[Smt-talk] Structure of intervals

Nicolas Meeùs nicolas.meeus at paris-sorbonne.fr
Fri Sep 16 12:16:16 PDT 2011

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.
     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.
     Yet the perceived result may be a fundamental at /about/ 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".
     Metric accents and shared attacks are, as here, a matter of phase 
angle. Difference tones are another matter.

Nicolas Meeùs
Université Paris-Sorbonne

Le 16/09/2011 18:07, Eric Knechtges a écrit :
>     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. 
> 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.
> -- 
> Eric Knechtges, DM
> Assistant Professor, Coordinator of Composition/Theory
> Northern Kentucky University
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