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
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