Double pulses of plucked strings

[Ricko]

On http://electro-music.com/forum/topic-69105.html I commented to Ian Fritz (name drop! Hero!) that I was not excited about double pulse wave forms (where one is positive and one is negative) because I could not find an example in literature about physical instruments.

This is just because my particular interests lie in trying to make available proven systems of sound generation as a springboard for new sounds, not for imitative synthesis as such: that is an angle I think has been missed, perhaps because physical modeling does a better job of imitation than the "acoustic modeling" of analog synths.

Then I tried it (with antiphase fixed pulses using two Blip! Modules) and I liked it. Fair enough.

Bingo! This week I have indeed found in some academic material where double antiphase pulses are generated in physical musical instruments: at the connection to the soundboard of plucked string instruments at the start of their envelope. So far from being rare, it is quite common!

A string pluck is an impulse, the shape of which (pointy, blunt) is determined by the width and give of the plectrum, the force or velocity, and the springiness of the wire. The pulses travel from the point of plucking (also acting as a dampener for harmonics at the ratio corresponding to the position along the wire) and propagated back and forward alone the string, gradually becoming more sine like as higher energy is absorbed faster. (The impulses may not show up on the wire like an oscillisope trace, unless the wire is highly elastic: instead the impulses are force travelling along the wire.)

The thing is, from the initial pluck point, a pair of impulse waves are generated, travelling both left and right along the string and getting reflected back antiphase when they reach the ends. So at the bridge, one is positive going, and the other is negative going and delayed by twice the length of the far section of string. There are slow motion videos of acoustic guitars where you can see the motion (dubiously) well.

Now in real life that impulse has its shape only briefly. Not only because the LP filtering effect of energy absorption, but because in a wire, especially slack wires, high frequencies travel faster than slow. This causes the waveshaper to smear, but because both pulses are have pretty much the same all-pass filtering phase changes, I dont think it will cause any phase cancellation: the faster harmonics of one pulse are chasing the the faster harmonics of the other pulse.

This is another example of a really common waveshape, as it turns out, where the phase difference of the two pulses models the pluck position. I think two fixed-breadth pulses (ie not a percent of the wavelength) like Blip!s will model it better (giving more dformant effect), but the variable pulses like Ian Fritz's is certainly in the same family.

[PHOBoS]

I think I actually understood that, or at least part of it.

[L´Andratté]

Thanks for sharing, Ricko! Very interesting!