Augmented Sixth Chords

Homework: Workbook Chapter 29

Preliminaries all
Longer Assignments 3
Study & Analysis #5, 10, 13

or

Textbook Chapter 30 Preliminaries 1 all #2 c, d, a
Write 16 bars incorporating at least 2 usages of textbook preliminaries 1
Workbook Study & Analysis #5, 10, 13

In chapter 27 we saw that the NII6 had a lowered -^2 that tended to resolved down to the leading tone. We saw that its natural melodic tendancy was to resolve by 1/2 step to ^1 and showed such a resolution via the resolution of a NII6 though a cad64. The tendancy of a tone to resolve, or lead, to its closest 1/2 step is now becoming quite familiar to us. We have seen it with the standard LT, syntactic motion such as -VII, V, I yielding -^7, ^7, ^1 and the chromatic alteration of tones in applied dominants. We have seen such progessions as the phrygian cadence (IV6-V in minor) lead into a cadence via half step. We talked briefly in our discussion of the viiº7 that an enharmonic respelling of that chord could lead us to a chord 1/2 step away from any tone in the original viiº7. The power of the 1/2 step to lead the ear, is a critical element in how we perceive music. Infact, its so powerful that we call such movement by halfstep Leading Tone Chromaticism

1.  Leading-tone chromaticism.

a. One very unique and important Leading Tone Chromatic movement is the Augmented 6th.
b. In general it is built on the -^6 and contains an Aug6th above (on +^4)
c. If we resolve the bass 1/2 step down and the Aug 6th 1/2 step up, we resolve into an octave on ^5
d. Note: The dissonant interval Aug 6 resolves UP. Why? We see that the very tone that is dissonant to the bass is actually a leading tone to the point of resolution. Therefore as a LT it will resolve up! (interestingly since the Aug 6th chord resolves to a V it would be possible to resolve the dissonant Aug 6 down to the chordal 7th of the V7 ;-)
e. Interestingly, unlike an applied dominant, the Aug6th chord does not diatonically belong to the chord of its resolution. Therefore, unlike applied dominants the arrival of the resolution of the A6 does not sound like a tonic
f. Since we know the -^6 can be implemented via Mixture into major mode, the Aug 6 chord can be effective in either major or minor.

2.  Contrapuntal Origin

a. We know from a phrygian cadence where the bass descends from -^6 to ^5 that the 1/2 step motion to ^5 leads very compellingly in a similar manner as the LT 1/2 step motion to ^1
b. If we insert a chromatic passing tone between the IV6 -V of the phrygian cadence, we get a passing Aug 6
c. This passing Aug 6 became its own syntax around the time of Beethoven and, as such is referred to as the Aug 6 chord.
d. With a double passing tone, we transform the A6 into a 4 voice chord and get an Aug 653 (+653).
e. With a single passing tone and an anticipation, we transform the A6 into a 4 voice chord and get an Aug 643 (+643)

3-6.  Geographical names

a. The geographical names listed below are meaningless. However they have achieved wide acceptance amongst musicians so we will use them.

b. Italian 6: the basic 3 voice Augmented 63 chord. It should be noted that in 4 voices one should double the 3rd above the bass to avoid ¶s

c. German 65: = the most common of the augmented 6th chords it contains the aug6th, 5th and 3rd above the bass on -^6. In order to avoid ¶5ths, this chord will often resolve to V through a Cad 64. This will have the effect of delaying the parallel motion.

d. French 43: = another 4 voice augmented 6th chord but this one arrives by a combination of a passing tone to +^4 and an anticipation of ^2. This anticipation removes the possibilities of ¶5ths and therefore the French 43 may or may not move to V via Cad64.

Analyze Beethoven Piano Sonata Op 13 III first theme.

7.  the augmented 6th chord with doubly augmented 4th (German 43)

a. Occassionally,when the g+65 leads to Major Cad64 we will see a doubly augmented 4th above the bass instead of P5. This allow the doubly augmented 4th to rise by step to the ^3 of the Major Cad64. This is rare and one should not be overly concerned.

8.  Approaching from IV and II

a. The most frequent immediate preparation for A6th chords is some form of IV
b. When following IV it continues subdominant harmony with chromatic inflection that propells us in the direction of V
c. Sometimes when we lead from II and IV in root position we get chromatic voice exchange to lead us in and out of A6ths
c. Sometimes we see an interpolated 64 between IV5 and A6th
d. When A6th are preceeded by a strong IV5 the chromatic progession ^4, +^4, ^5 will carry in the bass and the A6th will appear inverted.
e/ Similarly when A6ths are preceeded by a strong II5 step wise voice leading can support motion to A6ths in inverted forms.

9.  Approaching from altered IV and II

a. Frequently A6th chords originate in a chord applied to V with -^6 being introduced as a passing tone in the bass

10.  Approaching from I

a. Often, especially in minor the A6th can follow I or I6
Analyze Beethoven Piano Sonata Op 13 III first theme.
b. Since the A6 contains ^1 and the GA65 contains ^3, they can be used to harmonize part of a tonic Arpegio.
c. A very effective and dramatic use of A6 is to harmonize contrary stepwise soprano and bass

11.  Approaching from VI

a. Since VI in minor and -VI in major share the same bass as A6ths, they make an effective point of departure for A6ths
b. A6th frequently follow deceptive cadences

12. Augmented 6ths as neighbors of V

a. We saw that the A6th can work well with VI chords as they share a common bass. Just like the similarity and interchangability of II6 & IV (and others) which share a common bass tone, A6ths can be used interchangably with a deceptive cadence following a V. It in essence can become a deceptive-like cadence.

Details of Voice Leading

For a year and a half we have been very very rigid about voice leading. We have abandoned any hopes of using ¶5ths and ¶8s and have grimmaced at the thought and sound of a melodic Aug 2nd. Oddly ¶5s and ¶8s were used in counterpoint long before the establishment of the western tonal system that we have been studying and Aug 2nds are common fare in many tonal vocabularies that take advantage of modalities other than simple Major and minor and their derivations. The time has now come to relax our restrictions. HOWEVER this does not mean that you no longer have to pay attention to your voice leading. REMEMBER the reason we have been so judicious about our voice leading is to maintain the integrity of our individual voices. We have used 4 part writing to best demonstrate the function of these individual voices and you should continue to maintain that integrity. A beautiful piece of music works not only vertically with good syntax but contains excellent counterpoint that maintains individual coherent lines. You must always consider that the sound of ¶5s and 8s will to a certain degree diminish the individuality of the lines. You must always consider that strikingly dissonant melodic steps like the Aug2nd and the tritone will jump out and draw attention to themselves.

That being said, from here on out, ¶5ths and ¶8s and melodic Aug2ds are acceptible if they are used for specific logical, emotional and dramatic purposes and are presented in a way that softens their offending effects. If they happen as an oversight of good voiceleading, they will still be considered a poor choice.

13.  The melodic Augmented 2nd

a. Melodic 2nds frequently appear above an A6th chord or from another chord to an A6th chord and can create a beautiful and dramatic moment.

14.  The GA+65 and ¶5ths

a. We saw that the most common way to avoid ¶5ths is to resolve the GA+65 is to a Cad64 that leads to V.
b. However, if we soften the effect of the ¶5ths as is often done via arpeggiation, we can lead directly from the GA+65 to V.

15.  Moving to V7

a. Moving from an A6th to a V7 is a tremendous way to solve voice leading issues (especially with the GA+65) and add a color resoltuion to chordal dissonance.

16.  Moving up from the bass

a. Sometimes the bass of an A6th will rise by halfstep to ^6 before leading to V. H&VL sort of glosses over an extremely strong and profound harmonic implication of such a movement: The resultant syntax becomes and applied dominant of V! (note: try adding 9ths and 11ths to the applied dominants for a very sweet and rich sonority)

b. Raising the Bass a half step from -^6 to ^6 will transform a GA+65 to a viiº65>V
c. Raising the Bass a half step from -^6 to ^6 will transform an IA+65 to a vii6>V
d. Raising the Bass a half step from -^6 to ^6 will transform a FA+65 to a V43 >V

17.  Returning to tonic harmony

a. H&VL correctly states that the A6th has such a striking motion towards the dominant that it can serve to lead us convincingly back to tonic harmony even following prolonged modulatory passages.
b. This technique is particularly useful in transitions to tonic harmony that arrive through a sequential passage.

17b.  The Applied A6th (Please note this is not in H&VL)

a. Since the leading tone chromaticism of the A6 interval has such a strong tendancy to resolve outwards by 1/2 step and since that resolution has a very strong tendancy to act a dominant chord, we can, should, and do hear A6 as serving another yet similar function: The A6 chord can be an applied chord to a modulatory dominant. That is, the gravitational force of the A6th so strongly implies a resolution to V that when the A6th occurs on a scale degree other than -^6 it has the effect of confirming the subsequent modulatory or applied dominant.
b. When an A6th is built on a scale degree other than -^6, and is subsequently followed by an applied dominant to a new tonicized I, we will refer to the A6th as an Applied A6th
c. Please note that H&VL elludes to the concept of the applied A6th by stating in 29-18 (Modulation from I to V in major) that it can be used to support a modulation from I to V.

19.  Diminished 3rd Chords

a. H&VL states that chords with the same tones as the I,F & G A6ths but build on basses other than -^6 occur relatively infrequently
b. H&VL also states that sometimes such inversion are build on +^4 and implies that such inversions are weaker forms of the A6ths built on -^6 because there are other chords build on +^4 that effectively lead to V.
c. Furthermore, when you invert the A6th out of its root position on -^6 the Aug6th interval ceases to exist.
d. In the case of the inversion based on the +^4 root, we get an Id5d3, Gd7d5d3. and F6d5d3. These chords are collectively referred to as the Italian, German and French Diminished 3rds in H&VL.

PLEASE NOTE: Although H&VL state that the Dim 3rd chords happen less frequently and have a less poignant drive towards the dominant this should not deter you from experimenting with this and the other inversions of A6ths. Remember, just because something is a bit obscure or less poignant does not mean its wrong if it is used tastefully!

20.  Other Positions

a. H&VL states that you lose the effect of the double L.T. chromaticism with the bass (especially when built on ^1, ^2 (F only) and ^3 (G only)
b. Whereas this is true, we still have the doubled LT and thus can lead convincingly (although not as poignantly) to V
d. When an A6th is built on ^1 it yields a minor 6th and Augmented 4th and a minor 3rd. This inversion I will call by its regional name + A4th
b. When an A6th is built on ^2 (french) it yields a minor 7th and diminished 5th and Major 3rd. This inversion I will call by its regional name + d5th =Fd5th
b. When an A6th is built on ^3 it yields a minor 6th and Perfect 4th and Aug 3rd. This inversion I will call by its regional name + A3rd

21.  Augmented 6ths in sequential passages

a. We saw in 17b that The A6 chord can be an applied chord to a modulatory dominant.
b. As such, applied Augmented 6ths can be very useful as interpolated chords to applied dominants in sequence

22.  Resolving to I

a. When the A6 is built on the -^2 it takes on a "Neapolitan" flavor and can expand a minor tonic or intermediary harmony.

23.  Resolving to III+

a. When the A6 is built on the ^4 we get an applied dominant to VI

24.  An enharmonic relationship

a. If you havent seen it yet, if we respell the the GA6, altering the Aug6th to a minor 7th above the bass, we get a V>-II
b. The tones in the chord are enharmonically equivalent
c. yet the syntax of each is significantly different and therefore composers can exploit such relationships in wonderful ways