Re: [Audacity-nyquist] Basson and Feigenbaum numbers (period doubling

[Roger D. <rb...@cs...>]

paul beach wrote:
> Thanks Roger, your comments have helped me with this result. 
>
> The synth bassoon (double reed insturment) sounds like so:
>
> http://www.climatehoax.ca/music/bassoon.mp3
>
> Feigenbaum first studied the discrete equation, 
> f(x) = A * x * (1-x) on the domain 0<x<1, and found period doubling as
> "A" increases.
>
> The same principal is supposed to apply for other nonlinear equations,
> such as frequency modulation: An increase in M causes period doubling.
> F = sin(t + M * sin(t))
>   
I don't think period doubling applies here. FM produces sidebands that 
are the carrier frequency + or - multiples of the modulating frequency.
> There is also another principle, a male voice cannot become a female
> voice, simply by increasing the speed. This would NOT be time invariant. 
>
> Therefore each (bassoon)note has to have M readjusted. 
>   
The main attraction of FM in synthesis is that a time-varying index of 
modulation (essentially M) can be used to generate spectral evolution 
with low cost and few parameters. But I agree that the spectrum in 
steady state will vary as a function of amplitude and pitch.