[Smt-talk] Caution versus Generalization

Tue Aug 27 16:23:31 PDT 2013

Dear Joel,

Thank you for the extensive discussion. You focus on very interesting problems that I would like to address in the order of your paragraphs.  I will put the cadential six-four aside until your second paragraph.

1. "When a 6/4 chord (e.g., the one colloquially called "the cadential 6/4") follows a pre-dominant harmony and precedes a V or V7 (as in the progressions VII7/V--cad 6/4--V7  or II6/5--cad 6/4--V7), then I don't believe it makes syntactic sense to take the 4th above the bass of the 6/4 as a root.  If you want to assert that these particular 6/4 chords have tonic roots, then you also have to start explaining that although a V-of-V or a VII-of-V would normally go to V, it can also go to I, provided the I is in 6/4 position, and accented, and the 4th of the 6/4 resolves to the 3rd of the V, and etc. etc." 

You are right; not only do I explain that V/V and VII/V occasionally resolve into I instead of into V, but in those cases I do not label those chords as secondary dominants, because they do not tonicize any secondary tonic! As you mention later, the function of the chord does not depend on the structure alone but also on the context. In this sense, in the key of C major, for example, the behavior of F#dim.7 towards I, I6 and I6/4 (cadential or not), differs greatly from its behavior towards the dominant triad.  In fact, when resolving into the tonic or the cadential six-four, this chord is not an F#dim. 7 but a D#dim.7, and is known as #II dim.7 or "common tone diminished seventh". Its resolution into I, I6 and I6/4 (cadential or not) reveals an identical behavior as described by the tendencies and direction of resolution of its tones. Here, no tonicization of a secondary tonic takes place, the resolution is not deceptive, and therefore no secondary dominant is manifest.

Consequently, when D#dim. 7 resolves into the tonic or the cadential six-four, I describe it as an altered subdominant chord on the second scale degree (an altered supertonic). I do not agree with the explanation in some books that, in major, when the common tone diminished seventh resolves into the cadential six-four, it is a misspelled VII dim. of V. In fact, it is exactly the "misspelled pitch" that reveals the difference in function - the raised second scale degree points to and resolves upward into the third of the major tonic, while, as part of VII dim.7 of V, the lowered third scale degree points downward and resolves into the fifth of the dominant. In minor, where a raised second scale degree does not exist, the CT dim.7 is built on degree four, but this does not change its behavior towards the tonic and the cadential chord. Resolve #IVdim. 4/3 into Im, then, #IVdim.2 into I6, then #IVdim. 7 into Im6/4, and finally, #IVdim.6/5 into Im6/4 and you will feel no difference in the behavior (function) of this chord towards the chords of resolution.

Your comments above also tell me that you do not recognize the category of altered subdominants as a factor in functional thinking.  Perhaps you think that only dominant chords could be altered. We simply differ in this regard. For me, a raised fourth scale degree is not an immediate expression of a dominant of the dominant. To use your words from a passage below, "pitch content alone does not determine harmony" I offer you to play in C minor the following pitches: D-Ab-C-F#, and resolve them into Im6. This natural resolution shall be explained as a correspondence between a linear subdominant and a tonic, rather then as a deceptive resolution of V7b5 of V into Im. Walter Piston points to the subdominant qualities of typical augmented sixth chords, although he goes too far by generally announcing them as subdominants, no matter what.  I think that their function depends on the resolution, and I do not make a big deal of the interval of the augmented sixth - its mere presence does not deprive the chord of its root and function. D7 into G or D7b5 into G is the same expression of DD - D (dominant of the dominant resolves into the dominant). The inversions do not undermine this relationship.

2. "Nor do I understand why there should be a conceptual difference between a V whose third is delayed by a 4-3 suspension or accented passing tone and a V in which the 4-3 is accompanied by parallel 3rds above or parallel 6ths below.  If we have no problem interpreting the stand-alone 4th as an accented dissonance, why should the addition of a suspended or accented passing 6th alter the situation?  We gain, to be sure, melodic and rhythmic enrichment and often smoother voice leading by interpolating both a 6th and a 4th, but neither alters the harmonic situation, whether singly or together.  (IMHO, as the kids write.)"

I fundamentally disagree with you on the nature of the cadential six-four. I have exposed my arguments elsewhere, but let me list them briefly here. I think that the cadential six-four is not a mere V with suspensions - it is much more than that. Some of the more essential argument in support of this notion are:

a) a genuine dominant chord with suspensions may be placed directly before a tonic chord and still produce an authentic resolution/cadence, even if the suspensions are not resolved within the dominant chord prior to its resolution into the tonic. The cadential six-four is incapable of such treatment - placed before a tonic chord, it fails to produce an authentic resolution or cadence, and the connection I6/4 - tonic, is heard more as a part of a chord arpeggiation (arpeggiated six-four on an accented beat followed by the tonic). Therefore, the cadential six-four is not a genuine dominant with suspensions. It could never be a self-sustained, fully fledged dominant. This is why you would never come across such a "cadence" as I6/4 - I.

b) the cadential six-four is occasionally embellished by non-chord tones and altered chords as if it were a tonic. In other words, composers explore the structural equality of the cadential six-four with the tonic triad. There are numerous cases in the music literature where, what you would call "an accented passing sixth" is the actual consonant resolution of a dissonant suspension introduced to the cadential six-four chord.  If you want to imagine clearly the picture, introduce a 4-3 suspension over a tonic triad, but instead of harmonizing that suspension with the tonic, place the cadential six-four below it.  Then ask yourself the questions: Over which chord is this 7-6 suspension introduced? Do the same with a 9-8 suspension over a tonic, but replace the tonic with the cadential six-four. Then you will realize that what you call "an accented dissonant fourth" is the actual consonant resolution of an oddly labeled 5-4 suspension (in C major, the tone D suspended over I6/4 sounds dissonant to what you deem to be a dominant function, instead of sounding like a member of the dominant which it is!)

c) the free arpeggiation of the cadential six-four does not sound as a bunch of appoggiaturas over a dominant function but as an arpegiatted tonic chord over a dominant bass. 

d) the tonic melodic content that is often played over the cadential six-four most often clearly outlines a tonic triad rather than a dominant one.  Again, this context strongly suggests a tonic triad over a dominant bass.

Having said all of the above, I do not claim that the cadential six-four is a mere tonic either. I support the notion that it is a bi-functional chord in which a conflict between tonic and dominant takes place. "A tonic over a dominant bass" is quite different than "two non-chord tones over V". The outer tonic structure of cad.6/4 allows us to explore it as a temporary point of resolution - to embellish it by accented and unaccented non-chord tones as well as by dissonant and other altered chords. Now you understand my concept of an altered subsominant vs. dominant of the dominant.  Altered subdominants that contain the raised fourth degree and coincide with dominants of the dominant, resolve into the cadential six-four as if it were a tonic, and no tonicization or deceptive motion takes place during this resolution.

3. "As for the passing 6/4, let's take a motion between two closely related pre-dominant harmonies, such as II4/3 and V6/5/V or IV6 and II6/6, and let's soften the resulting leaps with passing tones.  Lo and behold, a 6/4 emerges.  But it is surely not a tonic chord with root ^1.  It happens to have the same pitches as  tonic chord, but that's just happenstance--the fortuitous result of a filled-in voice exchange, usually.  Do we really say in such instances that a II4/3 chord, which ought to proceed to a V (directly or by way of continued prolongation of the pre-dominant function), somehow changes it's mind (as it were), retreats to a tonic, then moves on to another pre-dominant?"

What I try to tell my students is that pitch content alone does not determine the harmony, and we cannot assume, just because a chord contains the same pitches as a tonic chord, that it actually is a tonic.  

In retrospect, allow me to re-phrase your own arguments in the last sentence above. Certainly, pitch content alone does not determine harmony, and we cannot assume, just because a chord looks like a VIIdim.7 of V it is actually so.  If it resolves into a tonic or cadential six-four it is not a secondary dominant. 

Now about passing and pedal six-fours. I think in this manner: functional perception is also influenced by tempo. In a slow or moderate tempo, the passing six-fours (for example, I64 between two subdominants and V6/4 between two tonics) are heard as consonant triads in inversion which bear the original function of the chord whose inversion they are. Their functional expression is weaker than that in root position and first inversion, but the conditions created for their use allow the perception of changing harmonies with a very low degree of ambiguity. In other words, I-V4/3-I is exactly that: tonic - dominant - tonic. In fast tempi, the function in the middle is assimilated by the surrounding harmonies and heard mostly as a prolongation of those.

I am puzzled by your implication that  connecting subdominant harmonies with the tonic violates the harmonic syntax. As far as I am concerned, there are plagal resolutions, and also plagal cadences which do exactly that - connect a IV or II to the tonic. In late romantic style the plagal cadence is more freely used, although it is never so frequent as the authentic, of course. If you listen to the second movement of the "In the Ne World" by Dvorjak, you would be delighted by some final plagal cadences that do not necessarily represent "post-cadential extensions of the tonic" (as a Schenkerian analyst would describe those). One great case of final plagal cadence is the end of the first theme of Jupiter by Holst (when it is exposed for the first time). There the cadence is exactly II6-I, although you may describe it as S sub6 - T. In the case of passing six-fours I am not saying that we hear cadences all over the place - I am simply surprised that you think it is a big deal to say "II is followed by I, or IV is followed by I" Yes, in slow tempo the progression II-4/3 - I6/4 - II6/5 may impress the listener with a plagal interaction, before going to I6/4 or V. However, in fast tempo such an analysis is not necessary and we could consider this as a prolongation of a subdominant chord on the second degree.

4. "To clinch the argument, I say that surely no one would take a C-major song ending with C-E-G-A or even C-E A as ending on a VI6/5 or VI6.  They end on tonics, even if the notes are the same as those that might appear in a VI6 or VI6/5.  

I agree with you! After V, the C-E-A will sound like a tonic with an added 6th. This is why we do not use VI6 deliberately as tonic substitute in classical and romantic style. However, if you introduce a deceptive progression V7-VI, and then change the position of VI5/3 into VI6, you will feel as if you move  within the realm of the submediant.

5. "First day of class tomorrow, and I expect that all the transfers, as usual,  will want to know why I don't label cadential 6/4 chords as tonics.  As always, there will be some that are unconvinced.  Well, as long as they use them successfully, I'll be happy.   It's a practical class (part writing, somemodel composition)--not really theory."

I would never label the cadential six-four as V 6/4, because for me, the latter means a dominant triad in second  inversion and has nothing to do with the structure of the actual chord in question. I was appalled to discover that a number of transfer students in different former classes of mine, built an actual dominant in second inversion and connected it to a final tonic, thinking they were applying a cadential six-four! The technical structure is tonic, and the function is T over D. In order to spell correctly this important predominant chord (the only genuine pre-dominant chord, because it is validated by V, it is designed to announce the upcoming dominant, whereas IV and II do not depend on V to exist or to function properly) students will have to have in mind a  tonic structure. If you claim that I cannot mechanically separate the supposed V6/4 label from its logical continuation (5/3), I will then ask you why I could do that with any genuine dominant chord with suspensions, and cannot do that with the cadential six-four...in other words, in the same manner we can use V7sus - I, or V13sus - I, or V7sus6 sus4 - I, without labeling the resolution of any of those suspensions, we should be able to use V6/4-I as a convincing label revealing "an authentic cadence". If a genuine dominant wish suspensions can be mechanically separated from a "clearer dominant" that brings the resolution of the suspensions, and still not lose its D qualities, why should we not be able to do the same with what is deemed to be a genuine V with suspensions?

All in all, I think that the repudiation of the subdominant function and the unquestionable embrace of what I think of as "exaggerated concepts of prolongation and linear thinking" has exercised a negative impact on functional thinking and teaching of harmony. I personally am convinced that the harmony school which stems from Rameau, Riemann and Rimsky-Korsakov is the most solid and right choice for studying of classical harmony. It builds the concept of tonality on three main functions: T, S and D, thus opening wonderful opportunities for musical practices in a colorful palette, a rich theory of altered chords and modulation, and diverse analyses of tonal pieces that do not inevitably end in a black and white T-D-T with a single fixed melodic contour for all tonal music! In addition, this school is much closer conceptually to jazz theory and practice as well as to analysis of popular music. In fact, second inversion triads in close position are used widely by keyboard accompanists in pop music as substitutes for root position chords, and  no one is alarmed by any dissonant qualities. Also, for a piece in C major, for example, in order to instruct a guitar player in a group (which also has a bass guitar), to play a cadentical six-four, all you have to do is to write the C chord in the chart. The bass will do the rest. Does that simple and clear harmonic approach not tell us what the functional nature of the cadential chord is?

Finally, if you think all 6/4 chords are dissonant sonorities, I would be curious about how you hear the arpeggiated six-four in waltzes, polkas and marches? When the bass plays the fifth of the chord in almost every measure, do you hear a bunch of alarmingly dissonant tonics, subdominants and dominants?

Thank you for taking the time for reading this letter.  I wish you a great semester's start!

Best regards,

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666