[Smt-talk] Abbreviated Lables of Seventh Chords and Labeling of Functions

[Bruce Grant]

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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