Study three from Twenty-Five Melodious and Progressive Studies Op. 60 by Matteo Carcassi (1792-1853) has always been my personal favorite from this famous set of studies for guitar. I am sure almost everyone reading this has played through it many times during his or her course of study. The harmony in this piece has always intrigued me. As a student there were many things that I didn’t understand, like that strange sounding chord on the first two beats of measure twenty-three or that unusual cadence on C# major in measure sixteen. What follows is my harmonic analysis of this beautiful little study with a few more years of experience under my belt.
Although Carcassi is not considered in the same league as Sor as a composer, he is certainly no slouch when it comes to harmony. The first thing you notice in this study is the frequent use of appoggiaturas (leaning tones) in the melody. This is a perfect example of what I discussed previously concerning earlier dissonances that gradually over time become acceptable consonances. The opening A major triad supports an F# (sixth above the bass) on beat two which then resolves to the chord tone E (fifth above the bass) on beat three. In measure two we have the same pattern in which the non-harmonic tone F# (seventh above the bass) on beat two resolves to the chord tone E (sixth above the bass) on beat three. This pattern continues through most of the piece and is best expressed as an interval pattern between the bass and soprano. The first eight bars look like this where the numbers represent intervals above the bass:
- Measure one: 6-5
- Measure two: 7-6
- Measure three: 4-3
- Measure four: 9-8
- Measure five: 7-6
- Measure six: 6-5
- Measure seven: 4-3
- In the final measure (eight) the melody comes to rest on the dominant (E) without an appoggiatura.
You could say that with modern ears these appoggiaturas could be considered integral parts of the harmony and heard as added sixths, added ninths, major sevenths, dominant ninths, etc., which would not require resolution within the same harmony as non-harmonic tones would require. Just as the seventh of the dominant seventh was originally always an unaccented passing tone, it eventually was accented over time and heard as an integral part of the harmony. A good example of this harmonic development occurs in measure five. Here we have a major seventh (G#) moving to a major sixth (F#) over an A bass. I am more inclined to hear this chord as a tonic A major with an added sixth than as an F# minor (vi) in first inversion.
The most remarkable harmony takes place in the middle section, measures nine through sixteen, which is typical in that most development generally occurs here. The harmony in the first four bars takes place over a pedal point E (dominant). When we reach measure eleven we encounter a diminished seventh chord that doesn’t quite do what we expect it to do; resolve up by half-step as a leading-tone diminished seventh does. From the spelling I have indicated the “root” as A#. We would expect that A# diminished seventh would resolve to B major or minor as it does in measure six and seven. Instead it moves into an E7 chord. This type of diminished seventh chord is known as a common-tone diminished seventh in which there is at least one common tone between the diminished seventh chord and its chord of resolution. In this case the common tone is the note E. The other three voices ascend chromatically: A# to B, C# to D, and G to G#. This type of diminished seventh chord is quite common in nineteenth century harmony as well as in jazz harmony. Please see my article “The Amazing and Versatile Diminished Seventh Chord” for a more detailed exploration of how this chord is used.
The E7 chord in measure twelve becomes an E# diminished seventh chord in measure thirteen with the chromatic ascent of the bass from E to E#. This time the E# dim.7 chord resolves as it usually does, up a half-step to F# minor. This temporarily moves us into the key of F# minor which clears up the remaining harmony in this section. The B minor in measure fourteen is the iv chord in this new key area. The D7 sound in measure fifteen is actually an Italian augmented sixth chord where the outer voices (D and B#) form the interval of an augmented sixth which resolve in contrary motion to the octave C# in measure sixteen bringing us to a cadence on the dominant of F# minor, the C# major triad. The last four eighth-notes serve to imply the E7 (dominant) chord to move us back to the home key of A major for the finish.
The last eight bars are a partial restatement of the first eight bars with a pedal point A (tonic) through the first four measures. By far the most dramatic harmonic feature is the French augmented sixth chord that we hear in measure twenty-three. To review, this harmony usually contains the interval of an augmented sixth in the outer voices filled with a major third and an augmented fourth in the inner voices. In this case the augmented sixth interval is inverted to create a diminished third. The effect is the same except that the diminished third resolves “inward” to an octave by contrary motion rather than “outward” to an octave in the case of an augmented sixth. One other interesting feature of this French augmented sixth chord is that it can have two possible roots which are related by tritone. I have indicated the two different roots in the chord analysis above the staff. Carcassi’s spelling would indicate a B root but we could also indicate F as the root with an enharmonic spelling of the chord: F-A-Cb-Eb. Again as we talked about in previous discussions this is considered a tritone substitution in jazz harmony where the F7(b5) is substituted for the B7(b5). In this case the two chords are identical and both function in the same way, resolving into the dominant of A major (E7). The dominant seven flat-five (7b5) and dominant seven sharp-five (7#5) chords can be considered as generated from the whole-tone scale (B-C#-D#-F-G-A-B). You will find this sound in the music of the French Impressionists (late nineteenth/early twentieth century) particularly Debussy. In jazz, the whole-tone scale is an excellent choice when improvising over these chord types.
That was quite an interesting little study in harmony! My hope is that we can better understand more advanced harmonic concepts if we can associate these concepts with pieces we know and love. You will find the analysis below. Stay tuned for part two as we will look at Carcassi’s study seven from the same set.