[Smt-talk] I - II- IV as a progression (counterpoint)

[Ildar Khannanov]

Dear Thomas,
 
thank you very much for your exciting input! As always, original and profound. 
 
Indeed, tonal functions are not fast attached to musical texture. They can be related to modalities, to Greimasian square, to narrative trajectories, to logic, to discoursive strategies,  to Aufhebung, to deconstruction, etc. Functions are the elements which connect musical thinking to thinking in general, as a category. In this sense, voice leading is just the icing on the cake.
 
The fourth element (the additional C) can be inscribed into binary opposition and its negation. 
 
Thank you again,
 
 
Best wishes,
 
 
Ildar Khannanov
Peabody Conservatory
solfeggio7 at yahoo.com

--- On Fri, 9/11/09, Thomas Noll <noll at cs.tu-berlin.de> wrote:


From: Thomas Noll <noll at cs.tu-berlin.de>
Subject: Re: [Smt-talk] I - II- IV as a progression (counterpoint)
To: "Ildar Khannanov" <solfeggio7 at yahoo.com>
Cc: "smt-talk smt" <smt-talk at societymusictheory.org>, "Nicolas Meeùs" <nicolas.meeus at paris-sorbonne.fr>
Date: Friday, September 11, 2009, 7:20 PM


Dear Ildar, dear Colleagues,

as Kevin Mooney points out in his introductory article "Riemann's Debut as a Music theorist" to his translation of "Musikalische Logik" (JMT 44/1), there is an interesting deviation in Riemann's analysis of the "grosse Kadenz"  C F C G C between the 1872 version from "Neue Zeitschrift für Musik" and the published version of his dissertation "Musikalische Logik: Hauptzüge der physiologischen und psychologischen Begründung unseres Musiksystems" from 1874. 


The (1901 reprint of the) 1972-version contains the Hauptmannian terms "Quintbegriff" and "Terzeinigung"
"Ich sehe in diesem zweiten Auftreten der Tonika den Quintbegriff, der sich dem Einheitsbegriff des ersten Auftretens entgegensetzt, und der seine Terzeinigung durch die Oberdominante wieder in der Tonika findet."


In the dissertation (as published 1974) he abandons the Hauptmannian terms in favor of "Antithese" and "Synthese" and he introduces a grammatical error! (a Freudian slip ?)   

"Ich sehe in diesem Auftreten der Tonika nach der Unterdominante die Antithese ..., die sich der These des ersten Auftretens entgegensetzt, und die ihre Synthese durch die Oberdominante wieder in die Tonika findet." 


A grammatically correct formulation would be:
"... und die ihre Synthese durch die Oberdominante wieder in der Tonika findet." 
But literally this would imply that the manifestations of Thesis, Antithesis and Synthesis are the three occurrences of the C-chord (the second typically as a six-four-chord).


But Riemann defines subsequently:
Thesis: C, Antithesis F C, Synthesis G C.


And finally he introduces the terms:
thetic chord: C, antithetic chord: F, synthetic chord: G  


In other words, it seems as if he shifts the scene of logical action from the C chords towards the F and G chords.
When this maneuver is done, he acknowledges that the cadence C F G C is more frequent and explains why the absence of the second C-chord doesn't matter.


The intellectual tension behind this shift is that – on the one hand – Riemann wishes to present his preferred analysis of the "typical" cadence, while – on the other hand – he wants to make peace with the frequent cadence.  Recall that he concludes his characterization of the "Grosse Kandenz" (both in 1872 and 1874) with: "Diese Gestalt der Kadenz ist der Typus aller musikalischen Form".  


I'd like to amplify this tension with a side glance to structural semantics: The first characterization Thesis: C, Antithesis F C_64, Synthesis G C  reminds about the structure of a semiotic square (which - of course involves different attitude towards logics):


C         C_64
|     X      |
G           F


Although I hesitate to choose semantic labels for the opposition between C (= C_53) and C_64, I would argue the square attributes a kind of narrative meaning to the "Grosse Kadenz"  
[NB: Christine Ohno reports in "Die semiotische Theorie der Pariser Schule" that Hegel was also an inspirational source for Greimas]


Under this particular perspective it would be even less plausible to merely subsume the C - F - G - C cadence under the roof of the "Grosse Kadenz".
best wishes
Thomas Noll   










*********************************************************
Thomas Noll
http://flp.cs.tu-berlin.de/~noll
noll at cs.tu-berlin.de
Escola Superior de Musica de Catalunya, Barcelona 
Departament de Teoria i Composició 


*********************************************************












Am 11.09.2009 um 23:37 schrieb Ildar Khannanov:







Dear Nicolas and the List,
 
in my view, this situation is much less dramatic. Roman Numerals are a scaled-down version of tonal functions.
 
As for the subdominant triad problem, it does not exist. Critics of Riemann have fallen in the trap they were preparing for the great theorist from Leipzig. Why is it the "weakness of Riemann's theory" to imagine a shadow of tonic between subdominant and dominant? Au contraire, it is a very elegant theoretical suggestion!
 
As for the revisionist idea that IV to V "is not a progression because there are no common tones," and the suggestion to substitute IV as a primary triad with supertonic triad, one may ask: so what if there are no common tones between S and D triads? There is a common tone between T and S triads! And, if to consider that Rameau suggested Dominant Seventh chord as the representative ot dominant function, then there IS a common tone between Subdominant and Dominant Seventh.
 
As for supertonic triad as a substitute for subdominant triad, it does not exist! If we are talking about root position supertonic  triad in major, it is used very rarely because there is a serious problem connecting it with tonic, and that is a very serious voice leading problem : there are no common tones indeed and no purpose of resolution. In minor this chord is an absolute nonsense. Only Snoop the Dogg uses it after the tonic triad ( "I've been a sittin in a Holiday Inn...etc). As for considering it a part of the circle of fifth, as a chord resolving to the dominant triad, there is another problem. A minor triad as it is, it cannot serve the function of a dominant and as such it does not require resolution into dominant triad. Nicolas in his previous email mentioned exactly that, that the presence of a leading tone makes the dominant sound like the dominant. Or else, why Sechter did not suggest to use minor v as a good substitute of a dominant
 triad in minor? We still use harmonic minor and raise sc st 7 for a reason.
 
It has been discussed for decades that supertonic triad in root position is not a function. The function is the subdominant. It often has an added 6 or substituted 6. Supertonic triad in major and in minor is not a structural function. Its addition to the number of structural functions does not solve the problem of progression because progression do not strart on ii. The problem is not to connect IV to V, but to go through the circle I--non I--I. Or, I--IV--V7--I.
 
As for adjacency as a factor determining function, there is also a big problem with logic. Mi to Fa seems to be an adjacency, but this connection does not constitute the leading tone. Mi can go to Fa and stay there. Or Fa can go to Mi and remain on Mi. What makes Ti a leading tone is not the adjacency but the fact that it is a part of the dominant function.  Adjacency is meaningless in music, while function is a constituting power.
 
My conclusion is that Riemann is not that easy  to criticise. The division of labor is such that Leipzig has always been a theory town, while Vienna had brilliant performers and composer.
 
Best wishes,
 
 
Ildar Khannanov
Peabody Conservatory
solfeggio7 at yahoo.com

--- On Tue, 9/8/09, Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr> wrote:


From: Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>
Subject: Re: [Smt-talk] I - II- IV as a progression (counterpoint)
To: "smt-talk smt" <smt-talk at societymusictheory.org>
Date: Tuesday, September 8, 2009, 1:02 PM


The relation between function theory and Roman numerals is a complex matter. It depends, in my opinion, on one's conception of a harmonic function.
    The problem not only is that the same function may be projected by harmonies built on different scale degrees, but also that the same scale degree may project different functions. In this respect, it is striking that Goetschius, whose rules quoted by Richard otherwise faithfully echo Simon Sechter's description (Die richtige Folge der Grundharmonien, 1853, p. 12-13), nevertheless include the IV-V progression which Sechter (and Bruckner or Schoenberg after him) wouldn't consider a progression properly speaking because of the absence of common tones. [R. Wason, Viennese Harmonic Theory, p. 154 n. 10, notes that Sechter's Grundsätze were known in American translation as early as 1871; 12th edition in 1912.]

That the function of IV in IV-V may be considered different from that in IV-I has been a major concern of harmonic theory since Rameau's double emploi. 
    In order to make IV a subdominant (S) in both cases, Riemann is compelled to view IV-V as conceiling a IV-(I)-V progression; this remains a major weakness of his theory: Riemann cannot imagine a simple path from one of the opposites of his dualist construction to the other, from Unterdominante to Oberdominante.
    Sechter, on the contrary, considers that IV in IV-V stands for II. If a function were to be assigned to IV-V = II-V, however, it would be a dominant function (in a sense inherited from Rameau), not a subdominant as in IV-I. As Wason states (p. 35), Sechter's "notion of the subdominant is completely unrelated to its use as dominant preparation".

The question then, is whether a harmonic function is a "chord quality", independent from context (as in Riemann), or arises from the context (as in Sechter, or more generally in theories based on cadential formulas). There is a tendency, in Germany, to consider Roman numerals as expressing a theory based on six (or seven) different harmonic functions. This may be true in some cases, but Roman numerals more often convey a conception of contextual functions. The distinction between the two is not always clear, however.

Cordialement,

Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr
http://www.plm.paris-sorbonne.fr



Richard Porterfield a écrit :
[...] 
Although some theorists such as Riemann track functions (T, D, S) which might be projected by a harmony built upon one or another scale degree, while others track scale degrees without regard to function, the historical association I speak of is longstanding and not limited to Schenker. 
[...] Regarding the North American theoretical tradition specifically, Bernstein refers to "a roman numeral style of harmonic analysis in America during the nineteenth century" of which Percy Goetschius is a prime mover (787-88). Consider the following passage from Goetschius's The Theory and Practice of Tone-Relations first published in Boston in 1892 (I quote from page 25 of the 1917 edition [New York: G. Schirmer], available on Google Books): 

Rule I: The tonic triad can progress, under all harmonic circumstances, into any other chord of its own, or of any other, key. This is its prerogative as chief of the harmonic system. Therefore I-V and I-IV are good.
Rule II: The subdominant triad (IV) may progress either into the I or the V. Thus: IV-I or IV-V.
Rule III: The dominant triad (V) may progress, legitimately, only into the tonic chord. Therefore V-I is good; but V-IV must be avoided [emphasis original]. There may well be a paper or even a Ph.D. in the subject of Goetschius's influence on American theory having made conditions favorable for the reception of Schenker's theories and methods later in the twentieth century. 
 
Regards, 
Richard Porterfield
Instructor, Mannes College of Music
Ph.D. Candidate,  


From: Paul.Sheehan at ncc.edu
To: porterfr at hotmail.com
CC: jcovach at mail.rochester.edu; smt-talk at societymusictheory.org
Date: Fri, 4 Sep 2009 01:03:06 -0400
Subject: Re: [Smt-talk] I - II- IV as a progression (counterpoint)

Dear Readers,
 
Re. Richard Porterfield's statement:
"That’s what the Roman numerals have been for, historically, not only identifying scale-steps but also their function in a tonal context."
I don't mean to be overly fussy, but is it the case that Roman numerals have _not_ historically entangled with function?  I am under the impression that, until Schenker, scale step theory (Roman numerals) was used as an analytical tool independently of function theory.  Furthermore, I am under the impression that Schenker in particular combined scale degree theory with function theory in a way that now seems almost automatic to many theorists and other interested parties (at least in North American academic culture).  Witness, e.g., many textbook treatments of such matters since Aldwell and Schachter, inclusive.  Do any historians of theory care to comment?
Paul Sheehan
<Paul.Sheehan at NCC.edu>


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