[sdiy] Analysis of frequency variation in analogue synths

[Eric Brombaugh]

ASSI wrote:

> Good question.  Off the top of my head (I haven't checked this 
> thoroughly, so take it with a grain of salt): Shifting bits into the 
> binary output words forms exponential pulses.  The spectrum of a 
> periodic expo pulse sequence is a mixture of square- and triangle like 
> components phase shifted by 90 degrees (~coskx/k² and ~sinkx/k).

Of course! Depending on how you shift the bits in (MSB, LSB or 
scrambled) you'll always get the same pattern in time creating a pulse. 
By looking at the spectrum as the superposition of these repeating 
pulses it all falls out. If you can assume linearity (and in this case 
we can) then superposition is a power analysis tool.

> With the 
> right combination of tap spacing and scrambling you can probably 
> produce "formant-like" noise.

That's an interesting idea. Make a 'scramble-modulated' noise source. 
The big trick would be to find a way to convert simple control values 
(CV or digital) so that they have an intuitive effect on the sound.

Of course, you're not limited to taking just one power-of-2 per delay 
tap, so instead of thinking about it as 'scrambling' think of it as 
pulse shaping. Then, you can use lookup tables or other digital 
synthesis techniques to create arbitrary pulse shapes. That becomes much 
more predictable/controllable and you end up with something that works 
very much like the formant synthesis used in the Yamaha FS1-R.

Eric