Theo Verelst Digital Sound Synthesis page

Some of the ideas I gathered up on digital synthesis. Note that due to lack of access to ANY computer system except an internet terminal currently (a not too slow notebook with sound would be more than suifficient), I can't program some of the things I already long thought of. I will include some of the digital / analog combination ideas I've used in the recent and far past as well.

Basic tunable sample sound synthesis

Roughly, there are two methods of changing the tuning of a digital sound sample: changing the playback sample rate, or use varying sample table increments. The first has the main disadvantage of either causing reconstruction filter problems or requiring much higher sample playback rates than strickly needed. The second may need averaging filters for (fixed point) point increment factors greater than one or interpolation filters to prevent sampling noise for increment factors smaller than one, depending on the sampling noise due to time or amplitude step inaccuracies.

... old Z80 fixed point sample pointer update using a 2pow(1/12) semitone increment lookup table. 


            register pairs (ops)
            ==============
             (ld BC,(notebase+desired_note))
             (ld DE,current_generator_sample_position)
             (ld H,sample_base)

Increment       B     C        ; sample incement, 0100h for base note
             (add, double)
Relative        D     E        ; per generator relative sample pos.
pointer      (ld L,D)
Table     H     L
Pointer
             (ld a,(HL))
             (out (n),a)
             (EXX)
             (repeat and loop)
...

Basic sine generators

A far more complex problem, coupled harmonic oscilators or waveguides has been tackled here (will add link). More deatils later.

4 pole time varying resonating and oscilating digitally controlled filter

Note that this is as yet untested! However, the oscilating wave guide worked even for lengths of thousands of coupled two pole units, so I see no reason why a pentium or so with 32 bit word width operations wouldn't work on this example. 

update_filter()
{
   for (i=0; i<4; i++) {                 /* four sections    */
      a[i] += fc[i]*ii[i]+fcb[i]*a[i];
   }
   a[0] += fb[3]*fc[0]*a[3];             /* and the feedback */
}
the a variables are the filter storage elements, fc the filter coefficients, fb the feedback (resonance) component. The rest is temporal storage + ...
It is quite possible to include non-linearities by including a table lookup or some kind of polynomial interpolative function during the feedback or feedforward increment.

Multiple sample playing generators

No additional filtering! Take n=8 for 8 note polyphony with dual oscilators per voice, and take SAMPLEVALUES as an array capable of holding at least 2n samples, or wathever alternative seems fit, these examples were used to do a course MIPS/MFLOP analysis which made clear these oscillators with the above filter and additional envelope generator++ stuff would without much difficulty run on for instance a sharc dsp (costing $29 industrial price, didn't check all others yet, it was just to have an idea), with time to spare.
ENVELOPES is an array of structures with a state(either up/down, or stage1..n, possibly extended with lin/log/table) a relative and a (quantized) absolute envelope generator value. 

all_update_oscilators()      /* eternaly looped samples */
{
   for (i=0; i(n; i++)
      for (j=0; j(2; j++) {
         p[i][j] = (p[i][j]+incr[i][j])%sl[i][j];
         o[i][j] = ot(p[i][j]);
      }
   output_samples(o)
}

output_samples(o)
SAMPLEVALUES o;
{
   SAMPLEVALUES oe, of;
   LONGWORD out;

   for (all generators) {
      envelope(o,oe);
      filter(oe,of);
      mixdown(of,out);
   }
   output_and _da_convert(out);
}

envelopegenerator()            /* 1mS or so interupt driven   */
{                              /* or faster for high accuracy */
   ENVELOPES e;                /* or split (dynamic timing)   */
   for (all generators)
   {
      update(&state,e[].quant);
   }
}