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<font size="-1"><font face="Georgia">Schenker's idea of *Züge* (lines)
is based on the fact that any note filling the 'tonal space' delimited
by a triad (see his *Erläuterungen* in the two last volumes of
*Tonwille* and the two first of *Meisterwerk*) necessarily is conjunct
to at least one of the tones of the triad.<br>
<br>
The present thread is about II-IV (or II-iv) progressions. Isn't it
obvious that the main characteristic of these progressions is the
chromatic semitone between the 3rd of II and the prime of IV or iv?
Even if these two notes are not in the same contrapuntal part, even if
they do not belong in the same register, the mind somehow links them to
each other and understands them as forming a single chromatic pc-line
at some higher level. <br>
<br>
Similarly, in a V-I or V-i progressions, there necessarily is a
diatonic semitone between the 3rd of V and the prime of I or i, at
least at the level of pc-leading, and this is, in my opinion, one of
the main reasons why we identify these chords as evidencing a
Dominant-Tonic relation. I would be tempted to say that all harmonic
functions arise from such pc-leading relations (see
<a class="moz-txt-link-freetext" href="http://www.plm.paris-sorbonne.fr/Textes/NMTransitivite.pdf">http://www.plm.paris-sorbonne.fr/Textes/NMTransitivite.pdf</a>).<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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JAY RAHN a écrit :
<blockquote cite="mid:435796.90023.qm@web88103.mail.re2.yahoo.com"
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<div>Although I have not been following this thread closely, I very
much like Nicolas's notion of pc-leading. With pc-leading as a sort of
baseline, one can go on to acknowledge degrees and kinds of salience
for successions from tone to tone: e.g., registral, metrical, rhythmic,
timbral, dynamic, or sonorous (i.e., with regard to simultaneities).<br>
<br>
As well, I had not noticed until my recent work with Mesopotamian music
that in a heptatonic setting, any immediate succession of 3rds/6ths
and/or 4ths/5ths involves at least one of the two tones in each dyad
proceeding by unison or step: <br>
e.g., CE to or from DF, EG, FA, GB, AC, or BD;<br>
CF to or from DG, EA, FB, GC, AD, or BE;<br>
CE to or from DG, EA, FB, GC, AD, or BE.<br>
<br>
Accordingly, in heptatonic music there is always at least one 'pc-path'
or (or more precisely, dc-path, i.e., degree-class path) of unisons and
steps through the immediately successive of 3rds/6ths and 4ths/5ths.
(In pentatonic music, there is always a 'dc-path' through the
immediately successive 4ths/5ths, or more precisely, 3rds/4ths). How
salient such paths might be is another matter.<br>
<br>
Jay Rahn, York University (Toronto)<br>
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