[sdiy] Thoughts on drum synth

[Magnus Danielson]

From: Tim Ressel <madhun2001 at yahoo.com>
Subject: [sdiy] Thoughts on drum synth
Date: Sun, 31 Mar 2002 15:27:34 -0800 (PST)

> Hi Y'all,

Hi Tim,

> Thought I would toss in my thoughts on the subject of
> drum synthesis. According to Olsen's "Music, Physics
> and Engineering", a drum has a six modes of
> oscillation which have a non-harmonic relationship.
> Here are the freqs:
> 
> 1st mode      Fo
> 2nd mode      1.59Fo
> 3rd mode      2.14Fo
> 4th mode      2.3Fo
> 5th mode      2.92Fo
> 6th mode      3.6Fo

But... there's more... in that range!

There is 10 modes in the range of 1-3.65 times base resonance, they
are:

f  (uniphase resonance)
 1

f  = 1.59 f  (cross-section - 2 regions of 180 degree each)
 2         1

f  = 2.14 f  (cross-section - 4 regions of 90 degree each)
 3         1

f  = 2.30 f  (circular-section - 2 regions)
 4         1

f  = 2.65 f  (cross-section - 6 regions of 60 degree each)
 5         1

f  = 2.92 f  (cross-section/circular-section - 2 cross-section regions
 6         1  combined with 2 circular regions)

f  = 3.16 f  (cross-section - 8 regions)
 7         1

f  = 3.50 f  (cross-section/circular-section - 4 cross-secion regions
 8         1  combined with 2 circular regions)

f  = 3.60 f  (circular-section - 3 regions)
 9         1

f  = 3.65 f  (cross-seciont - 10 regions)
 10        1

... and the list goes on. Effectively you can have any even number of
cross-section regions and any integer number of circular sections,
and you can have ANY mixture of those, each with its distinct
resonance frequency.

The higher mode number, the smaller is each section, and the more
these smaller sections will even itself out. You will induce less and
less energy into them, but you will also get a less total acoustical
output due to summing results. The more active regions you have, the
hairier plot of acoustic energy plotted against angle of membrane -
just as with multi-element speakers or multi-element radio/radar
antennas.

> Decidedly non-harmonic. As any frum player can tell
> you, where you hit the drum head changes the tone.
> What is happening here is different modes are being
> excited depending on where the drum head is struck.

Right.

Now, to make it even more fun... they decay at different rates!

If you also dampen the drum, you can dampen out certain modes while
leaving others relatively untouched. This is certainly no news to a
good drummer.

> So it seems to me what we have here is six sine
> oscillators and six VCAs. The amplitude of the VCAs is
> determined by the drum 'hit'. This is complicated by
> the fact that a drum 'hit' can excite more than one
> mode, and to differing degrees. Having fun yet?

Notice that you would need to adjust the peak level and release-time
individually for each of these modes. The number of modes you have,
the better "simulation".

Look at Turkish or Indian drummers... do their hands stay in place? No
bloddy hell... go figure why it sound different!

> If we drill down deeper, we find that the body of the
> drum forms a bandpass filter. A tom or kick drum body
> will be a single pole BPF with a real low Q. A Doumbek
> will have a more complicated filter structure.

Right.

> Now it seems a waste to dedicate complex VCOs just to
> make fixed freq sines. This sounds more like a bank of
> NCOs, which in turn sounds like a DSP. 

OUPS!

> Six modes of oscillation suggests six different places
> to hit our virtual drum. Plus a way to tell it what
> pitch to be at. Any thought on an interface?

Umm... circular drumpad? >:^)

> This scheme would be adaptable for all different kinds
> of percussion. 
> 
> This sounds like a lot of fun. A group project,
> perhaps?

We will see about that... good drum-simulations doesn't come very
cheap thought.

Cheers,
Magnus - learning my computer to lit LEDs, as a starter exercise...