There is another complication. Floating point numbers aren't stored
the same way that integers are, they are stored as a mantissa and
exponent. This technique also combats the precision problem. What
will happen is that the mantissa will stay the same and you are just
twiddling the exponent bits. No loss of precision. You could
definitely do this demonstration in chuck, and it is excellent, but I
think we will have to hear from Ge, Spencer or Perry about exactly
how much you will need to turn the gain down in order to achieve the
desired effect.
Yes, I think that explains what is observed. As I understand floating point we could force (some) data degradation by amplifying the signal by some ratio that can't be expressed exactly in the exponent, forcing adjustment in the data itself. Floating point does have rounding errors but I seem to remember those tend to show up in particular when very large numbers and very small ones are confronted with eachother.
A more practical way of demonstrating dithering might be to have some generated piece and record it (in ChucK) to a wave file at a low gain in order to leave headroom in case several elements decide to be loud at the same time. This data would be written to a fixed point file (since ChucK doesn't support floating point formats yet) After this ChucK might be used again to increase the amplitude to make the loudest part close to 0db at which point dithering would be usefull? If we are after a demonstration that might count as a fairly realistic real-world scenario, I could imagine somebody wanting to publish a algorithmic piece without clipping that would be made and processed entirely in pure ChucK. Personally I tend to be in favour of real-world scenarios for demonstrations but this isn't my experiment so maybe this isn't relevant at all.
Kas.