Friday, June 24, 2005

The so-called "French Sixth" Chord

When I was a doctoral candidate at The University of North Texas, I had the honor and distinctly providential good fortune to study with the consumate music theory master, Dr. Gene J. Cho. Sometimes I think he was one of the only reasons I was lead to study there, as along with another wonderful theorist, Dr. Paul Dvorak, Dr. Cho was one of only a couple of professors at UNT who had anything of substantive value to offer me at that point; the composition faculty being, as it was, populated with post-modern know-nothings in my view. Dr. Cho reminded me of a musical version of the Star Wars character "Yoda" (No physical resemblance; it was an "attitude thing" coupled with his ESOL pronunciations and Chinese accent), and so I am fond of saying that it was he who was responsible for completing my training as a musical Jedi. He also kept me quite insulated from the temptations of the "Dark Side" of atonality and post-modern dilletanteism.

In any case, Dr. Cho has the most complete "unified theory of tonality" of any theorist in all of music history in my opinion, Arnold Schoenberg being a relatively close second. This exegesis on tonal theory is presented in his startlingly slim monograph entitled Theories and Practice of Harmonic Convergence, which I think is a must for the library of anyone serious about tonal music theory and composition.

One of Dr. Cho's pet peeves was the "nationalistic names" that most traditional theorists use to describe some of the more unique and idiomatic sonorities found in Western art music. His position is that these names describe nothing and are useless if the idea is to convey to the student an idea of what they really are and how they actually function (He used to tell this lame joke about "Irish Sixths" in every class he taught, and I believe I was the only one who ever laughed at it, and I laughed every time I heard him tell it. I love that man and owe him an enormous debt of grattitude). He is right about that, of course, and so today we are going to consider the wrongly so-called French Sixth sonority.



Above I have presented two examples to show the theoretical origin of the so-called French Sixth chord (I should note that Dr. Cho does not share in my opinion about this subject, he being of the opinion that augmented sixth chords have a purely contrapuntal origin, and we got into some spirited exchanges over this topic. As much as I hate to disagree with my former master, for the purposes of harmonic theory I remain convinced that this is the best way to present the subject for direct ease of understanding. IMO, we were arguing semantics just for the pure joy of it).

In the top example I have shown the most usual situation that you find the French Sixth in: A ii diminished to V progression in the minor key wherein the ii is in the second inversion (Diminished fifth in the bass), and it's third is raised as in a regular secondary dominant chord. That is exactly what a so-called French Sixth is: A secondary dominant with a diminished fifth in the second inversion. So, that is why it get's the analysis symbol V(4/3/b)/V: It is the secondary dominant of the five chord in second inversion with the diminished fifth in the bass, and this arrangement creates an Augmented Sixth interval with the raised third degree. All of the augmented sixth chords share this interval, but this one is the easiest to theoretically understand, so we'll deal with the others later.

Note that the transformation between the V(4/3/b)/V and the V is the usual delayed crosswise transformation most commonly encountered with secondary dominants. Note also that the final tonic chord is incomplete because the bass stops transforming and becomes a constant root. This is one of the main reasons why composing chord progressions over a constant root bass line and maintaining the transformations in the upper voices is such an overwhelmingly superior technological method compared to the standard practice of the Baroque through Romantic eras where the bass transforms or not depending only on whim (Once the progression is completed, more plastic bass lines may be composed to the transforming voices using transformations other than the most natural ones, and vigorous melodies as well, as will be seen).

This native minor progression was also used in the major key by both raising the third and lowering the fifth of the second inversion of the ii minor seventh to get exactly the same structure. This would give a D7(d5) in the key of C. The natural place that most closely follows the diatonic pattern of this chord occurs in major is between the vii diminished minor seventh and the iii, as I have shown in the second example. Here, I have employed the constant root bass line and put the diminished fifth in an interior voice, so it is essentially now a root position chord. This is perfectly fine, and any inversion of this sonority may be used as long as the diminished fifth is below the raised third to keep the augmented sixth interval. The octave displacement inversion of the augmented sixth, the diminished tenth, is useable - and I have employed it in a couple of pieces where it goes by very quickly on a weak beat - but it really is not as effective as the augmented sixth. I encourage you to experiment and use your own judgement, of course.

Because the so-called French Sixth is just a special type of secondary dominant, it can target all of the same diatonic degrees that any regular secondary dominant can. If we return to the progression I used yesterday, a secondary V7(d5) can be introduced on the last eighth note of every measure that has a Progressive root motion. This does some wonderful things for that progression. Since the two lower canonic voices alternate between functioning as the root or fifth through their crosswise transformations, those voices can be alternately decorated with the diminished fifths and the canon can not only be maintained, but the canonic nature of those voices is actually enhanced and it becomes much more obvious that they are canonic in nature. Not only that, but since the first vii chord has a naturally diminished fifth that progresses diatonically down by a semitone, the first measures of both of those vioces can have pickup eighth notes since the tonic also progresses down by semitone from the original first measure. This adds a huge degree of elegance to the voice entries, and it even translates to better entries for the constant root bass notes.

Finally, we can allow this eighth note to propigate throughout the entire lower canon so that those two voices become a basic accompaniment texture of constant eighth notes. The canon is still maintained! The sketch for my Theorem of Pythagoras compositional exercise now looks like the following where the last eighth note of the lower canonic voices alternately introduce the diminished fifth. I'll cover the secondary diminished seventh and the enharmonic augmented seventh chords found in the penultimate measure at a later date.



Note that the final C major chord has it's tones arranged in the exact same arrangement and position as they appear in the Natural Harmonic Overtone Series after all the suspensions are resolved. ((To polite applause) "Thank you (Stage bow), Thank you very much." (Stage bow)).

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