[Smt-talk] Harmonic Functions

Tue Feb 14 05:50:48 PST 2012

Dear Bruce,

That was very informative - thank you! I only have two things to add. 

Regarding the terms parallel versus relative, I must tell you that in Europe most countries use "parallel" for what you refer to as "relative". It is just like the term "phrase" as you understand it and as some other theoretical schools (including Schoenberg's) understand it: we simply put a different content, and it has stuck in this manner. Nobody is wrong, we simply must take this into account when we write papers and deliver lectures abroad.

As for the letters or Roman numerals. I am in favor of a great simplicity - as great as it can become. For me, terms such as TRm or SMSM are visually too complicated and unattractive, and I can bet they will not be in circulation in most musical circles. In addition, these functions refer not to the tonal center, but to some other local centers, something that I do not agree with. 

I have ideas about expressing all the chromatic chords (mostly triads) in an extended tonality. I will use only Roman numerals. As for the SMSM, for example the chord F# in C major, I explain it as a chord borrowed from the Locrian mode (in C Locrian, the purely diatonic triad on flat 5 will be Gb). Its minor version (F#m) I explain as a variant of flat V (or sharp IV if you will - it does not matter) While some theorists (perhaps Shoenberg too) prefer a path that is based on extended tertian relationship between chords, i.e evry chord has its mediants, etc.

In his Structural functions of Harmony, Schoenberg in my view starts very simply, and then piles up harmonic labels to the point of anybody's confusion. It is not hard to understand what he means; it is hard to keep it constantly in mind and to use it on a daily basis.

Thank you  for now, but I hope we will continue to extend ideas!

Best regards,

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________________
From: Bruce Grant [bruce.grant at wanadoo.fr]
Sent: Monday, February 13, 2012 11:18 PM
To: smt-talk at lists.societymusictheory.org
Cc: Ninov, Dimitar N
Subject: RE: [Smt-talk] Abbreviated Lables of Seventh Chords and Labeling of    Functions

Dear Dimitar,

Thank you for the sympathetic answer to my posting on chord symbols. My system is in fact a synthesis of Riemann and Schönberg. It is unfortunate that Riemann's reduction of tonal functions to the three primary relationships is spoiled by his fascination avec the "undertone" series, which doesn't exist in nature, even if the minor triad happens to be the inversion of the major triad in equal temperament. Also the English translation of Harmony Simplified, or the Theory of the Tonal Functions of Chords (U.M.I. 2001, Vereinfachte Harmonielehre, oder die Lehre von den tonalen Funktionen der Akkorde",1893) uses the term "parallel" for the relative scales of major and minor and modern usage uses parallel for different modes of the same tonic.

Schönberg uses "M" like you as well as T, D, S but his "Chart of the Regions" (Structural functions of Harmony, page 20) gets pretty complicated when it gets to SMsm or bmvsm! So rather than using mediants, I prefer Riemann's DRm and TRm for the mediant and submediant in major, and TRM and SRM in minor, because the mediants in the extended tonality made possible by parallel modes don't have the same function. If the Rm or RM chords are altered I add a lower case "a" unless an A major chord in C is DSRm, for example. I also use "subdominant of", for example, Bb minor+6 in C can be Sm6S.

Apparently, Schönberg didn't notice that "SMSM", the submediant of the submediant, and bmM, the minor mediant of the minor mediant are enharmonically the same in equal temperament. F# and Gb are the relative minor of the relative minor and relative major of the relative major in C. A circle is therefore formed by chords of the same function as in color theory where the primary and secondary colors form a circle instead of the straight line of the spectrum from red to violet when magenta is produced. So I call the tritone relation the complement, TC, DC and SC, major or minor, by analogy with colors, magenta being the complement of green for example. To make a synthesis with another theorist, Hindemith, his "Series 1" of the twelve chromatic steps would be T, D, S, TRm, DRm, TRM, SRM, SRm, DRM, DC, SC, and TC. The three functions multiplied by the circle of four minor mediants give major or minor triads on all twelve notes of the chromatic scale.

I don't believe it's possible to be simple when dealing with extended tonality. My system is simpler than Schönberg's, or at least uses fewer letters, and the double mediants are combined. For diatonic music, roman numerals are very practical as are your M and SM, since one learns rapidly that SM is the TRm and M the DRm. However sharps and flats added to roman numerals use a lot of letters too, like bVIIm. DRMa uses only four letters instead of five!

I avoid lower case numerals also, and agree that indicating inversions is irrelevant in analyzing root progressions. But I think indicating T/5 >D7 as I proposed in my last posting is pretty clear for T6/4>D7 or V6-5/4-3. I discuss these questions in more detail (in French, since I work in France) on my website,

http://bruce.grant.pagesperso-orange.fr/8.%20complementaires.pdf

It might be interesting for Dr Meeus, Mme Poudrier, and the other francophones out there!

Bruce

Bruce Grant, DM, Indiana University

Chef d’orchestre et chef des chœurs,

Théâtre de l’opérette de Lyon, France

-----Message d'origine-----
De : smt-talk-bounces at lists.societymusictheory.org [mailto:smt-talk-bounces at lists.societymusictheory.org] De la part de Ninov, Dimitar N
Envoyé : dimanche 12 février 2012 01:58
À : smt-talk at lists.societymusictheory.org
Objet : [Smt-talk] Abbreviated Lables of Seventh Chords and Labeling of Functions

Dear Bruce,

https://synergy.txstate.edu/owa/?ae=Item&t=IPM.Note&a=New#

I am pleasantly surprised that you occasionally embark on Riemann's letter such as T, S, and D. These are great for generalizing if we teach American students that are used to Roman numerals only, but they could also be specific if we want to use them instead of Roman Numerals.

I find your system a little more complicated, however. But I think that it was Riemann who made is so complicated, by introducing Trm, etc. - ambiguous sybmols that reveal the mediant functions. I have been experimenting with symbols for teaching purposes, and with symbols for my own harmonization and analysis purposes, and tight now I am in favor of simplifying things as much as I can. For instance, from time to time I use the Schonbergian system (capital Roman numerals only) with no inversion symbols, as used in his "Structural Functions of Harmony". The dash across the letter would mean either a borrowed chord or a genuine altered chord. For instance, the progression I - #iio7-I6-IV-viio/V-V would be labeled by Schoenberg as: I-II (with a scratch)-I-IV-IV (with a scratch) and V. Of course, without seeing the music this could be a problem, because no specifics are provided, but when you analyze complicated things visually, this provides the freedom to think generally and to

  avoid the usual clutter.

Otherwise, I also use T, S and D, but I also introduce a two more functions: M (for both mediant and submediant, or you can use M and SM, if preferred), and K or Cad. (for cadential six-four, which for me is not V with two non-chord tones; I already submitted a thread with a treatise on that) Thus we have:

T (I)

S (IV)

D (V)

M (III)

SM (VI)

K (or Cad.) for the cadential 6/4

As for the II and the seventh chord, I could either mark them as SII (subdominant on the second scale degree) and DVII (dominant on the seventh scale degree), or place them under the umbrella of a general S and generalr D, respectively. Depends on whether I want to be specific or general.

Thus I acquire clear and uniform labeling system, which could also be used with inversion symbols from the figured bass as necessary. For the secondary dominants and subdominants (we should not not forget that there is also IV of...and II of...which could also be altered on top of that, for example CTo7/III, etc.) I use D of or S of such as in D/D (dominant of the dominant) or D/S (dominant of the subdominant). However, D/SM (dominant of the submediant) could have an alternative label such as D/VI.

For minor mode I use the same capital letters above; the size of the chords being suggested by the key signature and by different alterations if any. However, if a chord is borrowed from major minor to major, for instance, I would write -S or -D, for example.

There are various ways of using letters and symbols, and I am in a process of looking for a simple system that allows me to analyze chromatic and modulating passages without using so many symbols that make the labels clumsy and unattractive.

Best regards,

Dimitar

Dr. Dimitar Ninov, Lecturer

School of Music

Texas State University

601 University Drive

San Marcos, Texas 78666

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