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<font face="Calibri">Yes, I think so too. Difference tones arise
from non linearities in the transmission chain, eliciting
frequencies which are not present in the individual components.
This is quite different from the recomposition of the fundamental
(at the GCF frequency) when several of its (harmonic) partials are
heard together.<br>
Two notes of, say, 200 and 300 Hz may be heard as harmonics of
a fundamental at 100 Hz – and the absent fundamental may be
perceived. Two notes of, say, 200 and 301 Hz are the 200th and the
301th harmonics of a fundamental at 1 Hz. <br>
Yet the perceived result may be a fundamental at <i>about</i>
100 Hz, fluctuating (both in amplitude and in frequency) at a rate
of about 1 Hz. The trigonometry of this problem is utterly
complex: it is of the nature of frequency modulation, which
acousticians themselves describe as "messy".<br>
Metric accents and shared attacks are, as here, a matter of
phase angle. Difference tones are another matter.<br>
<br>
</font>Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<font face="Calibri"><br>
</font><br>
Le 16/09/2011 18:07, Eric Knechtges a écrit :
<blockquote
cite="mid:CAC7jrStc+qnfGfQ1s84M68-rN3g_c5kn2yCWwBd4trED1_PCUA@mail.gmail.com"
type="cite"><br>
<div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex;">
<br>
Difference tones are analogous to the metric accents that
accrue to the shared attack between two cycles of differing
cardinality. For example, a 3 vs. 2 rhythm (the combination
of "frequencies" 3 and 2) will create a higher-level attack at
frequency 3-2=1, much as two high pitches a fifth apart will
produce a difference tone an octave below the lower pitch. </blockquote>
<div><br>
Yes, your example works, but not for the reason you think, I
think. The GCF of 3 and 2 is 1, which is why there is a
higher-level attack there. There is certainly no higher-level
attack of 2 in a 5 against 3 pattern, but there is at 1
because the GCF of 5 and 3 is 1.<br>
</div>
</div>
-- <br>
Eric Knechtges, DM<br>
Assistant Professor, Coordinator of Composition/Theory<br>
Northern Kentucky University<br>
<br>
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