two notes act as leading-tones.

This characteristic has led many analysts [16] to compare the voice leading of augmented sixth chords to the secondary dominant V of V because of the presence of Scale deg 4.svg , 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, Scale deg 6.svg and Scale deg 4.svg , rather than just Scale deg 4.svg .

In most occasions, the augmented-sixth chords precede either the dominant, or the tonic in second inversion. [8] The augmented sixths can be treated as chromatically altered passing chords. [8]

Other functions

Augmented sixth chord
Augmented sixths as dominants in C major, according to Tchaikovsky. Notice the early resolution of an inner voice to avoid parallel fifths in the last example. [17]

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 remotely related keys, and possible dissonances with the juxtaposition of remotely related keys.

Tchaikovsky considered the augmented sixth chords to be altered dominant chords. [18] He described the augmented sixth chords to be inversions of the diminished triad and of dominant and diminished seventh chords with a lowered second degree ( Scale deg 2.svg ), 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 2nd degree, but on the altered 6th degree in major and on the natural 6th degree in minor", yet calls this view, "fallacious", insisting that a, "chord of the augmented sixth on the 6th degree is nothing else than a modulatory degression into the key of the dominant". [17]

The example below shows the last nine measures from Schubert's Piano Sonata in A major, D. 959. In m. 352, an Italian sixth chord built on scale degree Scale deg 2.svg functions as a substitute for the dominant.

Augmented sixth chord

Inversions

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.[ citation needed ] Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.

Rousseau considered that the chord could not be inverted. [19] Seventeenth century instances of the augmented sixth with the sharp note in the bass are generally limited to German sources. [20]

The excerpt below is from J.S. 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 octave.

Augmented sixth chord

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. [21] For example, F–A–C is a minor triad, so F–A–C is a doubly diminished triad. This is enharmonically equivalent to G–A–C, an incomplete dominant seventh A 7, missing its fifth), which is a tritone substitute that resolves to G. Its inversion, A–C–F, is the Italian sixth chord that resolves to G.

Classical harmonic theory would notate the tritone substitute as an augmented sixth chord on 2. The augmented sixth chord can either be (i) an It+6 enharmonically equivalent to a dominant seventh chord (with a missing fifth); (ii) a Ger+6 equivalent to a dominant seventh chord with (with a fifth); or (iii) a Fr+6 equivalent to the Lydian dominant (with a missing fifth), all of which serve in a classical context as a substitute for the secondary dominant of V. [22] [23]

Augmented sixth chord

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, the German sixth chord could be reinterpreted as the applied dominant of D.

Augmented sixth chord

Simon Sechter explains the chord of the French sixth chord as being a chromatically altered version of a seventh chord on the second degree of the scale, Scale deg 2.svg . The German sixth is explained as a chromatically altered ninth chord on the same root but with the root omitted. [24]

Augmented sixth chord

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.

Relationship between the different types

The following "curious chromatic sequence", [25] graphed by Dmitri Tymoczko as a four-dimensional tesseract, [26] outlines the relationships between the augmented sixth chords in 12TET tuning:

A tesseract. The diminished seventh chords occupy points on two diagonally opposite corners. Schlegel wireframe 8-cell.png
A tesseract. The diminished seventh chords occupy points on two diagonally opposite corners.

Minor seventh as virtual augmented sixth chord

The minor seventh chord may also have its interval of minor seventh (between the root and seventh degree (i.e.: C–B in C–E–G–B) rewritten as an augmented sixth (C–E–G–A). [27] Rearranging and transposing, this gives A–C–E–F, a virtual minor version of the German sixth chord. [28] Again like the typical +6, this enharmonic interpretation gives a resolution irregular for the minor seventh but normal for the augmented sixth, where the two voices at the enharmonic major second converge to a unison or diverge to an octave. [29]

Half-diminished seventh as virtual augmented sixth chord

The half-diminished seventh chord is the inversion of the German sixth chord [30] (it is its inversion as a set, rather than as a chord). Its interval of minor seventh (between root and seventh degree (i.e.: C–B in C–E–G–B) can be written as an augmented sixth (C–E–G–A). [27] Rearranging and transposing, this gives A–C–D–F, a virtual minor version of the French sixth chord. [31] [ need quotation to verify ] Like the typical +6, this enharmonic interpretation gives a resolution irregular for the half-diminished seventh but normal for the augmented sixth, where the two voices at the enharmonic major second converge to a unison or diverge to an octave. [29]

Tristan chord

Richard Wagner's Tristan chord, the first vertical sonority in his opera, Tristan und Isolde , can be interpreted as a half-diminished seventh that transitions to a French sixth in the key of A minor (F–A–B–D, in red below). The upper voice continues upward with a long appoggiatura (G to A). Note that the D resolves down to D instead of up to E: [32]

Augmented sixth chord

See also

Notes

  1. Notable examples include the themes of the slow movements (both in variation form) of the opp. 57 ("Appassionata") and 109 piano sonatas.

Related Research Articles

In music theory, the term minor scale refers to three scale patterns – the natural minor scale, the harmonic minor scale, and the melodic minor scale – rather than just one as with the major scale.

In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1200 cents.

An altered chord is a chord in which one or more notes from the diatonic scale is replaced with a neighboring pitch from the chromatic scale. According to the broadest definition any chord with a nondiatonic chord tone is an altered chord, while the simplest use of altered chords is the use of borrowed chords, chords borrowed from the parallel key, and the most common is the use of secondary dominants. As Alfred Blatter explains,"An altered chord occurs when one of the standard, functional chords is given another quality by the modification of one or more components of the chord."

A jazz scale is any musical scale used in jazz. Many "jazz scales" are common scales drawn from Western European classical music, including the diatonic, whole-tone, octatonic, and the modes of the ascending melodic minor. All of these scales were commonly used by late nineteenth and early twentieth-century composers such as Rimsky-Korsakov, Debussy, Ravel and Stravinsky, often in ways that directly anticipate jazz practice. Some jazz scales, such as the bebop scales, add additional chromatic passing tones to the familiar diatonic scales.

A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.

Chord (music) Harmonic set of three or more notes

A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords in the right musical context.

Modulation (music) Change from one tonality (tonic, or tonal center) to another

In music, modulation is the change from one tonality to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.

Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.

Augmented fifth musical interval

In classical music from Western culture, an augmented fifth is an interval produced by widening a perfect fifth by a chromatic semitone. For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C to G, and from C to G are augmented fifths, spanning eight semitones. Being augmented, it is considered a dissonant interval.

The term sixth chord refers to two different kinds of chord, the first in classical music and the second in modern popular music.

In music theory, a ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass.

The ninth chord and its inversions exist today, or at least they can exist. The pupil will easily find examples in the literature [such as Schoenberg's Verklärte Nacht and Strauss's opera Salome]. It is not necessary to set up special laws for its treatment. If one wants to be careful, one will be able to use the laws that pertain to the seventh chords: that is, dissonances resolve by step downward, the root leaps a fourth upward.

In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, usually built on the fifth degree of the major scale, and composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad together with a minor seventh, denoted by the letter name of the chord root and a superscript "7". An example is the dominant seventh chord built on G, written as G7, having pitches G–B–D–F:

In Classical music theory, a Neapolitan chord is a major chord built on the lowered (flatted) second (supertonic) scale degree. In Schenkerian analysis, it is known as a Phrygian II, since in minor scales the chord is built on the notes of the corresponding Phrygian mode.

The diminished seventh chord is a four-note chord composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root:. For example, the diminished seventh chord built on C, commonly written as Co7, has pitches C–E–G–B:

Augmented sixth musical interval

In classical music from Western culture, an augmented sixth is an interval produced by widening a major sixth by a chromatic semitone. For instance, the interval from C to A is a major sixth, nine semitones wide, and both the intervals from C to A, and from C to A are augmented sixths, spanning ten semitones. Being augmented, it is considered a dissonant interval.

Augmented second musical interval

In classical music from Western culture, an augmented second is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone. For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D is an augmented second, spanning three semitones.

Harmonic major scale

In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. In George Russell's Lydian Chromatic Concept it is the fifth mode (V) of the Lydian Diminished scale. It corresponds to the Raga Sarasangi in Indian Carnatic music.

In music theory, the half-diminished seventh chord is a seventh chord composed of a root note, together with a minor third, a diminished fifth, and a minor seventh. For example, the half-diminished seventh chord built on C, commonly written as Cø7, has pitches C–E–G–B:

Diatonic and chromatic Terms in music theory to characterize scales

Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.

In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".

References

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  8. 1 2 3 Rimsky, p. 121.
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  10. 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."
  11. Benjamin, Thomas; Horvit, Michael; Nelson, Robert (2008). Techniques and Materials of Music: From the Common Practice Period Through the Twentieth Century (seventh 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.
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  18. Roberts, Peter Deane (1993). Modernism in Russian Piano Music: Skriabin, Prokofiev, and Their Russian Contemporaries, p.136. ISBN   0-253-34992-3.
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  20. 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.
  21. Ernst Friedrich Richter (1912). Manual of Harmony, p.94. Theodore Baker.
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