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<font face="Calibri">It is not true that "a vibrating string
produces overtones in the lower partials of a major triad, then a
dominant 7th". Supposing that the string is of constant diameter
and density along its length (which requires quite a lot of
technicity in its making), the partials produced are: 8ve; 12th;
15th; 17th; 19th; then a note about a quarter tone lower that what
we would describe as the 21th (or a quarter tone higher than the
20th), etc. This may be considered to correspond to the major
triad and, in approximation, to the dominant 7th, but this
correspondence is far from obvious. (Many of you may have had to
count on their fingers what a 19th could be.)<br>
<br>
It is troubling, in addition, that the realization of the
existence of the overtones came roughly a century later than the
date Victor Grauer mentioned in a previous message for the
apparition of triads... The story of Pythagoras and the blacksmith
shop is a myth – and a joke – as is the medieval idea that the
pitch of bells is dependent on their weight. Even in the late 19th
century, it was considered (e.g. by Helmholtz and his translator
Ellis) that the overtones could not normally be heard.<br>
<br>
If there is a physical law behind all this, it is that of
consonance. It produced: the major triad, but also the minor one;
harmony; to some extent tonality. But the conditions of the law of
consonance are so strict (mainly, pitch stability) that they
require a technicity that has been developed only in the Western
world – precisely because that is where the question of consonance
has been considered of paramount importance.<br>
<br>
Hindemith's and other 20th-century composers' phantasms concerning
the overtones have proved quite fruitful, but that doesn't turn
them into physical laws. The diatonic scale can be described, with
some approximation, as formed of two intertwined dominant 7ths; it
could also be described (with roughly the same approximation) as
corresponding the 16th first partials of a fundamental which may
or may not be the 'tonic' of the scale (Momigny, unless I am
mistaken, considered that the major scale corresponded to the
overtones of its dominant).<br>
<br>
Tonal music does to some extent rely on triads (not necessarily
major, nor triads exclusively); it involves many other aspects,
for instance in its syntax. But "traditional music" is something
else: music can be made in an endless variety of combinations, not
necessarily including consonance, nor the diatonic scale, as
important categories.<br>
<br>
Nicolas Meeùs<br>
Professeur émérite<br>
Université Paris-Sorbonne<br>
<br>
<br>
<br>
</font>
<div class="moz-cite-prefix">Le 19/07/2014 00:16, CARSON FARLEY a
écrit :<br>
</div>
<blockquote
cite="mid:811832282.22878943.1405721806921.JavaMail.root@embarqmail.com"
type="cite">
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<div style="font-family: times new roman,new york,times,serif;
font-size: 12pt; color: #000000"><span style="color: rgb(0, 0,
0);">Considering the fact that a vibrating string produces
overtones in the lower partials of a major triad and then a
dominant 7th chord it would seem that the ubiquitous triad is
present in nature as a law of physics and heard consciously or
unconsciously throughout human history as overtones produced
in some manner by taught strings, overblown wind/brass
instrument partials, or in Pythagoras' case the differing
notes of a struck anvil/metallurgy as he passed the blacksmith
shop. How to overcome the "ubiquitous" triad? As a composer
I believe that the harmonic partials of a single tone are the
electrons to any fundamental pitch/atom. For example, a scale
can be created by extracting a dominant 7th chord (either
tempered or non tempered) from the lower 8 partials of a
single tone and then doing the same for another interval pitch
and combining the results - C and B for example resulting in
the following pitches: </span><font color="#ff0000">B</font>,<font
color="#3333ff">C</font>,<font color="#ff0000">D#</font>,<font
color="#3333ff">E</font>,<font color="#ff0000">F#</font>,<font
color="#3333ff">G</font>,<font color="#ff0000">A</font>,and <font
color="#3333ff">Bb</font> (or the normal form of <font
color="#cc0000">A</font>,<font color="#3333ff">Bb</font>,<font
color="#cc0000">B</font>,<font color="#3333ff">C</font>,<font
color="#cc0000">D#</font>,<font color="#3333ff">E</font>,<font
color="#cc0000">F#</font>,<font color="#3333ff">G</font>).
Hindemith explores the importance and gravity of partials and
overtones as compositional material and so do other 20th century
theorists like Mathieu in "Harmonic Experience." The way to get
away from/avoid the "ubiquitous" triad is to approach any
individual tone as it's own microcosm of overtone/partial
electrons and avoid using triads as the essential building
blocks so long taken for granted as the starting place for
harmony. Just as physics moved in modernity into the realm of
microcosm, so must music. A triad is in many ways a relic of
the past no longer relevant to contemporary science/practice
unless of course the desired result is traditional sound/music.
<div><br>
</div>
<div>Carson Farley</div>
<div>Composer/cellist/theorist</div>
<div>University of Washington Alumnus </div>
</div>
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<p class="" avgcert""="" color="#000000" align="left">Aucun virus
trouvé dans ce message.<br>
Analyse effectuée par AVG - <a moz-do-not-send="true"
href="http://www.avg.fr">www.avg.fr</a><br>
Version: 2014.0.4716 / Base de données virale: 3986/7884 - Date:
19/07/2014</p>
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