My project for this summer was to do a harmonic and formal analysis of Vals No. 3 Op. 8 of Agustin Barrios Mangoré. As in some of my other analyses I used a two staff system with the actual composition on top and a reduction staff below that shows what I believe to be the underlying voice-leading. For the most part I used a three part texture which I hope provides a clear rendering of the harmony.
The waltz is in rondo form conforming to the following plan:
(Intro)ABACA (coda)
Let's take a look at each section and see what's going on harmonically.
Introduction (measures 1-9)
A simple alternation between ii and V in d minor establishes the key and introduces the thematic material of the A section. The use of harmonics in the bass adds considerable interest.
A Section (measures 10-36)
Melodically it is based on the very short motive we hear in measures 10-11 transposed to various pitches. As usual I am more interested in the harmony that supports this melodic fragment as well as what is driving the music forward. The answer can be found in the reduction staff showing the underlying voice-leading.
Notice how Barrios begins simply with an alternation of tonic to dominant (mm. 10-15). Nothing special there but what follows is really special. Notice the bass line beginning in measure 15 (Bb) after jumping up an octave starts a long step-wise descent (with one exception, the third skip in measures 23-24) all the way down to the low A (dominant) in measure 30 concluding with the half cadence in measure 33 and full cadence (m. 36) after repeat. Within this descent of a ninth we get the beautiful chromatic harmony (mm. 25-29). This harmony is a product of the chromatic descending tenths shown in the reduction staff.
This passage (mm. 25-29) gave me some trouble at first. The harmony in measures 26-27 spells an Am7(b5) but it did not function as it should. When playing through it I noticed it sounded like a familiar jazz progression that included two passing diminished seventh chords:
A7/C# - Cdim7 - G/B - Bbdim7 - Dm/A
If you consider the G in measures 26-27 an internal pedal (replacing the F#) the progression now makes functional sense. Also notice the major IV chord (G) in measure 28. This chord is considered a borrowed chord from the parallel major (D major). Usually the quality of the subdominant is minor in a minor key.
B Section (measures 37-52)
We are still in the tonic (D minor) but a second theme is introduced. This is a short section characterized by a brief move to the relative major key (F major) in measure 43 and a dramatic deceptive move from V to VI (mm. 45-47).
C Section (measures 53-120); The longest and most developed section of the piece.
Here we have the completely new key of D major known as the parallel major key and an internal ABA-transition structure within this large section.
(a) mm. 53-69 consists of two eight measure phrases.
Phrase one (mm. 54-61, m. 53 is a pick-up measure) begins and ends in the tonic key and includes the common-tone diminished seventh chord in measure 60.
Phrase two (mm. 62-69) wants to move us into B minor but doesn't quite make it. The harmony in measure 68 also gave me some trouble until I finally realized the A# was missing! This then makes perfect sense as an F#7 chord (dominant of B minor) but before it can resolve Barrios changes it to A13 in measure 69 (keeping the F# in the upper voice) which brings us right back to D major.
(b) mm. 70-85 This section also contains two eight bar phrases very similar harmonically to the (a) section but this time Barrios does finally settle into B minor (relative minor) with the cadence in measure 85.
(a) mm. 86-102 Repeat of first part with cadence on the tonic (D major) this time in measure 102.
The next section (mm. 102-120) is transitional material to get us back to the home key of D minor for the final restatement of the A section with coda. Notice how Barrios introduces the Bb in measure 117, changing the quality of the ii chord (Em7b5) in order to prepare the return to D minor.
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