As we move closer to the present, harmony becomes more and more complex. The ear is now able to hear more and more complex tonal relationships and what were earlier dissonances have now become acceptable consonances in many cases. To illustrate this newer harmonic thinking I thought it would be appropriate to move into the late Romantic period (late nineteenth century) and discuss the harmony of Agustín Barrios Mangoré (1885-1944) as displayed in his well known composition Julia Florida.
Tonality is still in full force here as most harmonic relationships are as we would expect, following the principles of functional harmony as presented in the Sor etudes we examined earlier, i.e., dominant to tonic progressions as well as other standard chord progressions and successions. Key relationships are also typical although we do find some new and more remote keys occurring here. One of the main features that we find in this piece as well as other music of this period is a greater use of chromatic harmony and occasional use of non-functional harmony. In a nutshell non-functional harmony occurs when familiar harmonic structures are used in a non-standard way. Usually this non-functional harmony is found within a passage that is fundamentally linear or, in other words, the harmony that occurs is a bi-product of voice-leading. The step-wise movement of the voices from one harmonic structural point to another is the driving force of such a passage. The harmony generated is secondary. This will become clearer as we look at the music in more detail.
Let’s begin at the beginning. The A section of the piece (measures 1-20) is quite straightforward harmonically. Interesting features are the use of an augmented triad (measure five) and the chord succession V-iii-ii-iii-IV (measures 14-16) which includes two minor seventh chords. The augmented triad usually functions as a dominant in that it resolves down by perfect fifth as it does here. The augmented triad occurs in the context of an accented chromatic passing tone in the middle voice (A-A#-B). In jazz this is known as a 7(#5) chord and functions in exactly the same way.
The B section beginning at measure twenty-one is in the relative minor key of B minor. Again this is standard procedure. As you can see there is not a great deal happening in this section harmonically other than the striking G minor chord in measure twenty-nine. This is considered a borrowed chord from the parallel minor key of D minor and is one of the most common altered chords in tonal music. In the analysis I hear this as moving us back into D major as confirmed by the second ending where we have an authentic cadence in D major that includes a dominant thirteenth chord in measure thirty-three. This feature of extended harmonies is also an important new development during this period.
The C section beginning in measure thirty-five is where the real fun begins. The secondary leading-tone diminished seventh chord that occurs in measure thirty-six is nothing new. We had many examples in the Sor etudes. The first really new sound is the chord of the added sixth that occurs in measure thirty-eight. In this case it is a tonic triad (D) with an added B (sixth). In jazz this is known as the major six chord and is written D6 (not to be confused with a first inversion triad). In measure thirty-nine we move into F# minor or the mediant (iii) area. This takes us into the most complex section of the piece, measures forty-two through fifty-six.
This passage is best understood in terms of the voice-leading. I have included a supplemental page in which I isolate this passage and reduce it down to the bare essentials. Notice how all the voices move by step with the bass line moving generally in a downward direction culminating on the dominant (A9) in second inversion (E bass) in the home key of D major. Assigning Roman numeral analysis to this passage was a challenge to say the least, particularly measures fifty-three through fifty-six. This passage is a good example of what I would call non-functional harmony. Familiar sounds used in an unfamiliar way, like the G7 chord in measure fifty-five moving to A9 for example. It is clear that we have a chromatic bass line (G-F#-F-E) and two chromatically descending inner voices (E/C#-Eb/C-D/B that move with the bass ending on the dominant. My Roman numeral analysis stretches harmonic relationships to the limit. Clearly it is the voice-leading that explains this passage best. You will notice that this chromatic descent actually begins way back in measure forty-two. If you trace the middle voice beginning on the A you can follow it down chromatically all the way to C# in measure fifty-six! A (measure 42) G# (43, beat 4 implied-44) G (45) F#-F (46) E (47-53) Eb (54) D (55) and finally the goal C# (leading-tone) in measure fifty-six. Amazing! I still find this incredible. Is this part of a premeditated plan or is this intuitive to these great composers?
One final point of interest: The French augmented sixth chord that occurs in measure forty-four. This is our first look at this structure. The French augmented sixth chord is one of three types of augmented sixth chords. We have previously encountered the other two types: Italian and German, in the Sor etudes. I remember reading in some obscure theory book a simple way to build and compare these three types. The most important functional feature is the augmented sixth interval that usually occurs in the outer voices. The explanation was to first play an octave at the keyboard: Let’s use C-C. Move the lower C up a half-step to Db and the upper C down a half-step to B forming the interval of an augmented sixth. To form the Italian augmented sixth, fill in the interval with a major third (F). To form the German, fill in with a major third (F) and a perfect fifth (Ab). To form the French augmented sixth chord, fill in with a major third (F) and an augmented fourth (G). These chords then usually resolve back to the C major triad or the C7 (dominant) or commonly the tonic 6-4 (F/C). In our example in measure forty-four the augmented sixth interval is D (bass) to B# (alto). The filled intervals are F# (major third) and G# (augmented fourth). The resolution is as it should be: The augmented sixth interval moves in contrary motion to an octave (C#-C#) while the F# resolves down by half-step to E# and the G# remains as a common tone. In jazz this structure is known as a 7(b5) chord and is referred to as a tritone substitution. Its function is identical. Please refer to my earlier discussion of tritone substitutions for a more detailed explanation.
Below is the analysis and the supplement that I hope clarifies the voice-leading of the complex passage (mm. 42-56). Please comment. I would be interested in knowing your interpretation of this music and if you find this helpful in any way. Thanks for your attention. I know this can be migraine inducing!