[Smt-talk] function of aug. 6 chords

[Dave Headlam]

Hi -- it might be useful to point out that these issues are actually
considered at length in the pedagogical and research literature:  see, for
instance, Steve Laitz's "The Complete Musician" (2nd ed. Chapter 12 on the
predominant function where Steve thoroughly shows the actual Function of the
chord -- i.e., whether it functions to harmonize an additional note in the
structural melodic line, whether it is part of a sequence, whether it is
more harmonic or melodic in function etc., -- this defining of the function
in multiple contexts is important!  and in later chapters the chromaticisms
are added step by step, with similar criteria given) as well as Betsy
Marvin/Jane Clendinning¹s text, Theory and Analysis ( where they treat all
augmented sixth chords together with the Neapolitan Sixth in a single
chapter (29) on chromatic predominant chords, followed by a large chapter on
chr modulation where they consider the questions of harmonic/VL function
thoroughly) and, for an overview of chromatic and diatonic elements in tonal
music, see 
 
The Diatonic and the Chromatic in Schenker's "Theory of Harmonic Relations"
Matthew Brown.  Journal of Music Theory , Vol. 30, No. 1 (Spring, 1986), pp.
1-33 
Article Stable URL: http://www.jstor.org/stable/843407
 
Here Brown shows how a fully chromatic version of tonality is derived from
motion within the tonic triad. The distinction between mixture (the (b)6 in
the aug 6th)- derived and tonicization/modulation - derived chromaticism
(the #4)  is particularly germane.  See also Howard Cinnamon's dissertation
(1984, ³Third-Relations as Structural Elements in Book II of Liszt¹s Années
de Pèlerinage and Three Later Works ) for an expanded discussion of mixture
in the 19th c. (primary, secondary, and tertiary!)  and distinctions among
chromaticisms from mixture / tonicization-modulation.
 
 
Dave Headlam
 
p.s Vasili - great little piece! Thanks for pointing it out.  The
chromaticism and minor / major substitutions throughout are fascinating --
the "Italian 6th" however is (IMHO) just a passing tone -- [ play I-V6
vi-"iii6" (or I 6/4 var V) -ii6-V6/5 - V in major, then i-v6  VI-III6 ii6/5
- ii4/3 (passing Fr6 or It) - V in minor and you'll see it' s not a
substitution but a modal recasting], but look at the next bit - m. 71 ( in
v:)  N6-vii/V-V6/4-5/3 -i   with the Eb-E !  (that Eb business starts in m.
27, also D# m. 29, also see the preceding Allegro movement, mm. 152-53) --
I'll leave it to those better versed than I in such things, except to note
this article
 
http://www.mozartforum.com/Lore/article.php?id=166
 
which contains some interesting interpretations of the circumstances in the
writing of this piece -- if true, IMO, the rather extravagant chromaticisms
and generally flamboyant piano figuration here might have come from the
"improvisational" nature of the piano part
 
 
 
On 11/27/11 10:10 PM, "Dmitri Tymoczko" <dmitri at princeton.edu> wrote:
 
> Hi Vasili,
> 
> Nice to hear from you, and sorry we didn't get to talk about this stuff back
> in Minneapolis.  
> 
> As I see it, there are several issues to discuss here.
> 
> 1) What does the music actually show, and what claim am I actually making?
> 2) Does the fact that a chord Y *follows* chord X mean that Y "substitutes"
> for X?  (I say "no," you seem to imply "yes.")
> 3) Is it worth distinguishing "predominant function" from "secondary dominant"
> function? (I say "yes," you seem to say "no.)
> 4) Are functions in listener's brains or in composer's?  (I personally
> distinguish "syntactic function" [synfunction] from "[listener's]
> psychological function" [psyfunction].)
> 
> OK, in order:
> 
>>  in the situation you describe, both the V/V and the augmented sixth are
>> typically (but not always) preceded by (and therefore "substitute" for) a
>> diatonic predominant.
> 
> First, it is quite easy to find examples where a secondary dominant/augmented
> sixth pair is not preceded by a diatonic predominant.  Consider, Mozart Piano
> Sonata KV311/284c, II. Here you have a beautiful, predominant-free case:
> viio6/V in the opening (m. 14), Italian 6 in the repeat (m. 50).  Or Beethoven
> Piano Sonata #1, I, m. 42 [viio7/V] and 140 [Ger6/5].
> 
> Now reconsider the structure of my argument more carefully: I claim there are
> *tons* of examples like this in the classical literature (having just found a
> few more in Haydn just last week, and you having just graciously provided a
> new Mozart example), but hardly any cases where you have ii or IV in the
> opening, with an augmented sixth in the repeat.  Note that there is both
> positive and negative evidence here: it's not just the *presence* of secondary
> dominant/augmented sixth pairs, but also the comparative absence of diatonic
> predominant/augmented sixth pairs.
> 
> I don't see you offering an argument against either form of evidence, and
> particularly not the negative sort.  Instead you seem to be saying "look, V/V
> and ii/IV are pretty close, since they both go to the dominant."  I agree
> they're close, but I still think it's worth making a distinction between them,
> for reasons I'll discuss in a moment.
> 
> However, I totally reject the idea that "since the augmented sixth is
> typically preceded by a diatonic predominant, it therefore substitutes for a
> diatonic predominant." The mere presence of a schema X->Y does not imply that
> Y substitutes for X at all. I6/4 is typically preceded by ii6, but it does
> not "substitute for" it in any way.  (Even worse, I is typically preceded by
> V7.)  So I think our intuitions may simply be different here.
> 
>> The textbook example is Mozart's Violin Sonata in G major, (K. 279), third
>> movement, a theme and variations: the theme has a C­C# bass in m.  3 that
>> leads to a half cadence in m. 4. The harmonization of the bass, in
>> conventional Roman-numeral terms, is ii6­V6/5/V­V. The minore variation comes
>> as number four: here the C­C# bass of the theme is repositioned to the
>> melody. Its harmonization is now iio6/4­It.6­V. You might take this as
>> "substitution" evidence that aug. 6th chords are "dominants," as the It. 6
>> appears in the same formal and syntactic context as the V6/5/V.
> 
> Exactly!  This is precisely the point I'm making.
> 
>> But it's all in the eye (ear!) of the beholder.
> 
> Here I disagree.  As we discussed in Minneapolis, I think that the term
> "function" is systematically ambiguous: it can be used as a way of
> categorizing chords by their behavior [syntactical function] or by our
> perception of their similarity [psychological function].  My Musurgia article
> (available on my website in English as "Root Motion, Function, Scale Degree,"
> or available in the original French from your favorite dealer in back issues
> of Musurgia) talks about this, if you're interested.
> 
> I personally am interested in the syntactical question: is there enough of a
> systematic difference between V/V chords and ii6 chords to warrant postulating
> different categories?  I think there is plenty of good reason to do this.  For
> example, V6/5/V is sometimes inserted between I6/4 and V, but ii6 is hardly
> ever found there. Certainly, both ii6 and V6/5/V "lead to V" and are in that
> sense similar.  But I think there are enough systematic differences between
> them (the ability to substitute for augmented sixths being just one) so as to
> warrant postulating different syntactic categories.
> 
> Ultimately, though, there's no fact of the matter here: it's a question of how
> thin we want to slice the salami.  You might prefer a generic "predominant"
> category that encompasses ii, IV, V/V and the augmented sixths, in which case
> there's no interesting question whether the augmented sixths are more like V/V
> or ii.  I prefer a more specific set of categories, in which case that same
> question becomes interesting. In other words: if you are the sort of person
> who distinguishes ii from V/V, then there is very, very good reason to group
> the augmented sixth with V/V rather than ii.  You may not be such a person,
> but I certainly am!
> 
>> Would you say, in the antecedent phrase of this example, that there is a
>> change in function from "predominant/subdominant" (C) to "dominant of the
>> dominant" (C#) and then "dominant" (D)?
> 
> Yes.
> 
>> If so, what would this mean from a cognitive perspective?
> 
> There is a terrible tendency to use "cognitive perspective" to mean "the
> listener's cognitive perspective," as if we forget that composers have brains
> too!  (Or as if we think that listening is just "composing in reverse.")  I am
> interested in composer's cognition, as we can understand it through the traces
> left in musical scores.
> 
> In this case, it would mean that ii and V/V belong to different grammatical
> categories, and that they behave differently.
> 
>> What aspect of the listening experience does "dominant of the dominant"
>> capture better than "chromatically altered predominant/subdominant"? It seems
>> to me unnecessary at best, and problematic at worst, to claim that the chord
>> over C# must have a categorically different function than the chord which
>> precedes it on "geometric" grounds: that is, the chromatic alteration
>> produces a change in the chord's structure.
> 
> Let me just emphasize that I am not using the word "must" or resorting to
> geometry in any way.  I believe that there are good reasons for thinking of
> diatonic predominants and secondary dominants as belonging to different
> syntactic categories (which are in turn underwritten by systematic differences
> in how those chords appear in the music), and that I think it is pretty clear
> that the augmented sixths group with the secondary dominants.  It's a
> complicated story, but I do think the evidence is pretty decisive.
> 
> I'm more than happy to debate this issue, but we have to start from the same
> premises -- and in particular, to be willing to disentangle the psychological
> and syntactical meanings of "function."
> 
>> Tonal functions are not things chords or pitches have or are, but agencies
>> that listeners ascribe them in context, in terms of expectation, implication,
>> or what have you, and on the basis of past experience. (See the second
>> chapter of Steve Rings' recent book for a wonderfully lucid and perceptive
>> discussion of this, pp. 41-43 in particular).
> 
> Not necessarily -- there's also a whole syntactic dimension to the term.
> Tonal functions can be ways of grouping chords by their behavior, underwritten
> by how composers use them. I discuss this distinction in that Musurgia
> article.
> 
> By the way, I have grown somewhat nervous about just how much weight we should
> put on the intuitions of contemporary listeners.  The worry is that our
> hearing is strongly colored by our education.  If you've been taught that
> augmented sixths are altered dominants, you will be more likely to report that
> you hear them that way. (Or if you play a lot of jazz!) If you've been
> taught something different, you will be more likely to report something
> different.  What does this show, exactly?
> 
> I don't mean to discount listener phenomenology altogether, but I think it's
> more subtle than we sometimes like to think.  As Milton Babbitt used to say,
> there's no such thing as an immaculate perception!
> 
> Best wishes,
> DT
> 
> Dmitri Tymoczko
> Associate Professor of Music
> 310 Woolworth Center
> Princeton, NJ 08544-1007
> (609) 258-4255 (ph), (609) 258-6793 (fax)
> http://dmitri.tymoczko.com
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Smt-talk mailing list
> Smt-talk at lists.societymusictheory.org
> http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.o
> rg
 
-- 
 
Dave Headlam
Professor of Music Theory
Joint Professor of Electrical and Computer Engineering
Eastman School of Music / The College
The University of Rochester
26 Gibbs St.
Rochester, NY 14604
dheadlam at esm.rochester.edu
http://theory.esm.rochester.edu/dave_headlam
 



On 11/27/11 10:10 PM, "Dmitri Tymoczko" <dmitri at princeton.edu> wrote:

> Hi Vasili,
> 
> Nice to hear from you, and sorry we didn't get to talk about this stuff back
> in Minneapolis.  
> 
> As I see it, there are several issues to discuss here.
> 
> 1) What does the music actually show, and what claim am I actually making?
> 2) Does the fact that a chord Y *follows* chord X mean that Y "substitutes"
> for X?  (I say "no," you seem to imply "yes.")
> 3) Is it worth distinguishing "predominant function" from "secondary dominant"
> function? (I say "yes," you seem to say "no.)
> 4) Are functions in listener's brains or in composer's?  (I personally
> distinguish "syntactic function" [synfunction] from "[listener's]
> psychological function" [psyfunction].)
> 
> OK, in order:
> 
>>  in the situation you describe, both the V/V and the augmented sixth are
>> typically (but not always) preceded by (and therefore "substitute" for) a
>> diatonic predominant.
> 
> First, it is quite easy to find examples where a secondary dominant/augmented
> sixth pair is not preceded by a diatonic predominant.  Consider, Mozart Piano
> Sonata KV311/284c, II.  Here you have a beautiful, predominant-free case:
> viio6/V in the opening (m. 14), Italian 6 in the repeat (m. 50).  Or Beethoven
> Piano Sonata #1, I, m. 42 [viio7/V] and 140 [Ger6/5].
> 
> Now reconsider the structure of my argument more carefully: I claim there are
> *tons* of examples like this in the classical literature (having just found a
> few more in Haydn just last week, and you having just graciously provided a
> new Mozart example), but hardly any cases where you have ii or IV in the
> opening, with an augmented sixth in the repeat.  Note that there is both
> positive and negative evidence here: it's not just the *presence* of secondary
> dominant/augmented sixth pairs, but also the comparative absence of diatonic
> predominant/augmented sixth pairs.
> 
> I don't see you offering an argument against either form of evidence, and
> particularly not the negative sort.  Instead you seem to be saying "look, V/V
> and ii/IV are pretty close, since they both go to the dominant."  I agree
> they're close, but I still think it's worth making a distinction between them,
> for reasons I'll discuss in a moment.
> 
> However, I totally reject the idea that "since the augmented sixth is
> typically preceded by a diatonic predominant, it therefore substitutes for a
> diatonic predominant."  The mere presence of a schema X->Y does not imply that
> Y substitutes for X at all.  I6/4 is typically preceded by ii6, but it does
> not "substitute for" it in any way.  (Even worse, I is typically preceded by
> V7.)  So I think our intuitions may simply be different here.
> 
>> The textbook example is Mozart's Violin Sonata in G major, (K. 279), third
>> movement, a theme and variations: the theme has a C­C# bass in m.  3 that
>> leads to a half cadence in m. 4. The harmonization of the bass, in
>> conventional Roman-numeral terms, is ii6­V6/5/V­V. The minore variation comes
>> as number four: here the C­C# bass of the theme is repositioned to the
>> melody. Its harmonization is now iio6/4­It.6­V. You might take this as
>> "substitution" evidence that aug. 6th chords are "dominants," as the It. 6
>> appears in the same formal and syntactic context as the V6/5/V.
> 
> Exactly!  This is precisely the point I'm making.
> 
>> But it's all in the eye (ear!) of the beholder.
> 
> Here I disagree.  As we discussed in Minneapolis, I think that the term
> "function" is systematically ambiguous: it can be used as a way of
> categorizing chords by their behavior [syntactical function] or by our
> perception of their similarity [psychological function].  My Musurgia article
> (available on my website in English as "Root Motion, Function, Scale Degree,"
> or available in the original French from your favorite dealer in back issues
> of Musurgia) talks about this, if you're interested.
> 
> I personally am interested in the syntactical question: is there enough of a
> systematic difference between V/V chords and ii6 chords to warrant postulating
> different categories?  I think there is plenty of good reason to do this.  For
> example, V6/5/V is sometimes inserted between I6/4 and V, but ii6 is hardly
> ever found there.  Certainly, both ii6 and V6/5/V "lead to V" and are in that
> sense similar.  But I think there are enough systematic differences between
> them (the ability to substitute for augmented sixths being just one) so as to
> warrant postulating different syntactic categories.
> 
> Ultimately, though, there's no fact of the matter here: it's a question of how
> thin we want to slice the salami.  You might prefer a generic "predominant"
> category that encompasses ii, IV, V/V and the augmented sixths, in which case
> there's no interesting question whether the augmented sixths are more like V/V
> or ii.  I prefer a more specific set of categories, in which case that same
> question becomes interesting.  In other words: if you are the sort of person
> who distinguishes ii from V/V, then there is very, very good reason to group
> the augmented sixth with V/V rather than ii.  You may not be such a person,
> but I certainly am!
> 
>> Would you say, in the antecedent phrase of this example, that there is a
>> change in function from "predominant/subdominant" (C) to "dominant of the
>> dominant" (C#) and then "dominant" (D)?
> 
> Yes.
> 
>> If so, what would this mean from a cognitive perspective?
> 
> There is a terrible tendency to use "cognitive perspective" to mean "the
> listener's cognitive perspective," as if we forget that composers have brains
> too!  (Or as if we think that listening is just "composing in reverse.")  I am
> interested in composer's cognition, as we can understand it through the traces
> left in musical scores.
> 
> In this case, it would mean that ii and V/V belong to different grammatical
> categories, and that they behave differently.
> 
>> What aspect of the listening experience does "dominant of the dominant"
>> capture better than "chromatically altered predominant/subdominant"? It seems
>> to me unnecessary at best, and problematic at worst, to claim that the chord
>> over C# must have a categorically different function than the chord which
>> precedes it on "geometric" grounds: that is, the chromatic alteration
>> produces a change in the chord's structure.
> 
> Let me just emphasize that I am not using the word "must" or resorting to
> geometry in any way.  I believe that there are good reasons for thinking of
> diatonic predominants and secondary dominants as belonging to different
> syntactic categories (which are in turn underwritten by systematic differences
> in how those chords appear in the music), and that I think it is pretty clear
> that the augmented sixths group with the secondary dominants.  It's a
> complicated story, but I do think the evidence is pretty decisive.
> 
> I'm more than happy to debate this issue, but we have to start from the same
> premises -- and in particular, to be willing to disentangle the psychological
> and syntactical meanings of "function."
> 
>> Tonal functions are not things chords or pitches have or are, but agencies
>> that listeners ascribe them in context, in terms of expectation, implication,
>> or what have you, and on the basis of past experience. (See the second
>> chapter of Steve Rings' recent book for a wonderfully lucid and perceptive
>> discussion of this, pp. 41-43 in particular).
> 
> Not necessarily -- there's also a whole syntactic dimension to the term.
> Tonal functions can be ways of grouping chords by their behavior, underwritten
> by how composers use them.  I discuss this distinction in that Musurgia
> article.
> 
> By the way, I have grown somewhat nervous about just how much weight we should
> put on the intuitions of contemporary listeners.  The worry is that our
> hearing is strongly colored by our education.  If you've been taught that
> augmented sixths are altered dominants, you will be more likely to report that
> you hear them that way.  (Or if you play a lot of jazz!)  If you've been
> taught something different, you will be more likely to report something
> different.  What does this show, exactly?
> 
> I don't mean to discount listener phenomenology altogether, but I think it's
> more subtle than we sometimes like to think.  As Milton Babbitt used to say,
> there's no such thing as an immaculate perception!
> 
> Best wishes,
> DT
> 
> Dmitri Tymoczko
> Associate Professor of Music
> 310 Woolworth Center
> Princeton, NJ 08544-1007
> (609) 258-4255 (ph), (609) 258-6793 (fax)
> http://dmitri.tymoczko.com
> 
> 
> 
> 
> 
> 
> _______________________________________________
> Smt-talk mailing list
> Smt-talk at lists.societymusictheory.org
> http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.o
> rg

-- 

Dave Headlam
Professor of Music Theory
Joint Professor of Electrical and Computer Engineering
Eastman School of Music / The College
The University of Rochester
26 Gibbs St.
Rochester, NY 14604
dheadlam at esm.rochester.edu
http://theory.esm.rochester.edu/dave_headlam