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<font size="-1"><font face="Georgia">Dear Ildar,</font></font><br>
<br>
You wrote:<br>
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<div>I am glad that we can discuss this important topic on the
list. </div>
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Well, I am afraid the topic migth soon become boring for many readers
of the list, because it has been overdiscussed here and elsewhere...
Let's go on for a while.<br>
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<div>Yes, I have certain 'formation" and cannot complain about
it. I agree with you that the question of supertonic, its function, is
not a simple one.. German theorists are still leaning toward the
Funktionstheorie. From my conversation with Dr. Ludwig Holtmeier in
Freiburg I have learned that he did not mind the "Es Zwei" as he called
it at all. SII seems to be redundant, but it clearly states that scale
step 2 has the function of Subdominant. This is not clear from Roman
Numerals alone. For example, V is just a cadinal number, which means
five objects, five eggs, five cars, etc. It can be interpreted as
an ordinal number (the fifth in the row), but then it also does not
tell anything about being the Dominant.</div>
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You should be aware that writing Roman numerals is a much older
tradition than assigning functions; the Roman numerals date from Georg
Joseph Vogler's <i>Handbuch</i> <i>der Hamonielehre</i> of 1802. As
Robert Wason (<i>Viennese Harmonic Theory</i>) noted, Vogler seems
preoccupied with the description of "chord identity", i.e. with
something that resembles functions. There has been much discussion
whether a theory based on Roman numerals could be considered a theory
of seven functions – in contradistinction with the German (Riemannian)
theory which envisages only three. There is abundant literature on the
subject. You argue that V is just a cardinal number; one could as
easily object that "dominant" is but a name and says nothing of what a
dominant really is... In origin, the name "dominant" denoted something
different (roughly speaking, the principal note of a modal melody); it
is only because that note often was the fifth degree that the name came
to denote the function of the fifth degree...<br>
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<div>I really liked your quote from Campion. If you do not
mind, I will use it in my classes at Peabody. Indeed, if my students in
Ear Training will learn how to discern the local leading tones in a
four-part texture, to hear the leading tone in any of the inner voices,
this will guarantee that they will understand digressions and
modulations by ear. <br>
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Well, don't use my quote, because it is not to be found as such in
Campion – I cannot figure out today where I found it (and I cannot
check it right now). It corresponds to what Campion says, but he never
says so in these terms. For Campion's writings, see
<a class="moz-txt-link-freetext" href="http://www.chmtl.indiana.edu/tfm/18th/18th_Index.html">http://www.chmtl.indiana.edu/tfm/18th/18th_Index.html</a>. And note that
Campion calls "octave" what we'd call "tonality" or "key".<br>
I am not sure that it is (always) a good idea to hear each new
leading tone as the token of a new key, as so doing one misses the
tonal unity of the piece.<br>
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<div> </div>
<div>I am not surprised that Schenker has derided the French
tradition. He seems to deride everything and everybody around. </div>
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No, Schenker's opinion about the French is quite particular, dictated
both by his ideas on World War I and the downfall of the
Austro-Hungarian and Russian Empires, and by his opinion about Rameau's
theories.<br>
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<div>Schenker has derided Simon Sechter as well. In
Kontrapunkt, book 1, he mentions the name of Sechter in passing,
without even providing his first name, as follows: "One need only
compare Sechter's work, for instance, with my own to recognize that the
practical artistic purpose of generating and increasing content is
better served by the psychology of scale degree progressions as I
present it, and that my theory presents viewspoints on issues of
chromaticism and alterations which are far more pure, unified and
compelling." (p. xxxi of the Author's Preface). That is pretty much
all Schenker had to say about Sechter. I could not find any more
references to Sechter in Freie Satz, Harmonielehre and Kontrpunkt. I
also remember reading another footnote, in which Schenker expresses his
anger at the teachers at the Vienna conservatory.</div>
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1) We do speak of Riemann (or Schenker) without their first name –
which may be our way to pay tribute to their fame. In the case of
Riemann, we should do better to give the first name, however, because
there exists another Riemann, the mathematician, Bernhardt Riemann,
from the theories of which evolved a mathematical theory of ...
harmonic functions! These have nothing to do with Hugo's functions, nor
with music!!!<br>
2) If you read Simon Sechter's <i>Grundsätze</i>, you'd probably agree
that Schenker's presentation is better – even if, as a matter of fact,
Schenker probably never developed in writing the functional aspect of
his own view of the theory of scale degrees; I'll leave that for
another discussion. The true theoretical content of the <i>Grundsätze</i>
is limited, even if it proved extremely influential, because the book
is mainly practical in its aims.<br>
3) Schenker knew Sechter's theories mainly through Bruckner, the
teacher about which he wrote the footnote that you have in mind.
Schenker may not often have quoted Sechter, but his theories evidence
how deeply influenced he was by Sechter...<br>
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<div>Simon Sechter does not belong to the same category as
Riemann or Rameau. His achievements in music theory are much more
modest. One book (in three volumes) and few smaller texts and a couple
of compositions. Nothing to compare with the output of Riemann. I
teach at the oldest conservatory in the United States. Our library is
filled with books of Riemann, Reameau and Marx. I could not find
Sechter. And many other libraries in the country carry stacks of
Riemann. After all, if not for him and Guido Adler, we would not have
our precious jobs at the Universities. So, maybe "scale step theory"
exists only in the minds of its followers?</div>
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Well, perhaps, but his followers include Bruckner, Schoenberg, Sechter,
and most of the American theorists. Sechter's fame in his own time was
extremely high, he was considered the best music teacher in Vienna;
Schubert chose to study with him. I don't know the particulars of the
publication of Sechter's <i>Grundsätze</i>; the book is extremely
difficult to find in Europe as well. Certainly, the commercial
conditions for the publication of such a work were not the same in the
mid-19th-century as what they became 20 or 30 years later, when Riemann
published his treatises.<br>
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<div>As for the conceptual difficulty of connecting S and D, it
is ultimately exagerrated. Has it become less difficult conceptually to
connect these sonorities after the S has been renamed into Predominant?
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The difficulty is not of connecting S and D, but of theorizing about
it. By viewing them as the extremes (<i>Dominante </i>and <i>Gegendominante</i>)
on an axis of which the tonic is the center, as "thesis" and
"antithesis", Riemann (and other German theorists of the same
tradition) certainly don't make things easy. The name "Predominant" is
useful pedagogically because it takes no specific position in this
debate, assuming merely that in order for the dominant to be truly
functional, something specific must prepare it, different both from the
tonic and from the dominant.<br>
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<div>As for tension/relaxation and mysterious cognitive
mechanism behind functions, your placement of this statement between
"scale step theory of Sechter" and tonal functional theory of Riemann
will be more fun to deal with if you accept that such mechanism has
been described by....Schenker in his Harmonielehre. He writes there
about the "biological urge" of dissonant chords to resolve. </div>
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Schenker has a specific position in this matter, as he does not admit
dissonant chords as such: for him, any dissonance is a contrapuntal
device that must resolve contrapuntally. Resolution of dissonances may
not necessarily be the same thing as tonal tension/relaxation – or
"attraction". The leading tone, in particular, is not a dissonance in
the ordinary sense. I don't think it necessary to accept all of
Schenker's metaphors ("biological urge") to acknowledge that Schenker
is an exceptional musician and theorist (in that order!). My own claim,
to which I stand, is that ideas of tension/relaxation (or attraction,
or obligato resolution) always are cultural constructions. They have no
permanent acoustic fundation. In other words, even although I recognize
that the idea of tension/relaxation may exist in many musical cultures,
I cannot believe that the phenomenon always is based on the same
premises. The idea as it may have existed in Greek antiquity has little
if anything to do with the similar idea in the frame of tonal, harmonic
music.<br>
<br>
Yours friendly,<br>
<br>
Nicolas Meeùs<br>
<a class="moz-txt-link-abbreviated" href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
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