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<font size="-1"><font face="Georgia">Dear Ildar,<br>
<br>
I am very much willing to discuss the pros and cons of approaches to
harmonic function, but if you decide a priori which is good and which
is bad, you leave very little space for discussion.<br>
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You wrote :
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<div>This may lead to some dangerous pedagogical innovations,
such as the idea that ii and II function the same way before V. I have
heard this from some other teachers of harmony. </div>
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<small><font face="Georgia">I think neither that this is a pedagogical
innovation, nor that it is particularly dangerous. The matter has been
in discussion since almost three centuries now. Rameau, for instance,
appears to have favored the idea that ii and II do function similarly
before V, as many a Viennese theorist did (including Schenker), while
Riemann considered that ii was a subdominant, II a secundary dominant.
Your own formation obviously is Riemannian.<br>
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<div>Sii is subdominant. Before V it functions as a part of
non-modulating progression, in the key. The DD before V functions as a
sign for us to leave the key, as a pointer to a possible modulation
into the sphere outside. In this case the fact that the two chords are
situated on the same scale step does not make them mutually
replaceable. What is extremely important is that they belong to
different functions. That is why I mentioned earlier that function is
function because it is function.</div>
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<small><font face="Georgia">This, indeed, is the point of view of
Riemann, as are the signs you are using. It must be stressed that the
question arises for no other degree than ii/II : this is not merely a
case among many, it is the most vexing problem of what our American
colleagues very elegantly came to dub the "predominant", the chord(s)
of dominant preparation. Once again, this has been under discussion
since almost three centuries and I certainly would not dare decide who
is right and who is wrong.<br>
The problem is not that simple, anyway, and if you consider it from
a pedagogical point of view, then the "right" answer may depend on the
context in which you teach. We, in Paris, do teach that ii and II
before V behave in the same way, and we consider it dangerous to teach
otherwise. This is because of a particularly French context, where our
students have been taught in their Conservatoire that any accidental
creates a modulation. This too is the result of a three-century old
tradition: François Campion (the theorist of the Règle de l'octave)
claimed already in 1716 that "tout dièse extraordinaire fait sortir du
ton" ("any accidental sharp induces a change of key"). Schenker derided
this French tradition. The French, he said, are like blind people: they
guide themselves by sliding the hand along the wall, of which they feel
each asperity.<br>
As to Riemann's theory, a problem that has been noted about a
century ago (e.g. by August Halm) is the difficulty to explain how one
passes from subdominant to dominant, conceptually extremely distant
functions. Riemann himself had problems with that (which led him to
suggest, in his early writings, that there should be a T – represented
by V<sup>6</sup><sub>4</sub> – between S and D; he later abandonned
this idea).<br>
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<div><small> </small></div>
<div> Scale steps by themself are not functions yet. There is a
mysterious cognitive mechanism (which, I hope, will be studied one day
by Carol and Fred) behind functions. It is not merely psychological or
culturally predetermined. It is psycho-somatic, because many listeners
perceive Dominant the same way (and this is a secret advantage of
"common practice music" before the "20th-century music"). The cognitive
mechanism which is responsible for Dominant may choose certain scale
stepts to represent the Dominant.</div>
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<small><font face="Georgia">Stating this, you merely take a personal
position in the century long opposition between scale step theory
(Simon Sechter) and function theory (Hugo Riemann). As my own theory is
different from those two, I do not need to take a position.<br>
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<div> How about this theorem of Dominant:</div>
<div> Dominant is function, i.e. relationship* as such</div>
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<small><font face="Georgia">And you add the corollary that
"relationship is the basic organizational principle of function; it
cannot be visualized or reduced to concatenation of scale steps".<br>
If you want. But tell me then what is "subdominant", or "tonic": are
they also "relationship as such"?<br>
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<div> Dominant is commonly represented by scale step five
in the context of both major and minor tonality*</div>
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<small><font face="Georgia">Add you add that "tonality is not the
diatonic collection of pitch classes". I fully agree on both
statements. <br>
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<div> Dominant must be a major triad <br>
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<small><font face="Georgia">I do not think so myself, but I am
perfectly aware that many important and respectable theorists
(Schoenberg) were of this opinion. <br>
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<div> tonality is the set of relationships, for which the seven
scale steps play the same role as the acustic basic scale plays for the
set of modes.</div>
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<small><font face="Georgia">As I have no idea of the role played by the
"acustic basic scale" for the "set of modes", I cannot comment on this.<br>
<br>
**********<br>
<br>
The matter of tonal function is sufficiently complex to allow for
various theories, each of which stresses or enlightens specific aspects
of the whole. I don't think that any of the available theories exhausts
the problems.<br>
<br>
Yours,<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>
<a class="moz-txt-link-freetext" href="http://www.plm.paris-sorbonne.fr">http://www.plm.paris-sorbonne.fr</a><br>
<br>
<br>
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