[Smt-talk] Abbreviated Labels of Seventh Chords

Ildar Khannanov solfeggio7 at yahoo.com
Sun Feb 12 17:33:13 PST 2012

Dear List,
I am puzzled by this vehement defense of Schenker, "figured bass" and “counterpoint” against the theory of harmonic functions. Is there something important at stake? 
The arguments like “point-by-point’ chord definitions" are quite old. They remind me another one, “the gloves do not fit.” Yes, the theory of tonal-harmonic functions implies that chords in a harmonic progression must have functions and they have to be heard. I just do not understand why it is necessary to disregard them, or even throw them away in order to understand musical meaning of the progression. Do you normally throw away the words from the sentence in order to understand it? So, if I say: “I do not like potato salad” you need to reduce it to “I like the potato salad,” or “I like the potato,”  or, even,  “I am the potato?” How do you know, which notes to eliminate, beside the claim that there is a mysterious Urlinie—a claim, which is impossible to substantiate?
Concerning the theory of harmonic functions and the French tradition, I find it fascinating how Schenkerians, obsessed with revenge to European tradition of the 19th century, just as their teacher, tend to read texts selectively, omitting the paragraphs containing the undesirable information. However, if they took time and read slowly, say, Fétis’ famous treatise on harmony, they would find the following: 
“Je demandai quels accords existent par eux-mêmes, comme de conséquences de tonalité actuelle, indépendamment de toute circonstance de modification, et je n’en trouvait que deux: le premier consonant, compose de trois sons, et appelé accord parfait; le deuxième dissonant, composé de quatre sons placés à des intervalles de tierces l’un de l’autre, et appelé accord de septième de dominante. Je vis que le premier constitue le repos dans l’harmonie, parce que lors-qu’il se fait entendre, rien n’indique la nécessité de succession; l’autre, au contraire, est attractif, par la mise en relation de certains sons de la gamme; par cela même il a des tendances de résolution, et il caractérise le movement dans l’harmonie.
[] l’isolement absolu me permettait de me livrer sans distraction à mes rêveries sur la théorie de l’harmonie. Après avoir fixé le caractère et les fonctions des deux accords consonant et dissonant, je cherchai avec soin si quelque autre aggrégation harmonique était nécessaire pour constituer la tonalite; mais je n’en pus découvrir, et j’acquis la conviction que tous les autres accords sont des modifications de ceux-là, et que leur destination est de jeter de la variété dans les forms de l’harmonie, ou d’établir des relations de gammes différentes.”
François-Joseph Fétis, Traité complet de la théorie et de la pratique de l’harmonie, http://books.google.com/books, 1853, page viij. 
The terms in italics are carefully copied by Fetis from Rameau’s Traité de l’harmonie. In fact, these two paragraph provide a better definition of the concept of harmonic function than the texts of Rameau. They are tied to the interpretation of tonality. Thus, this is the theory of tonal-harmonic functions, advocated by one of the most brilliant French theorists of the 19th century who also taught at the Conservatoire. Riemann considered him one of his most important influences.
Theoretical position of Fétis does not support Schenkerian revisionism at all. It supports Rameau and Riemann. I can provide the documented evidence that Simon Sechter (who alledgedly created or supported a teaching of scale steps, alternative to Rameau-Riemann’s functions) fully supported functional theory. There are many statements in Kirnberger which show profound understanding of Rameau’s contribution. 
I do not know what Nadya was teaching. The CPE’s libel of Rameau present little interest. In fact, his Versuch is not a book on counterpoint and voice leading. Again, this is a common misconception (just as Zarlino did not write a book On Counterpoint; it was  a subtitle of a 4-volume treatise on harmony, called Institutione harmonische). CPE’s book is about musical emotions and the task of a performer. As such—a rare topic, preceded, perhaps, only by Tinctoris’s Compendium. As for CPE’s recommendations concerning voice leading, I would not recommend any sane composer to follow them. His contemporaries had the reason to doubt his sanity precisely because his harmonic progressions in Fantasias and Rondos did not carry syntactic unity. 
J.S. Bach was the first composer to fully realize tonal-harmonic function and functional syntax in music. I can write another email about that.
K6/4 is a smaller fish, comparing to these issues.
Ildar Khannanov
Peabody Conservatory
Solfeggio7 at yahoo.com

From: Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>
To: smt-talk <smt-talk at societymusictheory.org> 
Sent: Sunday, February 12, 2012 1:44 PM
Subject: Re: [Smt-talk] Abbreviated Labels of Seventh Chords

It occurred to me also that some of Catel's notation can be found in CPE Bach – with important differences, though. CPE's 4+ is a 4 with an extended horizontal line and a stripe crossing it. Catel writes +4, or even such combinations as +/2 (meaning +4/2) or +/4/3 (obviously for +6/4/3). Both CPE and Catel use 2 alone to refer to the third inversion of a seventh which is not a dominant. For the diminished 5th, CPE writes 5b; barred figures for him usually indicate raised intervals and his 4+ may be a mere barred (i.e. raised) 4. (On the other hand my cursory glance through the Versuch did not allow me to find a barred 5). For Catel, on the other hand, a barred figure is a diminished interval.
    I believe that Catel's intention was to specifically indicate one or the other note of the augmented 4th/diminished 5th characteristic of the dominant, by either a + or a barred 5. This was never stated, that I know, neither by him nor by his followers; but the Paris Conservatoire makes such a point to distinguish the "natural" (dominant) seventh from any other ("septièmes d'espèce") that the intention, conscious or not, seems unescapable.

Writing harmony in open score and C clefs (more precisely, chiavi naturali) was standard practice in the Conservatoire. We still did that in the Brussels Conservatoire during my studies (hum! some time ago...), working the basses and sopranos given at late-19th-century final exams in the Paris Conservatoire. For us, at least, voice-leading considerations were indeed paramount, but boiled down to avoiding parallel or "hidden" fifths and octaves. There was no question of melodic fluency (on the contrary: the exercises often requested tricky voice movements). We did try imitations (which the exercises often made possible). I always had the feeling that our classes were not in harmony, but in some kind of free tonal counterpoint, a counterpoint that reduced to avoiding parallels (one never spoke of good or bad successions of chords, my teacher and most of my colleagues students new nothing of harmonic functions, nor even of Roman numerals).

Nadia Boulanger's teaching of harmony does not seem very different from that. I presume that she was able to turn to musical advantage what in our case sounded musical nonsense. What we did had no style at all, and was not meant to; but it did more than earning us the right to be free, it also shew us how to be free and really gave us a facility of writing. A lot is done today in the Conservatoire to learn writing "in the style of", to write pastiches "à la Fauré", "à la Debussy", "à la Messiaen", etc. This may give the students the (false) impression of writing "real" music, but certainly does not help understanding what the Masters did (one does not write "à la Beethoven", that I know: it would be too difficult).

Nicolas Meeùs
Université Paris-Sorbonne

Le 11/02/2012 16:32, Donna Doyle a écrit : 
As a former Boulanger student, overloaded these days with teaching, I nevertheless make stabs at completing my dissertation 
>on Boulanger's methods and their tradition. All the materials I have that are associated with her (incl basses and figures I copied from her sheets and my realizations approved by her), show the Conservatoire's figured bass tradition, e. g., 4+, without the 2, 
>for V4/2. I believe this notation comes not only from Catel, as you point out, Nicholas, but from CPE.  As Phil Duker offered, 
>CPE lists several figures for this disposition (p 252). Indeed, on p 260 CPE reminds readers that 4+ is an abbreviated 6/4/2.  
>NB also used 7 over + for V7, 6 over barred 5 for 6/5 and only +6 for 4/3. The leading-tone chord was considered a 
>"dominant FO" (fundamental omitted). She used few romans. Voice-leading was paramount. She insisted on 
>realizations written in open score, C clefs, and played for her. (And the performance had better be musical or she 
>would jump in her chair. ["But, my dear!  Zhe poor tenor!"]) She delighted in various realizations, especially those 
>employing imitation and little canons between the voices--techniques of her oral tradition. And, of course, 
>this was done in conjunction with intense ear training, enabling us to see what we hear and hear what we see.
>For Boulanger, as with CPE, bass realization was an aspect of Accompaniment. It seems to me that our insistence on elegantly 
>logical numbering systems is defying the rich, sometimes messy nature of this once vibrant practice. Apart from Schenkerian analysis, figured bass is a chord-labeling shadow of its former self.  Let's restore its life! (Perhaps not for undergraduates, 
>but in graduate curricula, for composers, theorists, organists, maybe also pianists and conductors.) As NB said, "It's not 
>that you're going to write in this style. But after working with it, you'll have earned the right to be free." Isn't this what composers/theorists/performers used to do? I find it remarkable that NB, despite being called "French provincial," 
>continued to transmit this tradition into the 1970s.
>Donna Doyle
>Queens College CUNY
>On Feb 9, 2012, at 3:40 AM, Nicolas Meeùs wrote:
>The French tradition, that of the Paris Conservatoire, is to write +4 in this case, the + meaning that the 4 is the leading tone (similarly, one would write +6 in second inversion). This tradition, which is not mine and against which I am trying to fight in Paris, has several drawbacks, one of them being that the French use labels that hardly anyone else understands.
>>    I wondered about the origin of this figuring, without performing a thorough research. It certainly goes back to Catel's treatise, and perhaps earlier. The + sign is in origin merely a stylized #. Catel makes use of it (and of the barred 5) with the specific (although unstated) intention of specially labeling dominant seventh chords, the ones that he considers "natural", all positions of which always have either a + or a barred 5 (from fundamental position to third inversion: +3; 6/5barred; +6, +4; this is tricky, because 4/3 becomes +6, 2 or 4/2 becomes +4). Applied dominants are labeled in the same way, with the other perverse effect that French students see modulations everywhere (as the French did since François Campion in 1716: tout diese extraordinaire fait sortir du ton, "any accidental sharp leads outside the tonality").
>>    Labeling third-inversion dominants as V4/2 may result from an attempt to reconcile the two systems. In this respect, I'd be pleased to know how Nadia Boulanger labeled chords, if anyone on this list knows (it has been discussed here some time ago that her teaching of harmony followed the tradition of the Conservatoire, but her ciphering was not specifically discussed, that I remember).
>>My own view about the labeling of seventh chords is that it should indicate the dissonant interval: (8)/7, 6/5, 4/3, 2/(0), the 8 and 0 being omitted as redundant with the written bass, of course; this is what Dimitar describes, with a slightly different explanation. The main difference with the French system is that it does not specifically indicate dominant sevenths, which may be viewed (by the French) as a shortcoming, or (by the others) as an advantage.
>>Nicolas Meeùs
>>Université Paris-Sorbonne
>>Le 9/02/2012 04:50, Ninov, Dimitar N a écrit : 
>>Dear Colleagues,

My students were asking me why I wrote V2 instead of V4/2. I guess I had to ask them why they wrote V4/2 instead of V2. This is not a big deal, of course, but I wanted to bring to your attention the fact that number 4 is irrelevant to the logic of derivation of the abbreviated labels of seventh chords. 

The abbreviated labels are derived by two intervals: 1) the interval between the bass and the root on the one hand, and 2) the interval between the bass and the seventh on the other. Thus in root position the only number is 7, because the interval between the bass and the root is unison; in first inversion we have 6-5; in second inversion 4-3, and in third inversion the only number is 2, because the interval between the bass and the seventh is unison. 

Why 4? It shows the interval between the bass and the third of the seventh chord, which does not have to be shown unless we work in minor and use only figured bass with no Roman

When I flip through the pages of some European and older American books of harmony (as well as some relatively new) the above explanation is provided. Author such as Piston, Tischler, Schoenberg, Horvitt, Cook, and all Russian theorists use 2 instead of 4/2, but the massive tendency in the US is to write 4-2. Is this tradition based on ignoring the logic of derivation, or is there something special that stands behind this label? 

I would appreciate any ideas in this regard.

Best wishes,


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