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I wanted to briefly address a few points related to the eternal topic – 6/4 chords. By doing this, I do not expect to change your opinion, but to let you know how a large group of musicians around the world think and feel about this.
1. From pedagogical point of view, I would teach all six-four chords in the theory I period, dividing them into two groups: weak and strong, in a similar way they are presented in the Kostka/Payne "Tonal Harmony" and many other books. For me, it does not make sense to study the weak six-fours near the end of the theory II period, after non-chord tones, making the students wait for two semesters to learn how to harmonize a simple "do-re-mi" or "fa-sol-la" bass line, for example. Besides, occasionally the cadential six-four fuses with an accented passing tonic six-four – an interesting event which could be heard in the main theme of Mozart's Rondo a la Turka (mm 20-21).
2. I strongly disagree with the allegation that "all six-four chords are dissonant". Weak six-four chords are not dissonant. I very much doubt that in a simple waltz or polka one hears alternations between consonant tonics (T5) and dissonant tonics (T6/4, via arpeggiated six-four)...Neither are the passing and pedal six-four chords dissonant. In fact, second inversion triads do substitute for a root position triad when special conditions are created for that. These conditions are impersonalized namely in the passing, pedal and arpeggiated 6/4 chords.
By nature, the perfect fourth is never a true dissonance, because it is an inversion of a perfect consonance. However, depending on context, it is heard as a simulated dissonance under those circumstances outlined in my article on K6/4:
a) when it is a non-chord tone;
b) when it is a member of a chord whose dissonant quality depends on the presence of a true dissonance such a seventh, ninth or a second;
c) when it is a member of a typical accented six-four chord such as the cadential six-four whose bass becomes a prominent acoustic phenomenon demanding its own overtones.
The above dissonant character of the fourth is not present in the typical weak major or minor six-four chords – passing, pedal, or arpeggiated – all of which are weak representatives of an original fifth chord (5/3). Even when an arpeggiated six-four chord falls on an accented beat, it is still a consonant triad!
If you play three different progressions: 1) I - V - I 2) I - V6 - I, and 3) I - V6/4 - I6, you will hear the functional T-D-T exchange from its strongest expression (1), to its weakest expression (3). There are no "dissonant fourths" here, and no harmonic conflict within the D chord itself is manifest. You may put V6/4 in parenthesis if you wish, you may say that, depending on the tempo, it extends the surrounding tonic harmony, but labeling it as V6/4 is correct, because it matches the mind's perception of functional harmonic exchange.
On the contrary, labeling the cadential six-four as V6/4 is erroneous and confusing: while a true dominant with suspensions may be directly connected with the tonic and still produce an authentic resolution (for example V7/4 - I), the cadential six-four cannot do that (V6/4 - I?) - it needs a "moderator" between itself and the tonic, for it is not a genuine dominant chord. Behind the D-T connection a whole array of self-sufficient dominant chords may stand, but the cadential six-four may not stand there alone. This is why no musical piece ever ends with V/6/4 - I...such cadence does not exist.
Practical piano accompaniment and three part women's choirs often make use of close position 6/4 chords which carry the main function of a fifth chord (5/3). Amazingly, 6/4s are more freely treated in such textures.
Finally, with all due respect, I think that Schenkerian and post-Schenkerian theories seem too detached from real music making, and too narrowly-focused to be able to generate a harmony book with a broad discourse on functional harmony in general, and on convincing presentation of six-four chords in particular.
I will not enter the role of Gordano Bruno who, before being burnt at the stake, cried out: "Nevertheless, is spins!" but I will declare calmly, "Nevertheless, second inversion major and minor triads do exist, and in certain conditions they do function as representatives of their parent chords!" I hope nobody will burn me at the stake for this statement :)
Thank you for your attention. I will appreciate any opinions on that topic.
Dr. Dimitar Ninov
Texas State University, San Marcos