Harmonics question

[Stopp,Gene]

Right - subharmonics are all over the place in the real world.

Analog synthesis is only a crude approximation of real world mechanics -
it's functions are "analogies" of actual movements, hence the name. For
example, these waveforms we talk about are just different ways of
"plucking" an imaginary string with zero mass and zero diameter, made of
a single dimensionless fiber, stretched to a certain tension across a
certain distance, between two infinitely rigid points. If you pluck
exactly in the center, you will get only odd harmonics (try it on an
acoustic guitar and see how much it sounds like a square wave!). If you
pluck it close to one of the rigid endpoints, you will get both even and
odd harmonics. The closer to the endpoint, the narrower the "pulse"
gets.

Analog synthesis is far from the real mechanical world, where strings
have mass and diameter and the metal stretches and heats. In a way it
lets you listen to one parameter at a time, stripping away all other
effects that would complicate the sound, allowing you to add more
parameters one by one. If you really want to simulate a real string, you
can, but it would take a *lot* of individual parameters and therefore a
*lot* of synthesizer modules. But why do that? Analog synthesis is not
about doing that - that's what samplers and physical modelling DSP's are
for. For me, the sounds of the naked laws of nature are every bit as
interesting as the complex "real" sounds. I love the sound of a hi-res
4-pole lowpass as it slowly picks out the harmonics of a bright
waveform.

Speaking of interesting harmonic sweeps, this reminds me of a pulse
shaper that I came up with a while back that produced really interesting
sounds. It was an expansion of a circuit in Electronotes (the "Dual
Pulse Waveform Shaper") which used four comparators to create a
symmetric-around-ground pulse width modulated waveform. If you feed it
with a triangle wave and sweep the PWM input, you will get a PWM'ed
sound with only odd harmonics (i.e. satisfying the mirror-image
requirements). I'd forgotten about this - now I want to build one again!

 - Gene

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From: Mikko Helin
To: synth-diy at mailhost.bpa.nl
Cc: MHELIN at tne01.tele.nokia.fi
Subject: Re: Harmonics question
Date: Wednesday, May 20, 1998 6:38AM


  Btw, in real life all harmonics are not an integer function of
  the fundamental. Obviously they are with "perfect" square or
  saw waves, but not with the sampled piano wave (whatever it is)
  or detuned saw VCO's. Which also makes me believe there are
  harmonics that are below fundamental.

  -Mikko