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<font size="-1"><font face="Georgia">Do you realize that one problem
with this thread is that it is, in one way or the other, in search of
the <u>truth</u>, as if such a thing could exist?...<br>
<br>
To start with, your way of notating 6/4 chords begs for the answer.
Trying to follow this discussion, I spend way too much time counting on
my fingers in (at times vain) attempts to understand what was meant,
say, by ii6/4 or V6/4 – or, worst of all, I6/4. This last figure is, I
think (and I hope), forbidden in all classes in my university, where we
teach that a I chord can (almost) never occur in 6/4 position – or
else, that anything that might seem to call for a I6/4 ciphering
actually is something else, a double appoggiatura in most cases.<br>
I personally teach that it is almost impossible that any harmonic
degree would ever be presented as a triad in second inversion, unless
by some kind of analogy, and that such an apparent inversion usually
must be discussed in terms of voice leading (I teach analysis, not
tonal writing). Doing so soon evidences that the same apparent 6/4 (I
mean, the same degree in 6/4 position) could result from a variety of
situations: this is one reason why Dmitri's statistics is questionable:
it apparently assumes that all 6/4 can be identified and classified as
second inversions, and so doing forms categories from things that
cannot be compared.<br>
<br>
Schenker spent some time, especially in <i>Der Tonwille</i>,
describing what he dubbed <i>Quintteiler</i> – either as <i>Überquint-
</i>or <i>Unterquintteiler. <br>
</i>The divider at the lower fifth (a notion that Schenker soon
abandoned) is the true neighbouring 6/4, i.e. 5/3–6/4–5/3 above a
standing bass (or, at least, above a standing root: the prolonged
degree may pass from root position to first inversion, or the reverse).
The very notion of the <i>Unterquintteiler</i> makes the hypothesis
that a 5/3–6/4–5/3 voice leading and a <i>x</i>–<i>(x</i>+4)–<i>x</i>
bass progression are to some extent equivalent.<small></small><br>
The divider at the upper fifth is in origin a case where the bass
arpegiates 1-5-1 without change in the other voices (resulting in an
apparent central 6/4); neighbour notes in the upper voices would result
in an apparent <i>x</i>–(<i>x</i>+5)–<i>x</i> </font></font><font
size="-1"><font face="Georgia">progression </font></font><font
size="-1"><font face="Georgia">which forms the true <i>Quintteiler</i>.
The fundamental bass arpegiation itself, at the deepest level, is of
this kind.<br>
<br>
The "passing" 6/4 is, in my opinion, a situation where the bass passes
under basically standing upper voices, leading from a root position to
a first inversion, or the reverse. I see no essential difference, say,
between I–(V6/4)–I6 and I–(vii°6)–I6: this is prolonged I–– in both
cases.<small></small> And if the choice between V6/4 and vii°6 defines
a style, it merely proves that style is a matter of surface (which is
well known).<br>
<br>
Dmitri is right when he states that a correct imitation of, say,
Mozart's style requires keeping to the statistics of this style. The
problem, inherent in statistics itself, is that (a) none of Mozart's
individual works exactly conforms to the overall statistics; (b) it is
hard to say whether the student should match the statistics in each
individual exercize, or in his overall production; (c) it remains that
the student should be able to correctly write the exceptions, as rare
as they may be in a given style.<br>
<br>
With my apologies for once again arousing this moribund thread. Keep in
mind that half the humanity is under the average...<br>
<br>
Yours,<br>
<br>
Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<br>
<br>
<br>
<br>
<br>
<br>
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