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

[Thomas Noll]

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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>
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