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Ildar,<br>
<br>
While I fully agree with you that detecting sets and collections of
pitches is a Western concern, I believe it to be older than you
think. In the case of Arabic music, the Western musicians present at
the Cairo Congress of 1932 advocated a conception of the Arabic
system as formed of 24 quarter tones, against all evidence as we can
see it today, and this had the most nefarious influence on Arabic
theory itself.<br>
<br>
We should realize, I believe, that even in Occidental music, even if
we think it based on an underlying dodecaphonic system, it would be
more reasonable to view tonalities as founded on heptatonic scales,
of which the 3d degree determines the major or minor character (but
with the possibility of passing from the one to the other as a
result of a possible mobility of this degree), with the mobility of
the 7th or the 4th degree possibly (but not necessarily) opening
paths to modulations by a fourth or a fifth (flatwards or
sharpwards), and the mobility of other degrees (mainly the 6th and
to a lesser extent the 2d) opening paths to other, more remote
regions.<br>
<br>
To view the mobility of these degrees as changes of scales (from
major to Mixolydian or Lydian, from 'natural' minor to 'harmonic' or
'melodic', etc.) seems to me quite unmusical. Our note names, be
they letters or solmization syllables, count only seven degrees in
the octave, with additional signs to denote the mobility; and our
keyboards show 7 white keys in the octave, with black keys for the
mobility. Pitch class set theory replaced these with 12 numerals in
the octave, or tried to, but may not have been so successful for
describing our music of the past.<br>
<br>
I can follow your description of Rimsky's gradual modulation through
pivot chords (e.g. the minor subdominant), and I would easily agree
with it. The question, however, is whether he understood such shifts
as resulting from scale shifts, say from 'natural' (or 'diatonic')
major to 'harmonic' major, which would seem to me an unduly complex
description, so much more complex than explaining that the
subdominant can become minor as a result of the mobility of the 6th
degree. You certainly know Rimsky better than any of us, and I'd be
eager to know how he conceived this.<br>
<br>
Nicolas Meeùs<br>
University Paris-Sorbonne<br>
<br>
(PS. While you certainly know Rimsky better than any of us, you
should refrain from statements about Schenker based on a superficial
knowledge... There is much more in Schenker than Oster's <i>Free
Composition</i>.)<br>
<br>
<br>
<br>
<div class="moz-cite-prefix">Le 2013-11-29 09:30, Ildar Khannanov a
écrit :<br>
</div>
<blockquote
cite="mid:1385735418.80846.YahooMailNeo@web125305.mail.ne1.yahoo.com"
type="cite">
<div style="color:#000; background-color:#fff;
font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial,
Lucida Grande, sans-serif;font-size:12pt">
<div><span>Dear List,</span></div>
<div><span><br>
</span></div>
<div><span>I can add to Dimitar's post that harmonic major
played a significant role in Rimsky-Korsakov's and, further,
in Russian views of harmony not only as a pitch collection,
but as a means to other goals. In general, it is only after
WWII the theory of music in the West has focused on
detecting various sets and collections of note heads. This
has become a favorite pastime of theorists with mathematical
background. It is important to remember that theorists of
the 19th century were composers working in the domain of
real tonal music. For them, the categories of theme, motive,
classical forms, tonal-harmonic function and, ultimately,
modulation (all of which has been carelessly discarded by
Schenker) have been the tools of the trade.
Rimsky-Korsakov's inclusion of harmonic major was a result
of his work on theory of modulation. In his concept of
degrees of kinship of keys the modulations to keys that
differ in 3-5 signs in a key signature present the most
difficult tasks. Still, he and Tchaikovsky suggest that in
the large-scale form modulation should unfold slowly,
step-by-step. In the so-called gradual modulation the remote
key should be reached as a result of simple pivot chord
modulations (or sequences). The use of a minor subdominant
provides a shortcut when one modulates towards the flatted
keys. That is why Rimsky-Korsakov included the minor
subdominant into the list of closely related keys in major.
Hence the harmonic major.</span></div>
<div><span><br>
</span></div>
<div><span>Best wishes,</span></div>
<div><span><br>
</span></div>
<div><span><br>
</span></div>
<div><span>Dr. Ildar D. Khannanov</span></div>
<div><span>Peabody Institute</span></div>
<div><span><a moz-do-not-send="true"
href="mailto:solfeggio7@yahoo.com">solfeggio7@yahoo.com</a></span></div>
<br>
</div>
</blockquote>
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