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FM Spectra; was: Yaphi spectrum and tuning

🔗Kees van Prooijen <keesvp@...>

5/9/2009 3:18:59 PM

On Sat, May 9, 2009 at 1:47 PM, Cameron Bobro <misterbobro@...> wrote:

> FM is completely predictable, and easy as far as what partials are going
to appear,
> but calculating the resulting amplitudes uses Bessel functions and is
beyond me.
> However you can get a very good feel with practice. One curious thing
about FM
> is the energy distribution- basically when you increase the modulation
amount,
> you're spreading the energy into more sidebands, and that's part of the
> "FM sound". It gets weedy sounding because > when you're making more
> high partials, you're robbing energy from the low to do so, if that makes
sense.

If you look at my 1978 paper here:

http://www.kees.cc/tuning/interface.html

in section 5.2 you'll see that I have done my share of fiddling with fm
sidebands.

Kees

🔗Cameron Bobro <misterbobro@...>

5/9/2009 3:58:14 PM

--- In tuning@yahoogroups.com, Kees van Prooijen <keesvp@...> wrote:
>
> On Sat, May 9, 2009 at 1:47 PM, Cameron Bobro <misterbobro@...> wrote:
>
> > FM is completely predictable, and easy as far as what partials are going
> to appear,
> > but calculating the resulting amplitudes uses Bessel functions and is
> beyond me.
> > However you can get a very good feel with practice. One curious thing
> about FM
> > is the energy distribution- basically when you increase the modulation
> amount,
> > you're spreading the energy into more sidebands, and that's part of the
> > "FM sound". It gets weedy sounding because > when you're making more
> > high partials, you're robbing energy from the low to do so, if that makes
> sense.
>
> If you look at my 1978 paper here:
>
> http://www.kees.cc/tuning/interface.html
>
> in section 5.2 you'll see that I have done my share of fiddling with fm
> sidebands.
>
> Kees
>

I think the time I'd need to wade through the math there is more likely to be spent on Sudoku. :-) What I've done with FM sidebands is a lot more quick and dirty, but I've found by experience that certain kinds of ratios get you "strangely pleasantly inharmonic" spectra very quickly, and they are the same ratios that seem to do this in tunings. Phi is a winner here, but so are other irrationals of course.