clarinet vs. violin

Paul's questions:

>1. Won't the violin also have the 1800 and 1764 partials?

Sure, but they are further out and would likely be lower in amplitude and
hence contribute less to the beating (by stating the example as I did, I was
implicitely assuming equal amplitudes for each of the first five partials, and
nothing beyond that - obviously an oversimplification). What we really
should do is pick the spectrum precisely, and then calculate the sensory
dissonance - I was trying to give a simple explanation of why the effect
might occur with carinetish vs violinish timbres. The actual sensory
dissonance will inevitably depend on the specifics of the timbre.

>2. Tuning the clarinets in this register to a 5:4 would only speed up
>the beating, lowering the roughness only slightly. Tuning them to a 9:7,
>however, would eliminate the beating entirely. So is a 9:7 more
>consonant than a 5:4 for low clarinets? (Gary, you made the original
>comment, so tell us what you think.)

By playing with the exact tuning relationships and the exact timbres, you
should be able to get just about any ordering you can think of. This kind of
example highlights the danger of divorcing "consonance" calculations from
the timbre/spectrum of the sounds involved.