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Harmonics & beats are better .. (Paul E)

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

5/25/1997 11:33:02 AM
From: PErlich

Ray Tomes wrote,

>I would suggest that it would be possible to make some tempered tunings
>which are not too far from equitempered tunings, but which have beats
>that are reasonably well in tune. Has anyone ever investigated this?
>It might be a fruitful exercise.

First, let's get some acoustics straight. Beats only occur between tones
that are very close (within a critical bandwidth) and are never heard as
musical tones, even when they are rapid enough to match the frequency of
audible tones. Helmholtz is a good reference for all this, and should be
quite readable to a 19th century mind like Ray's :). However, at loud
volumes, nonlinearities in our ears cause "difference tones" as well as
other, weaker "combination tones" to be heard. So Ray's analysis is
mathematically valid but applies not to "beats" at all but to difference
tones. Difference tones are important (Heinz Bohlen believes difference
tones to be the foundation of all harmony) while matching beat rates to
scale pitches can have no musical significance whatsoever.

Now, to answer the question, with "beats" changed to "difference tones," I
believe Erv Wilson's meta-meantone tuning has some difference tones that
are in tune with each other. It should also be possible to devise meantone
tunings where some difference tones are in tune with some scale tones.
Perhaps John Chalmers or Manuel Op de Coul have compiled a list of such
tunings? The nice thing about meantone tuning, of course, is that re-la is
what it "wants to be."

--
P.S. (MOdC) Interesting thought but I haven't.

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