User:Mscuthbert/sandbox/Six-four chord

A six-four chord is one of the most common chords used in common-practice Western music. The structure of the chord gives it its name, as it comprises three pitches: a bass note, a second note a fourth above the bass, and a third note a sixth above the bass. Either of the non-bass tones can be found in any octave above the bass. The term second inversion chord is often used as a synonym for the six-four chord. However, this term is contentious as it is sometimes seen as implying an incorrect derivation for the chord, and is avoided by some writers. .

The six-four chord is commonly found on strong beats just before musical cadences, as a passing chord on weak-beats, and a part of an arpeggiating bass line. It has historically been heard and discussed in widely divergent ways and even today its analysis is the subject of controversy.

Definition and History
The six-four chord when thought of as a second inversion is unusual among the three ways of arranging a major or minor triad in that it contains an interval commonly thought to be dissonant: the fourth above the bass. As such the second-inversion chord does not tend to substitute for the root position chord, as the first-inversion chord does, but instead plays different roles and is often thought of as a fundamentally different chord than the same pitches arranged in root position, or even as not a real chord at all.

The first important discussion of the six-four chord as such is found in Jean-Philippe Rameau's Traité de l'harmonie in 1722. In the treatise, Rameau introduced the concept of chordal inversion and, drawing on acoustical theory, declared that inversions of consonant triads were themselves consonant. Though he would modify this view in his much later Code de musique pratique allowing for the six-four to be considered as a suspension, it was the view of the Traité which was influential on later writers. For instance, Georg Andreas Sorge clearly invoked the earlier thought of Rameau when he wrote in the Vorgemach der musikalischen Composition, "No consonant chord can become, by inversion, a dissonant chord." Friedrich Wilhelm Marpurg came to the same conclusion as Sorge, that the six-four chord was consonant, while disagreeing entirely with the line of reasoning leading to the conclusion.

Contrasting with these views are those of theorists concerned with figured bass such as Johann David Heinichen and Johann Mattheson who considered chords as intervals above the bass rather than inversions of chords and thus regarded the six-four chord, with its fourth above the bass, as dissonant. However, Heinichen did note that the six-four chord was a peculiar sort of dissonance, since it did not require preparation, only resolution.

Johann Albrechtsberger followed Sorge and Rameau in writing that second inversion triads are consonant, but disagreed in part by suggesting that six-four chords on strong beats in which only the bass can be doubled (i.e., cadential six-fours) are essentially root position (five-three) chords delayed by suspension, and thus dissonant. Albrechtsberger's views did not represent the end of a consonant interpretation of the cadential six-four chord. Gottfried Weber, the creator of roman numeral analysis, considered the six-four both consonant and of tonic function:

The tonic harmony (I or i) very frequently occurs in the second inversion (in the fourth-sixth position) particularly on the heavy portions of the measure.... Our ear is so accustomed by this means to hear a tonic harmony occur in such a way that it has become thereby inclined to take every large or small fourth-sixth chord that occurs in this way as a tonic harmony.

The nineteenth century saw an increase in the number of important theorists considering the cadential six-four as dissonant even as the label of tonic harmony became entrenched. Moritz Hauptmann's views are in some ways typical of his era: the six-four chord is a position of the tonic triad which has a resolution in the dominant. Non-cadential six-four chords were rarely discussed in the 1800s and the views of important theorists on these chords' consonance are unknown.

Doubling
Since. C.P.E. Bach (from Beach (1967), p. 5.) in the Essay on the True Art of Playing Keyboard Instruments, gave examples of unusual doublings of the six-four.

Examples
Mozart K310 (A-minor sonata), I, has numerous examples of 6-4 moving to 7-3.

... (with pictures both in isolation and from real pieces. Will try to get sound files if I can figure out how .ogg works)

Cadential uses
A cadential second-inversion chord is a chord, typically found just before a musical cadence, that contains the notes of the tonic triad with the fifth scale degree in the bass. In roman numeral analysis, the chord has been labeled either $$\mathrm{I}^6_4\,\!$$ or $$\mathrm{V}^6_4\,\!$$, with strong adherents to both positions.

Labeling and controversy
It is entirely possible for a writer to use the label $$\mathrm{I}^6_4\,\!$$ while also asserting a dominant quality for the chord, as we see in Piston (1962, p. 96):


 * By far the commonest of [six-four chords] is the familiar "tonic six-four" found in cadences. This is a actually a dominant chord in which the sixth and fourth form appoggiature to the fifth and third respectively:


 * [[Image:Second_inversion_piston_ex_189.png|center|150px]]

...

(Schenkerian issues with the ^5 line and the "unsupported ^3")

Music theory textbooks which use the $$\mathrm{I}^6_4\,\!$$ label

 * Piston (3rd edition) -- uses $$\mathrm{I}^6_4\,\!$$ - V or just V alone, but never $$\mathrm{V}^6_4\,\!$$
 * Benjamin, Hovat, and Nelson 2008 -- uses [ $$\mathrm{I}^6_4\,\!$$ ]
 * Mayfield, Connie E. Theory Essentials: An Integrated Approach to Harmony, Ear Training, and Keyboard Skills, (Belmont, Calif.: Thomson and Schirmer, 2003). p. 208:
 * At cadence points...just before the dominant triad...the chord that is typically used is a tonic triad in second inversion, often called the cadential six-four chord.
 * When the tonic chord is in second inversion, it has the same bass note as the dominant triad....In a sense, the tonic six-four chord can be seen as an embellishment, or ornamentation, of the dominant chord.

Music theory textbooks which use the $$\mathrm{V}^6_4\,\!$$ label

 * Aldwell and Schachter
 * Clendinnging and Marvin

Recent uses and the "emancipated" six-four chord

 * Straus (2003)