[Smt-talk] Nature and Labeling of the Cadential Six-Four

[Ninov, Dimitar N]

Dear Nicholas,

I had attached a file with samples to clarify this, but it looks like the list does not transmit attachments. I am attaching the samples again with the hope they will reach you via your personal email. I am providing a verbal explanation below. Of course, within context.

Try the following progression. In C major,  introduce I, then II6 (with the root in the soprano), then tie the soprano note over a bar line and introduce the cadential six-four on the downbeat of the next measure. At this very moment, if you play in close position, you will have the following notes: G in the bass; E in the tenor, G in the alto, and D in the soprano. Then the tone D in the soprano will resolve into C (still above the cadential six-four), thus producing a 9-8 suspension as referred to the root of the tonic (which, if referred to the bass would be awkwardly labeled as "5-4"). At the moment of the collision with the cadential six-four, you will hear the tone "D" as a dissonant suspension to I6/4. Then, if you tie the tone of resolution"C" over the next bar line and follow with V, you will hear another dissonant suspension, this time over V. Thus a chain of two suspensions - one over the cadential six-four, and another one over V will be performed.

You can try the same experiment with a 4-3 suspension as referred to the tonic, but harmonize it with the cadential six-four. This time you introduce IV with the root in the soprano, or II6 with the third in the soprano, and then proceed in the same manner.

I hope this helps to grasp the main idea that the cadential six-four occasionally serves as a point of resolution. Such situations are more rare, but they defy the general equalization of the cadential six-four with V. 

You are saying: "I do believe that a 6/4 chord whose bass is V should be labeled V6/4 if it goes to V5/3, whether or not it is adorned with appoggiaturas or other neighbor notes – and this, to me, means that a cadential V6/4 should be labeled as such: how would it be cadential otherwise? 

It does make a big deal what you adorn over this dominant bass: the tonic or the dominant. You certainly cannot adorn the dominant by using its own tones! But you can certainly adorn the cadential six-four by using a dominant tone, which resolves into the cadential six-four just in the same manner as it resolves into the tonic. At the moment of resolution of a non-chord tone into the cadential six-four (thanks to its tonic structure) the cadential six-four reveals its latent tonic potential. This is why there is a difference between "a dominant with two non-chord tones" and "a tonic over a dominant bass". The latter concept allows you to explain the embellishment of the cadential six-four; the former does not.

If even this sounds unclear, think of a dominant pedal upon which different functions unfold. At given moment the tonic occurs over this dominant pedal and it is embellished by a 9-8 suspension or by a 4-3 suspension. Does the dominant bass prevent us from hearing the suspensions introduced to the tonic structure above and their resolutions? No it does not. Here I am also opening another door: functional prolongations in the bass do not necessarily erase implied harmonic functions over the bass. 

This is why, (think in C) when you give a chart of a jazz or popular music piece to the accompanist (pianist or guitarist) you will not label the cadential six-four and the following dominant as as G6/4-5/3 but as C/G - G, which say it clearly - play a tonic chord over a dominant bass, then resolve the tension by playing the genuine dominant.

And finally, if you still think that the cadential six-four is a genuine dominant chord with suspensions, test its qualities by resolving it directly into the tonic. Does it produce an authentic cadence? No. Now resolve a genuine dominant with suspensions: any V5/4, 7/4, 9 sus 4, 13 sus 4 into the tonic, without resolving the suspensions within the V chord prior to its resolution into the tonic. Does it produce an authentic cadence? Yes. Inference? A genuine V with suspensions does not need a "clearer" dominant to be inserted between it and the tonic; it can proceed directly into the tonic without handling the suspensions first and still produce an authentic cadence. The cadential six-four is not capable of that; it needs to be attached to a genuine V. Therefore, it is not a genuine V. Its structural equality with the tonic, which produces a certain aural effect, prevents it form functioning as a self-contained dominant.

Best regards,

Dimitar
 

________________________________________
From: Nicolas Meeùs [nicolas.meeus at paris-sorbonne.fr]
Sent: Sunday, February 12, 2012 4:10 PM
To: Ninov, Dimitar N
Cc: smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Nature and Labeling of the Cadential Six-Four

Dimitar,

On this point, my position is quite simple, albeit quite radical: I do not know what the meaning, or the function, or whatever, of a chord is if I do not know the chord that follows (or, less often, that precedes). I do not believe in attractions (e.g. of the leading tone) or other obligato movements (e. g. of a descending 7th), unless they happened. I do not know the meaning of C and E above G unless I know what follows. I cannot identify a tonic if it is not preceded by some sort or dominant (or subdominant), nor a dominant if it is not followed by some sort of tonic.

I am not sure to understand your 9-8 over a second inversion tonic. Do you mean, say, G-D-E, with D resolving on C (i.e. G6/5-4)? This, to me, in an ornamented G-C-E, about which I still know nothing without knowing what follows (or what precedes).

For too many of our students (not to mention ourselves), figuring chords boils down to labeling them, without any attempt to understand their function in the harmonic progression. In the end, they (we) produce a series of chords, each of them wearing its own label, without any consideration for the meaning of the series as such. Music should not be heard as a mere succession of independent chords: it is how chords depend from each other that count; and harmonic figuring may (and should) help developing that hearing.

I do believe that a 6/4 chord whose bass is V should be labeled V6/4 if it goes to V5/3, whether or not it is adorned with appoggiaturas or other neighbor notes – and this, to me, means that a cadential V6/4 should be labeled as such: how would it be cadential otherwise? I do agree that it probably should not be labelled V6/4 if it does not go to V5/3. I am not really interested by the interval on the bass: a cadential 6/4 can be "inverted" without loosing its function (see my recent exchange with Rick Cohn, and Eric Wen's comment).

Yours,

Nicolas

Nicolas Meeùs
Université Paris-Sorbonne





Le 12/02/2012 20:34, Ninov, Dimitar N a écrit :

Dear Nicholas,

I agree with you that it depends on the context. In a typical context, where the cadential six-four is followed by the dominant, we may be able to explain the cadential six-four as a dominant with two foreign tones on top, although this is more of a visual explanation rather than aural; the addition of C and E over the tone G makes our ear detect a chord that structurally coincides with the tonic triad. This structure does not have the intensity of a genuine dominant with suspensions such as V5-4 or V7-4, because no matter how you invert a genuine dominant with suspensions, it remains dissonant in all of its inversions, but when you invert the cadential six-four, it sound perfectly consonant. Therefore, the intensity of the cadential six-four is not caused by a dissonance, but by a by-functional conflict between T and D.

Therefore, there is a discrepancy between the visual labeling of the cadential six-four as a V chord, and the aural result which suggests a chord that coincides with a tonic triad. In addition, the Roman numeral "V" becomes ridiculously misleading when the six-four becomes a point of resolution itself and its structural equality with the tonic is called for.

How would you label the 9-8 appoggiatura over the tonic, which is harmonized with cadential six-four instead of the tonic? The tone D sounds dissonant to the cadential six-four and resolves into C. Play that to yourself and try to explain why the tone D which is a member of V sounds like a dissonant suspension over what you deem to be a V chord itself? Why does the tone C which is deemed to be a non-chord tone sound like a resolution?

I can only regret that many students are not even given the chance to inquire into this problem. All they are told is that the cadential six-four is a V chord, and if they dare to think otherwise, they would be penalized. How do we encourage critical thinking if we teach like that? But when these students encounter a six-four chord embellished by non-chord tones itself, they do not know how to explain it and how to label it. Why? Because their teachers do not know how to do that, and they have never discussed that issue before!

Usually Schenkerian analysts avoid discussing the embellishment of the cadential six-four, because if they did not, they would have to recognize it as a structure on its own. But their theory is not flexible enough to afford such a "heresy".

Also, how about this idea: the interval of the fourth, when the bass is not involved is not a dissonance. When the bass is involved, it is a "feigned dissonance", because its inversion is a perfect consonance. Usually, in a three- or four-part harmony, the fourth may be perceived as a dissonance if there is another, real dissonance, present in the chord, such as a second or a seventh or both, as for example in V-5/4 or V7/4. In the I6/4 structure you could never prove that it is a dissonance, especially when you follow with I6.

Best regards,

Dimitar

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


From: Nicolas Meeùs [nicolas.meeus at paris-sorbonne.fr<mailto:nicolas.meeus at paris-sorbonne.fr>]
Sent: Sunday, February 12, 2012 12:34 PM
To: Ninov, Dimitar N
Cc: smt-talk at lists.societymusictheory.org<mailto:smt-talk at lists.societymusictheory.org>
Subject: Re: [Smt-talk] Nature and Labeling of the Cadential Six-Four

Pierre Boulez, in Penser la musique aujourd'hui, complains about the very principle of figuring which, he writes, remains less precise than the score itself. This misunderstands the essential aim of analytic figuring, which is to simplify the music in order to make it more easily understood. In other words, a figuring cannot give a full account of what is happening, it always is a simplification. And the corollary is that it would be pointless to read a figuring (or a Schenkerian graph, or any such representation) without keeping an eye on the score.
    In the case of the ambiguous 6/4 dominant preparation, the analyst cannot hope to convey the ambivalence with simple figures and, in complex cases, only the score will express the full ambiguity. The figuring chosen depends on what one wants to stress. If you want to stress the "moment of occurrence" on the beat, you may write I6/4; but if you want to draw attention to the overall meaning of the passage, V6-5/4-3 will be better. In any case, the reader would be fool not to consider the score itself, which says all.

Nicolas Meeùs
Université Paris-Sorbonne



Le 12/02/2012 16:44, Ninov, Dimitar N a écrit :

Dear Ciro,

Thank you for the comment. At the moment of occurrence which occupies the beat taken by the cadential alone, you label it as V-6/4. This is what is confusing. But how would you label it when you resolve non-chord tones into it as if it were a tonic? Such moments defy the notion of suspensions or appoggiaturas to V, because what is being introduced is suspensions or appoggiaturas to I, only that the vertical sonority is not I but I6/4. A 9-8 suspension to I, or a 4-3 suspension to I, each of them harmonized by the cadential six-four. What would you say about that?

Best regards,

Dimitar
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