natural beats

[BobDavis88@rudoff.com]

Howard Rosen writes:
> Virgil's so called
>  "natural" beats have to come from some pair of coincidental partials. 

Howard, I agree with Keith that Virgil is probably talking about an average 
of multiple coincidences rather than a single pair.

I too have disagreed with Virgil's articles, particularly his claim that 
single, double, and triple octaves can be tuned "beatless." However, even 
limiting the discussion of "natural beats" to octaves (and multiple octaves) 
for the moment, I think that Keith was on the mark when he was talking about 
"cumulative." 

Talk even of a "beatless" octave drives me nuts - I think it's inaccurate and 
a physical impossibility. Indeed, a 2:1 octave will not sound "clean." (For 
those unfamiliar with the term "2:1," that is an octave in which the 2nd 
partial of the lower note equals the fundamental of the upper note and 
therefore does not produce a difference frequency, or beat). Because of 
inharmonicity, as we know, the 4:2 coincidence will be narrow, the 6:3 
narrower yet, and so on. Their beats will not be as loud as the 2:1 was, but 
they're there. Raising the pitch ever so slightly makes the higher 
coincidences closer FASTER than it makes the 2:1 coincidence worse, so the 
octave becomes "cleaner." That term at least suits me a little better than 
"beatless." The amount it takes to reach the "cleanest" octave depends upon 
the amount of each partial present, and therefore upon the voicing, as well 
as the scale. 

Keith says,
>  that Virgil's natural beats "come from listening to the cumulative
>  relationship of all the partials" .

The ear averages the amount of noise (beating) produced at each coincidence 
of partials, and a clean octave results when the average noise is least. 

I don't think I'm alone in saying that three 2:1 octaves stacked on top of 
one another will NOT produce a good-sounding triple octave. However, neither 
will three "clean" octaves. Inharmonicity causes the upper partials to be 
sharp enough that individual octaves actually need to be a little wide of 
clean to produce a clean triple octave.

    "The contradiction so puzzling to the ordinary way of thinking comes from 
the fact that we have to use language to communicate our inner experience 
which in its very nature transcends linguistics."     --D. T. Suzuki

Sometimes a model doesn't have to be scientifically accurate to be useful, 
but I think this is a case where Virgil's description is less useful than 
others I have heard.

Bob Davis