Harmony in Practice-Fernando Sor, Etude 13 Op. 29 The "Golden Section"

Study 13 from Fernando Sor’s Op. 29 (study nineteen in the Segovia collection) is unusual from a key perspective, at least from a guitarist’s point of view in that it is in Bb major. This key as you know requires quite a bit of barre technique since the open E and B strings are flatted much of the time. This has always been a difficult study for me as my left hand will sometimes fatigue. I have always considered this piece one of the more beautiful of Sor’s studies and thought it would be worth a closer look.

As you can see from the harmonic analysis, most everything here has been discussed earlier in depth. I would like to point out a couple of interesting features though that were less common in the previous studies. First of all, the use of a “deceptive” resolution of a dominant seventh chord that we find in measures thirty-three through thirty-six. We would expect the D7 chord in measure thirty-three to resolve to G minor as it does in measures forty-nine through fifty-two, as dominant seventh chords usually resolve down by perfect fifth. Instead the resolution is to C minor in first inversion. This is known as a “deceptive” resolution where the dominant seventh chord resolves to something other than a tonic. The most common type of deceptive resolution is when the V moves to VI instead of i (minor keys). This one is even more unusual in that Sor resolves to iv (of G minor) in first inversion (C minor/Eb). We still get the characteristic move of the bass up a step but the tritone is partially unresolved, leaving the note C as a common tone between the two chords D7 and C minor.

The second feature occurs in measure thirty-seven where by changing one note (the G in the tenor voice to A) Sor changes the C minor triad to an Am7b5 chord which is the leading-tone seventh chord (vii) in the home key of Bb returning us to tonic for the finish. I labeled the Am7b5 chord as dominant (V) since we know that vii has a dominant function. It also clears up the following harmony (the A diminished seventh) in measure thirty-seven. We are still within the dominant (V) harmony; the Gb is a chromatic passing-tone between the G and F and creates a full diminished seventh chord which is considered a “borrowed” chord from Bb harmonic minor or the parallel minor key. Note that in jazz this is equivalent to the dominant seven flat nine chord (F7b9) with root omitted.

So what makes this piece so beautiful? Could it be partly due to its architecture? I decided to reduce the music down to the essential voice-leading using a two-part contrapuntal texture. The bass line remains intact as written but the upper voice includes the essential or structural notes of the voice-leading. In other words I included the notes in the upper voice that really define the harmony. These notes are sometimes buried in middle voices in the actual composition. When you play the reduction you will easily hear all the harmony of the original in a simple two-part format. If you are familiar with contrapuntal writing you will notice that this is first rate in terms of interval choice and voice-leading principles.

From the reduction we can now appreciate the beauty of the architecture. I laid it out to clearly show the phrase structure and sections of the piece. There is an important principle at work here that is known as the “Golden Section” or the “Golden Ratio”. Basically this principle involves structural ratios that are roughly 2:3 in their relationship. It is a pattern found throughout the natural world as well as in architecture and art. I learned of this originally as the ratio between two numbers of the Fibonacci series in mathematics. The series is simple in structure and involves beginning with zero and one, then adding these together to get the next number in the series. Continue by adding together the last two numbers to get the next one. For example: 0, 1, 1, 2, 3, 5, 8, 13, 21 etc. The higher you go in the series, the closer you get to the Golden Section as expressed by the ratio of any two adjacent numbers. The idea is that perfect symmetry is boring and predictable whereas asymmetry is much more interesting and vital. It is a fascinating topic and I would encourage you to study it in more detail.

When we look at the first section of the piece (mm. 1-20) assuming you agree with my segmentation, we have two, four measure phrases (8) followed by three, four measure phrases (12). The ratio of the two parts is exactly 2:3.

The second section (mm. 21-40) has exactly the same structure: Two, four measure phrases (8) followed by three, four measure phrases (12), again displaying the Golden Section proportions of 2:3.

The final section (mm. 41-58) is a bit more symmetrical in that we have four, four measure phrases. Although with the addition of the last two measures which I consider the equivalent of putting a period at the end, we do have a six measure phrase giving us something closer to 2:3.

Also note the ratio of the first part (mm.1-20) defined by the move harmonically from tonic (I) to dominant (V) is roughly a ratio of 2:3 to the second part (mm.21-58) defined by the move from dominant back to tonic.

Please see the written musical example below for clarity. Play through the study and ask yourself if this structure is perceptible. I would think that it must be apparent on some subconscious level since it would be extremely difficult to compare parts of a musical composition that only exist in real time during a performance. Any psycho-acousticians out there?


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