It was suggested to me to work on an analysis of Etude No. 2 from Heitor Villa-Lobos' Twelve Etudes for Guitar by an excellent Chilean guitarist. Because this work is still under copyright I have only included the notes within the first beat of each measure as a guide. Please use your score to follow along with this analysis in conjunction with the pdf below.
This little etude is an excellent example of harmonic practice at the end of the nineteenth and early twentieth centuries. The use of extended harmonies, borrowed chords as well as unexpected resolutions give this piece its "modern" sound without ever leaving the tonal system.
Let's take a look at the most interesting features.
Formally, I hear this piece in two parts; part one comprising measures 1-12 and part two, measures 13-27.
Villa-Lobos begins with the typical tonic to dominant (A-E7) in the first two measures but surprises us with the unexpected move to A#dim7 in measure three. This is a secondary leading-tone diminished seventh chord of the ii chord (Bm) which resolves as it normally would, but Villa-Lobos adds the sixth (G#) to the B minor triad for color. In traditional harmony this is referred to as an added sixth chord, not to be confused with a sixth chord or triad in first inversion. We also find this same type of harmony in measure sixteen.
In measures five and six the return to tonic is first major and then minor as shown. The A minor triad is what is called a borrowed chord or a harmony taken from the parallel minor key of A minor in this case.
We get the same thing in the next two measures but now with the dominant (E). It is first major as it normally occurs followed immediately by the minor form which again is borrowed from the parallel minor key.
Measure nine introduces V/V (B7) which moves to V (E7) in measure ten and is extended through measure twelve ending section one with a typical move to the dominant.
Part two begins with a move from tonic (A) to submediant (F#m) before introducing the C#9 harmony in measure fifteen. I hear this following section (mm. 15-18) as being in the key of C# minor (iii) with first the introduction of the note D# and most definitely with the introduction of the B# in the dominant harmony (G#7) in measure eighteen. Villa-Lobos builds our expectation for a resolution to C# minor with the strong cadential formula i-six/four to V7 in measures seventeen and eighteen (reminiscent of his Etude No. 1 from the same set just before the series of diminished sevenths) but surprises us by moving to C#7 setting up the final fifth progression of secondary dominants.
This is basically a iii-vi-ii-V-I progression but altered to form a series of dominant seventh chords resolving through the circle of fifths eventually reaching tonic. This as you know is very common in jazz harmony. Notice the intervening diminished seventh chord in measure twenty-two. The inherent ambiguity of this harmony can cause us to expect many different resolutions. I first heard this as a possible move to C# minor (enharmonic B#dim7) but since the move is to E9, I now hear it as an extended V/V as shown.
The final harmony of interest is the FMaj7 in measure twenty-five. This harmony is again considered borrowed from the parallel minor key and makes for a very striking and beautiful cadence.
The final section of my analysis shows the harmony and voice-leading in block chord form which can only be played on a keyboard for the most part, but I hope gives you some idea of how the chords connect. Don't be intimidated by the tempo that you hear this piece performed. It makes an excellent and satisfying study at any tempo. Take your time and enjoy it!