MU182: Theory II R. Vigil Advanced Chromatic Harmonies I: The Neapolitan, and Augmented-Sixth Chords as a Combination of Modal Borrowing and Applied Procedures I. Modal Borrowing The most basic aspect of chromaticism in harmonic practice comes with the borrowing of elements from the parallel mode (e.g., c minor in the context of C major). The most common place that this happens involves the importation of minor-iv and diminished/half-diminished-ii into the major mode. Another common occurrence is the importation of VI as the goal of a deceptive cadence. 6 I iv V I I ii o 5 V I I IV V7 VI! DC VI may also be used as a predominant. Note that if the 6-5 motion is in the bass the progression must utilize a Cadential Six-Four in order to avoid parallel fifths. 7 Bad: Fine: Cadential Progression: Par. 5ths I VI V I I VI 6 V 6 I VI ( V 4 3 ) I
2 The Neapolitan-six Chord ( II 6 ) is another example of modal borrowing (this time from Phrygian). The smoothest voice-leading employs a Cadential Six-Four, but the motion may be directly to a five-three Dominant. 14 I II 6 ( V 4 3) I I II 6 V 7 I II. Applied Chords The next step introducing chromatic elements into a given key involves the tonicization of Dominant harmony. This may employ a diminished triad, diminished seventh chord, major triad, or dominant seventh chord. 19 vii-i-type resolution: I 6 =[IV 6 vii o ] V I=[IV vii o 6 5 ] V 23 V-I-type resolution: I=[IV V] V I 6 =[IV 6 V 7 ] V
3 III. Augmented-Sixth Chords Augmented-Sixth Chords can be seen to emerge from the so-called Phrygian Cadence, where the motion is in the lower voice ( 2-1). Traditional two-voice cadence (Ionian): Phrygian cadence: 27 6 8 6 8 In common-practice tonal music, any progression to the dominant involving a descending motion in the bass is grouped under the general category of the "Phrygian Cadence" (for example: iv 6 -V). This includes the three types of augmented-sixth chords. Augmented Sixth Chords involve the approach to scale-degree 5 in contrary motion from its two chromatic neighbors (#4 and 6). When the chord contains the 6 in the bass (the more common Phrygian Cadence-type voicing), the interval formed between the two notes is an augmented sixth - hence the name. 31 +6 8 Augmented Sixth Chords may be best understood as combining elements of applied functionality (#4 as leading-tone to 5), and modal borrowing ( 6, from minor). When an augmented sixth chord is used in minor it is less "foreign," due to the originality of b6 to that mode.
4 A. The Italian Augmented-Sixth The simplest type of Augmented Sixth Chord, the Italian, is contained within the two others. It includes only scale degrees 1, #4, and 6. As shown below, it can be seen to combine elements of vii o /V and minor-iv. 33 + [vii o6 ] V iv 6 V It +6 V B. The French Augmented-Sixth The French Augmented-Sixth Chord is an Italian Augmented-Sixth plus scale degree two. As shown below, it can be seen to combine elements of V 7 /V and ii-half-diminished. 38 + 4 4 [V 3] V ii o 3 V Fr +6 V
5 C. The German Augmented-Sixth The German Augmented-Sixth Chord is noted for its aural identity with a dominant seventh chord. It consists of an Italian Augmented-Sixth plus #2/ 3. The German Augmented-Sixth Chord is spelled differently depending on whether is resolves directly to a root-position dominant (in order to avoid parallel fifths this is only possible in the rarer circumstance when the #4-5 motion is in the bass), or passes through a cadential six-four. When passing through a cadential six-four the augmented-sixth chord contains #2 (which resolves to 3). It has its origins in a diminished seventh chord which should also be re-spelled when it passes through a cadential six-four (thus demonstrating a common-tone resolution - as opposed to the standard resolution of a diminished seventh chord, where no tones are held common between the two chords). 43 I [vii o 6 ( 5] V 4 3) I I Ger +6 ( V 4 3 ) I When going straight to a root-position dominant the chord contains 3 (which resolves to 2). Again, note that in order to avoid parallel fifths the 6-5 motion cannot be in the bass: 50 Bad: Fine: Par. 5ths Ger +6 V I Ger +6 V I