"Roots" of Augmented Sixth Chords
Simon Sechter, in 'Die Grundsätze der musicalischen Komposition', explains the chord of the French Sixth A♭—C—D—F♯ in the key of C as being a chromatically altered version of a seventh chord on the second degree of the scale, and therefore gives the root as 'D'. The German Sixth A♭—C—E♭—F♯ is explained as a chromatically altered ninth chord on the same root, but with the root omitted. (In Sechter's theory, the diminished seventh chord F♯—A—C—E♭ is invariably described in the same way, i.e. a ninth chord on D with the root omitted, hence its equivalence to the augmented sixth.)
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.
On the contrary, Tchaikovsky considers the augmented sixth chords, rather than being built on the minor sixth degree (A♭ in C), as being altered dominants. In his Guide to the practical study of harmony considers the augmented sixth chords to be 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 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". This would make the chord of the augmented sixth a member of a large group of chords with an altered second degree (which includes the Neapolitan chord). For an exhaustive discussion of the possibility of augmented sixth chords resolving to tonic (or other scale degrees), see Daniel Harrison's article, "A Supplement to the Theory of Augmented-Sixth Chords."
Read more about this topic: Augmented Sixth Chord
Famous quotes containing the words roots, augmented, sixth and/or chords:
“Though of erect nature, man is far above the plants. For man’s superior part, his head, is turned toward the superior part of the world, and his inferior part is turned toward the inferior world; and therefore he is perfectly disposed as to the general situation of his body. Plants have the superior part turned towards the lower world, since their roots correspond to the mouth, and their inferior parts towards the upper world.”
—Thomas Aquinas (c. 1225–1274)
“Another success is the post-office, with its educating energy augmented by cheapness and guarded by a certain religious sentiment in mankind; so that the power of a wafer or a drop of wax or gluten to guard a letter, as it flies over sea over land and comes to its address as if a battalion of artillery brought it, I look upon as a fine meter of civilization.”
—Ralph Waldo Emerson (1803–1882)
“If you are willing to inconvenience yourself in the name of discipline, the battle is half over. Leave Grandma’s early if the children are acting impossible. Depart the ballpark in the sixth inning if you’ve warned the kids and their behavior is still poor. If we do something like this once, our kids will remember it for a long time.”
—Fred G. Gosman (20th century)
“Love took up the glass of Time, and turned it in his glowing hands;
Every moment, lightly shaken, ran itself in golden sands.
Love took up the harp of Life, and smote on all the chords with
might;
Smote the chord of Self, that, trembling, passed in music out of sight.”
—Alfred Tennyson (1809–1892)