<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">If we assume a directional markedness in the pitch height dimension (e.g. downwards being unmarked) we might assume an analogous markedness along the line of fifths (e.g. flatward being unmarked). Such an assumption implies an interesting question: How do the two kinds of markedness interrelate? Jacques Handschin argues in favor of an affinity between ascending pitch height and sharpward oriented fifths. That same type of affinity would then hold between descending pitch and flatward oriented fifths. This affinity is contrapuntally supported by the ultimate progression between tenor and bass in the cadence (as well as in the Ursatz). But for modal tone relations Handschin's assumption might nevertheless be wrong. There are good mathematical reasons to postulate that the combination between ascending pitch and flatward oriented fifths is the unmarked one.<div>Sincerely</div><div>Thomas Noll <br><div><br class="Apple-interchange-newline"><blockquote type="cite"><div bgcolor="#FFFFFF" text="#000000">
<font face="Calibri">Curt Sachs writes, in one of his books, that
descending motion is more common, in all musics of the world, than
ascending one. He does not say, however, how common it is to
describe such motion as 'descending'. In general, though, melodies
end at the pitch at which they began: they can but descend what
they first climbed. the 'descending' effect probably results from
the fact that they go up by leaps and come down by conjunct steps.<br>
There is an interesting paper on the verticalization of pitch
in Western music by M. E. Duchez in Acta musicologica 51/1, 1979.
She indicates that the verticalization by no means is universal
and that it appeared slowly and lately in the West (after the 9th
century). The verticalization of pitch may be the consequence
(rather than the cause) of the vertical disposition in notation.
It does not seem to have existed in Latin (or Greek), where
pitches were described as acutus (oxus) and gravis (barus). For
some time, no clear distinction was made between pitch and
intensity ('musica alta' was loud, not high).<br>
In harmonic music, singing in just intonation tends to shift
pitch. With respect to the cycle of fifths (Pythagorean tuning)
taken as reference, the pitch shifts down a comma for each
ascending major or descending minor third, and the reverse. Think
of a neo-Riemannian network and of the change of line
corresponding to 3d-relations: horizontal lines are a comma apart
in just intonation. Tonal harmonic progressions tend to shift down
– one of the reasons why a capella choirs shift down: they sing
too much in tune!<br>
<br>
</font>Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<br>
<br>
<font face="Calibri"><br>
</font>
<div class="moz-cite-prefix">Le 30/07/2012 03:23, Christopher Bonds
a écrit :<br>
</div>
<blockquote cite="mid:5015E223.5010504@willy.wsc.edu" type="cite">
A quick comment. Seems like success in relating any kind of
musical event to gravity depends on the answers to a couple of
questions. First, whether descending intervals, stepwise lines,
root progressions, etc., generally always create a sense of
closure or at least a lessening of tension; and if so, are these
style and culture independent? Second, if so, could there be other
explanations for this phenomenon? Third, if some sort of
relationship could be established between the physical law and
gravity, what effect, if any, will Einstein's general theory of
relativity have on musical perception, now or in some future time?
Finally, is the concept of "up and down" in music universal and
innate, or is it something we have learned by association?<br>
<br>
(For the record, my personal thinking is that the musical brain
has learned to associate higher and lower pitches with up and down
in space. Maybe because low sounds are associated with heavier
objects, which seem to be tending downward more seriously than
lighter objects (although they accelerate at the same rate when
falling.))<br>
<br>
Christopher Bonds<br>
Wayne State College (retired)<br>
<blockquote class=" cite" id="mid_2ED0C71B_BA17_4B58_9832_DF5232F963BD_cs_tu_berlin_de" cite="mid:2ED0C71B-BA17-4B58-9832-DF5232F963BD@cs.tu-berlin.de" type="cite"> </blockquote>
<br>
<blockquote cite="mid:2ED0C71B-BA17-4B58-9832-DF5232F963BD@cs.tu-berlin.de" type="cite"> </blockquote>
<br>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<br>
<pre wrap="">_______________________________________________
Smt-talk mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Smt-talk@lists.societymusictheory.org">Smt-talk@lists.societymusictheory.org</a>
<a class="moz-txt-link-freetext" href="http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org">http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org</a>
</pre>
</blockquote>
<br>
</div>
_______________________________________________<br>Smt-talk mailing list<br><a href="mailto:Smt-talk@lists.societymusictheory.org">Smt-talk@lists.societymusictheory.org</a><br>http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org<br></blockquote></div><br><div>
<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div><br class="Apple-interchange-newline"><br><div><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://user.cs.tu-berlin.de/~noll">http://user.cs.tu-berlin.de/~noll</a></div><div><a href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div><div>Escola Superior de Musica de Catalunya, Barcelona </div><div>Departament de Teoria i Composició </div><div><br class="khtml-block-placeholder"></div><div>*********************************************************</div></div></div></div><div><br></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline"></span>
</div>
<br></div></body></html>