<html><div><font face="Verdana" size="2">Andrew has located a critical point: The idea is to be alive in one's time. The "more democratic, less hierarchical and more ambiguous" era in which we live calls for flexibility in every department, not least in our ability to listen. All the more reason to make clear that our visual responses are different from our auditory responses and to keep the auditory choices open to the fullest possible extent.</font></div><div><font size="2"> </font></div><div><font size="2">Most of the comments on this thread are posted by advanced scholars: But the skills to which such scholarship applies are open to all beginners in the study of music, and especially music theory, and would seem to call for cultivation of auditory diversity. </font></div><div><font size="2"></font> </div><div><font size="2">I cannot resist an anecdote: Seated next to a prominent avant-garde pianist, I was subjected to the whacking to bits of a Haydn minuet by a dutifully trained youngster. Incredulous, I asked my colleague: "Can you believe that people are still teaching children to play like that?" Reply: "It's my student."</font></div><div><font size="2"></font> </div><div><font size="2">Nancy Garniez</font></div><div><font size="2">New York City</font></div><div><font size="2"></font> </div><div><font size="2"></font> </div>
http://nancygarniez.blogspot.com
<br>
www.tonalrefraction.com<div><font color="#0000ff" face="Verdana" size="2"></font> </div>
<blockquote style="padding-left: 5px; margin-right: 0px; margin-left: 5px; border-left-color: rgb(0, 0, 255); border-left-width: 2px; border-left-style: solid;"><font face="Tahoma" size="2">-----Original Message-----<br><b>From:</b> Andrew Milne [mailto:andymilne@tonalcentre.org]<br><b>Sent:</b> Thursday, July 24, 2014 07:31 PM<br><b>To:</b> 'JAY RAHN'<br><b>Cc:</b> 'Nicolas Meeùs', smt-talk@lists.societymusictheory.org<br><b>Subject:</b> Re: [Smt-talk] Harmonics<br><br></font><table width="100%" height="400" id="201179" border="0"><tbody><tr><td width="100%" valign="top"><div>There are many aesthetic decision to be made in art. Given the psychoacoustical qualities of a major triad — which include low roughness and a strong virtual pitch (root) — a musical culture can “choose" to privilege such sounds and the qualities of order, clarity and hierarchy (privileged root) that they manifest. Alternatively a musical culture may choose to privilege the more dissonant intervals favoured in the music described by Ambrazevičius. </div><div><br></div><div>Common practice harmony, with its insistence on asserting a strong tonic, establishing hierarchies, moving away from them and then reasserting them is perhaps a reflection of the culture in which this music developed. The revolutionary — and highly rule-based — serial method of imposing different organizational principles onto all twelve chromatic degrees without favouring any of them is perhaps a reflection of its time. And what about recent pop music, which commonly uses triads but connects them in ways that don’t seem to assert such a strong sense of a tonic — it uses modes, ascending fifths progressions, repeating cycles of harmony, and softer IV-I and modal cadences (e.g., bVII-i). This harmony is arguably a reflection of our more democratic, less hierarchical and more ambiguous age.</div><div><br></div><div>This is just a long way of saying that acoustical properties matter (and structural properties too — e.g., evenness of scale pitches and pulse). Under the control of an artist or cultural tradition, they can be organized so as to produce a compelling aesthetic form. But there is no single “right” way in which the precise palette of such properties is chosen, and the method by which they are organized. However, if we subscribe to the Russian formalist belief that the purpose of art is to make the familiar unfamiliar, then novelty is hugely important — we can’t just carry on doing the same old thing over and over. The last thing I am attempting to suggest here is that we return to the past.</div><div><div><br>—<br><br>Dr Andrew Milne<br>Postdoctoral Research Fellow</div><div><a href="http://marcs.uws.edu.au/research/mca" target="_blank" mce_href="http://marcs.uws.edu.au/research/mca">Music Cognition & Action Group</a><br>MARCS Institute</div><div>University of Western Sydney</div><div>Australia<br><br></div><div>Email: <span class="Apple-tab-span" style="white-space: pre;"> </span><a href="mailto:a.milne@uws.edu.au" target="_blank" mce_href="mailto:a.milne@uws.edu.au">a.milne@uws.edu.au</a><br>Web: <span class="Apple-tab-span" style="white-space: pre;"> </span><a href="http://www.dynamictonality.com/portfolio/" target="_blank" mce_href="http://www.dynamictonality.com/portfolio/"><font color="#4180ff">Portfolio</font></a> • <a href="http://www.dynamictonality.com/" target="_blank" mce_href="http://www.dynamictonality.com/">Dynamic Tonality</a> • <a href="https://soundcloud.com/andrew-j-milne" target="_blank" mce_href="https://soundcloud.com/andrew-j-milne">SoundCloud</a> • <a href="http://scholar.google.com.au/citations?sortby=pubdate&hl=en&user=s-4z35cAAAAJ&view_op=list_works" target="_blank" mce_href="http://scholar.google.com.au/citations?sortby=pubdate&hl=en&user=s-4z35cAAAAJ&view_op=list_works">Google Scholar</a></div></div><div><br></div><div><br></div><br><div><div>On 25 Jul 2014, at 12:26 am, JAY RAHN <<a href="mailto:jayrahn@rogers.com" target="_blank" mce_href="mailto:jayrahn@rogers.com">jayrahn@rogers.com</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style='font-family: HelveticaNeue, "Helvetica Neue" , Helvetica, Arial,"Lucida Grande" , sans-serif; font-size: 14pt; background-color: rgb(255, 255, 255);'><div><span style="font-size: 18px;"><span>Andrew Milne and others might attribute 'beauty and richness' to a 'well-tuned major triad.' But singers of, e.g., certain traditional idioms of eastern Europe have actually realized simultaneous intervals of ca. 200 cents throughout individual polyphonic songs. (See, for instance, </span><span>Ambrazevičius,
R., & Wiśniewska, I. 2009. Tonal hierarchies in Sutartinės. Journal </span><span>of
Interdisciplinary Music Studies 3/1&2: 45–55.) </span></span></div><div style='font-family: HelveticaNeue, "Helvetica Neue" , Helvetica, Arial,"Lucida Grande" , sans-serif; font-size: 18px; font-style: normal; background-color: transparent;'><span style="font-size: 18px;"><br></span></div><div style='font-family: HelveticaNeue, "Helvetica Neue" , Helvetica, Arial,"Lucida Grande" , sans-serif; font-size: 18px; font-style: normal; background-color: transparent;'><span style="font-size: 18px;">'Richness' does not seem to have been a term that has been widely employed in studies of psychoacoustics or music cognition. And, arguably, beauty is in the ears and brain of the beholder.</span></div>
<!--EndFragment--><div style='font-family: HelveticaNeue, "Helvetica Neue" , Helvetica, Arial,"Lucida Grande" , sans-serif; font-style: normal; background-color: transparent;'><span style="font-size: large;"><br></span></div><div style='font-family: HelveticaNeue, "Helvetica Neue" , Helvetica, Arial,"Lucida Grande" , sans-serif; font-style: normal; background-color: transparent;'><span style="font-size: large;">Jay Rahn, York University (Toronto)</span></div><div style='font-family: HelveticaNeue, "Helvetica Neue" , Helvetica, Arial,"Lucida Grande" , sans-serif; font-size: 19px; font-style: normal; background-color: transparent;'><span> </span></div> <div class="qtdSeparateBR"><br><br></div><div class="yahoo_quoted" style="display: block;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 14pt;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;"> <div dir="ltr"> <font face="Arial" size="2"> On Wednesday, July 23, 2014 9:04:14 AM, Andrew Milne <<a href="mailto:andymilne@tonalcentre.org" target="_blank" mce_href="mailto:andymilne@tonalcentre.org">andymilne@tonalcentre.org</a>> wrote:<br> </font> </div> <blockquote style="padding-left: 5px; margin-top: 5px; margin-left: 5px; border-left-color: rgb(16, 16, 255); border-left-width: 2px; border-left-style: solid;"> <br><br> <div><div id="yiv5207109808"><div><div>It is actually very easy for almost any to human to produce a pitch with a perfectly harmonic spectrum — by singing. And it is, perhaps, in singing with others that the richness and beauty of a well tuned major triad is most apparent.</div><div><br clear="none"></div><div><div>—<br clear="none"><br clear="none">Dr Andrew Milne<br clear="none">Postdoctoral Research Fellow</div><div><a href="http://marcs.uws.edu.au/research/mca" target="_blank" rel="nofollow" shape="rect" mce_href="http://marcs.uws.edu.au/research/mca">Music Cognition & Action Group</a><br clear="none">MARCS Institute</div><div>University of Western Sydney</div><div>Australia<br clear="none"><br clear="none"></div><div>Email: <span style="white-space: pre;"> </span><a href="mailto:a.milne@uws.edu.au" target="_blank" rel="nofollow" shape="rect" ymailto="mailto:a.milne@uws.edu.au" mce_href="mailto:a.milne@uws.edu.au">a.milne@uws.edu.au</a><br clear="none">Web: <span style="white-space: pre;">
</span><a href="http://www.dynamictonality.com/portfolio/" target="_blank" rel="nofollow" shape="rect" mce_href="http://www.dynamictonality.com/portfolio/"><font color="#4180ff">Portfolio</font></a> • <a href="http://www.dynamictonality.com/" target="_blank" rel="nofollow" shape="rect" mce_href="http://www.dynamictonality.com/">Dynamic Tonality</a> • <a href="https://soundcloud.com/andrew-j-milne" target="_blank" rel="nofollow" shape="rect" mce_href="https://soundcloud.com/andrew-j-milne">SoundCloud</a> • <a href="http://scholar.google.com.au/citations?sortby=pubdate&hl=en&user=s-4z35cAAAAJ&view_op=list_works" target="_blank" rel="nofollow" shape="rect" mce_href="http://scholar.google.com.au/citations?sortby=pubdate&hl=en&user=s-4z35cAAAAJ&view_op=list_works">Google Scholar</a></div></div><div><br clear="none"></div><br clear="none"><div id="yiv5207109808yqt02738"><div><div>On 23 Jul 2014, at 6:51 pm, Nicolas Meeùs <<a href="mailto:nicolas.meeus@scarlet.be" target="_blank" rel="nofollow" shape="rect" ymailto="mailto:nicolas.meeus@scarlet.be" mce_href="mailto:nicolas.meeus@scarlet.be">nicolas.meeus@scarlet.be</a>> wrote:</div><br clear="none"><blockquote type="cite">
</blockquote></div></div></div><div id="yiv5207109808yqt06096"><div><div>
<font face="Calibri">It is disappointing to see that the same
misunderstandings come back and again. In such conditions, the
whole discussion is pointless. Let me try for the last time:<br clear="none">
<br clear="none">
1. The question of enharmonic notes produced on a string or
overblowing a wind instrument and that of harmonic overtones are
only remotely related. Consider the following facts:<br clear="none">
– Brass winds usually are built today to play in ET. This is
obtained by complex adjustments of the bore, with the result that
the different notes obtained by overblowing correspond to those in
ET and not to just intonation. Yet, these instruments still can
produce harmonic overtones for each of their notes, the
harmonicity of overtones in this case being more dependent on the
conditions of blowing than on conditions of the bore.<br clear="none">
– Clarinets are known not to overblow their even harmonics,
because their reed acts as a closed pipe (i.e. closes when the
wave returns); yet their sounds of course can include all harmonic
overtones.<br clear="none">
– Natural pipes (conchs, tusks, horns and the like) are very
unlikely to overblow to harmonic notes, even if they might be
blowed to produce more or less harmonic overtones.<br clear="none">
– The production of harmonic notes on a string is dependent on the
kink in the string moving at the same velocity on both sides of
the dividing finger. Velocity is directly dependent on linear
density and section. Making strings with a constant density and
section along their length is a complex technology; strings so
made are called "harmonic strings". Natural strings (e.g. vines,
braided or not) are unlikely to be harmonic.<br clear="none">
– If the pipes or strings are not "harmonic" in this sense, they
may still produce different notes in the same conditions as for
harmonic notes, but the intervals between them will not correspond
to those in the harmonic series, and each of them may or may not
include harmonic overtones.<br clear="none">
<br clear="none">
2. The conditions for producing harmonic overtones are described
by Fourier's theorem. They reduce to one, periodicity. A truly
periodic vibration produces a stable pitch, and a stable pitch
produces harmonic overtones. Reducing the stability reduces the
harmonicity of the overtones, until the concepts of pitch and of
overtones loose pertinence.<br clear="none">
– Vibrato, for instance, by disturbing the stability of pitch,
reduces the harmonicity of the overtones (which allows more easily
playing 'in tune', as the fusion of the overtones becomes somewhat
blurred).<br clear="none">
– Slightly non-harmonic strings may appear to produce stable
pitches, but yet become difficult to tune (this was the case with
early nylon harp strings, because it was difficult to maintain a
constant diameter on such lengths).<br clear="none">
– Pipes or strings that are significantly non harmonic in the
definition under 1 above cannot be forced to produce stable
pitches and therefore do not produce harmonic overtones. <br clear="none">
– Stability of pitch requires a sustained supply of energy, as is
the case with winds and bowed strings. It can be approximated by a
high initial supply of energy and a slow dissipation, as in pianos
and some plucked string instruments. Percussion instruments do not
normally produce harmonic overtones (see for instance
<a href="http://soundmath.blogspot.be/2010/08/percussion-instruments.html" target="_blank" rel="nofollow" shape="rect" mce_href="http://soundmath.blogspot.be/2010/08/percussion-instruments.html">http://soundmath.blogspot.be/2010/08/percussion-instruments.html</a>).<br clear="none">
<br clear="none">
3. About Pythagoras and the smithy, Calvin Bower writes in the
Cambridge History of Wester Music Theory that "The roots of this
myth so fundamental to the history of Western musical thought are
buried within ancient values and archetypes that can never be
fully fathomed. The empirical data offered in the myth is wholly
specious, for hammers of comparable weights would not sound the
musical intervals presented in the story. However, the myths and
dreams of a civilization are judged not by their empirical truth
or falsity, but by the expression of intellectual and spiritual
complexes they reveal within a culture."<br clear="none">
...The myths and dreams of some SMT-Talk participants
similarly must be judged by their expression of intellectual and
spiritual complexes...<br clear="none">
<br clear="none">
Nicolas Meeùs<br clear="none">
Professeur émérite<br clear="none">
Université Paris-Sorbonne<br clear="none">
<a href="mailto:nicolas.meeus@scarlet.be" target="_blank" rel="nofollow" shape="rect" ymailto="mailto:nicolas.meeus@scarlet.be" mce_href="mailto:nicolas.meeus@scarlet.be">nicolas.meeus@scarlet.be</a><br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
</font>
<div>Le 22/07/2014 23:03, CARSON FARLEY a
écrit :<br clear="none">
</div>
<blockquote type="cite"><span style="background-color: rgb(255, 255, 255);">If
I pick up my guitar or bass I can produce strong harmonics</span></blockquote>
<br clear="none">
</div>
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