[Smt-talk] More "Neighboring" 6/4

[Charles J. Smith]

Folks,

I wish I had time to write about this more fully. In haste, with a  
meeting looming, I have time only for a few isolated points:

1. My own preference is to use descriptions for chords that capture  
what is going on in the bass. Calling a Tonic-prolonging progression  
over a 1-7-1 or 3-4-3 bass a neighbour progression (and the middle  
chord a neighbour chord) seems reasonable and appropriate under this  
assumption. I would prefer to describe the succession of Tonic to IV  
6/4 to Tonic as a pedal succession (rather than a neighbour  
succession) for just the same reason, because the common-tone (pedal)  
bass is what governs the succession; upper-voice patterns seem to  
have so much less to do with the larger impact of the harmony.

2. Of the four neighbour progressions that prolong Tonic (1-7-1,  
1-2-1, 3-2-3, and 3-4-3), the 1-2-1 and 3-2-3 are clearly the rarest.  
Now that the question has been raised, I wonder whether a 6/4 chord  
ever appears over the bass 2 in a 3-2-3 neighbour...but haven't had  
time to check my notebooks of examples.

3. When 1-2-1 does occur, the bass 2 almost never supports a 6/4 or a  
6/5 chord (the latter a slight correction that needs to be made to  
Matt's fine post below). What does tend to appear is a 6/3 or (most  
often) a 4/3 chord. A first hypothesis about this might be that the  
3rd above the 2 is necessary, perhaps as a tendency-tone pointing  
down to 3, to compensate for the lack of a tendency-tone in the bass.  
(NB the common neighbour basses both involve tendency-tones!) This  
hypothesis might seem to be falsified by the rarity of the 6/5 chord— 
except that its infrequent appearance over a 2-1 bass can be  
accounted for by voice-leading issues—avoiding the parallel/direct  
5th of 6-5 over the bass 2-1. Other possible falsifications of this  
hypothesis will likely occur to all of you, as they have to me, but I  
don't have a better one yet.

4. In the end, I am no more (and no less) puzzled by the absence of  
an apparently grammatical progression in the literature than I am by  
the idiomatic eccentricities of any language.

I well remember learning Russian in England in my teens, from a set  
of two lovely OUP books that I still have: the first entitled Russian  
Grammar, which explained all the declensions and conjugations and  
what they entailed, and the second Russian Syntax (probably not the  
term linguists would use these days) which highlighted which forms  
were actually used in the language and which weren't. It has always  
seemed to me that harmony instruction has tended to be relatively  
deficient in this second area. I find it quite gratifying that  
Dmitri, Matt, and others have begun to focus more on this aspect of  
harmony in recent years; it is a subject that occupies me, as well,  
in whatever time I can spare these days.

Cheers,
Charles



> Dear Colleagues:
>
> I'm heartened to see the volume of dialogue my brief query has  
> initiated. I must say, however, I'm not sure I've found among the  
> many worthy musings a convincing answer to my original question.  
> Perhaps there isn't one. At the risk of repeating myself, let me  
> rephrase the question and append some relevant commentary from  
> three of the responses to the SMT list below.
>
> Given that ^1-^2-^1 bass paradigms that expand tonic seem to be  
> considerably rarer than either passing ^1-^2-^3 bass lines  
> prolonging tonic or than ^1-^7-^1 and ^3-^4-^3 bass neighbor  
> motions prolonging tonic for reasons many on this list have  
> hypothesized, is it true that when ^1-^2-^1 bass lines prolonging  
> tonic do occur, unaccented 6/4 chords above ^2 in the bass are  
> rarer than other harmonizations of the same figure (say, with V 4/3  
> or vii65 [RATHER vii°6?] chords), or is ^1-^2-^1 just such a rara  
> avis that it almost never occurs as a tonic prolongation figure in  
> common-practice music regardless of how it is harmonized? In either  
> case, why? Is mode a factor?
>
> Let me also say that the scare quotes around "Neighboring" in my  
> original post title were intentional. I was taught that unaccented  
> 6/4 chord labels, like sequence labels, followed no consistent  
> logic. They were named for a variety of functions, sometimes  
> describing the upper voices, sometimes the bass, sometimes either.  
> More specifically, a "neighboring" 6/4 was an unaccented, tonic- 
> prolonging sonority in which the upper voices moved 5/3 - 6/4 -  
> 5/3. More recently, textbooks have been naming unaccented 6/4  
> chords consistently by the bass motion, calling what I have  
> described above a "pedal" 6/4. Using this nomenclature, is there  
> such a thing as a "neighboring" 6/4 in which a harmonized upper  
> neighbor in the bass line serves to prolong a given sonority? (A  
> related—one might say "inverted"—question is do unaccented passing  
> tones in the soprano harmonized by 6/4 chords appear with any  
> regularity as prolongational devices in common-practice music?)  
> Does anyone have a database that could begin to answer such questions?
>
> Thanks to the three scholars below for their understanding and  
> augmentation of my initial query:
>
> Olli Väisälä:
>
> What is written above does not help much to explain the original  
> question in this thread. Why does I–V6/4–I occur so rarely, even  
> though the progression would seem correct in both harmonic and  
> contrapuntal terms? The previous mails contain several valuable  
> points, the multitude of which helps to remind us that for  
> questions about compositional practice we should not expect to find  
> simple explanations, based on a single factor alone, since  
> successful compositional solutions usually combine several  
> desirable features. For what it's worth, however, here is a summary  
> of the factors that I find most crucial in this case: First,  
> passing motion is a more effective and fundamental way of  
> dissonance treatment than neighboring motion; therefore I–V6/4–I6  
> arises more readily than I–V6/4–I. Second, for a bass line ^1–^2–^1  
> there is a very effective harmonization in I–V4/3–I (or I–VII6–I)  
> involving parallel tenths; hence no need to use a neighboring V6/4  
> easily arises. Third, neighboring chords involving only upper-voice  
> motions are much less weighty in character than those involving the  
> bass; therefore I–IV6/4–I arises more readily than I–V6/4–I.
>
> Ed Klorman:
> Of course, none of this answers Matt's original query regarding why  
> a second-inversion dominant appears commonly as a passing chord but  
> rarely as an upper neighbor to I (with bass ^1-^2-^1) or, for that  
> matter, as a lower neighbor to I6 (with bass ^3-^2-^3). My best  
> instinct, which is not at all rigorous, would appeal to a the  
> Gestalt principle of "good continuation" and to an idea of musical  
> momentum or inertia. That is, a bass motion of ^1 to ^2 would most  
> naturally continue on to ^3 (as in the passing progression I  V  
> 6/4  I6). In contrast, in a neighbor progression such as I V 6/5 I,  
> the bass goes from ^1 to ^7, but the strong pull from leading tone  
> up to tonic forces the bass to change direction; the tendency-tone  
> principle presents the bass from continuing downward. The same  
> principle explains I6 V 4/2 I6 (with bass of ^3 ^4 ^3, where ^4 is  
> pulled back to ^3 because it is a tendency tone).
>
> Scott Murphy:
> For those with corpora at their beck and call, here's one test  
> suggested to me by Edward's cogent reply that might tease things  
> out: compare minor to major. Regardless of what immediately follows  
> the progression (i.e. putting the distinctions between passing and  
> neighbor aside) or other details as listed above, does "tonic in  
> 5/3 followed by major dominant in 6/4" with a non-modulatory  
> continuation appear in minor (e.g. the Beethoven example)  
> significantly more often than it does in major? If so, why, and  
> could the answer be related to an answer to Matt's original query?
>
> Best,
>
> Matt
>
> ________________________________
>
> Matthew Bribitzer-Stull
> Associate Professor of Music Theory
> University of Minnesota School of Music
>
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Prof. Charles J. Smith
Slee Chair of Music Theory & Chair of the Department
Music Department, 220 Baird Hall, University at Buffalo
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cjsmith at buffalo.edu
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