[sdiy] Generating acyclic waveforms?

[Magnus Danielson]

Ian Fritz wrote:
> At 03:19 PM 3/21/2010, Tom Wiltshire wrote:
>> Does anyone (physicists?) on the list know whether this harmonic
>> stretching occurs only with strings, or do similar things happen in
>> wind instruments? reeds?
>>
>> What I'm really asking is whether this is a 'string' effect or an
>> 'acoustic' effect.
>
> It's a string effect.  The higher harmonics require a sharper bending 
> radius and therefore they see a stiffer elastic constant.  Since the 
> string is vibrating freely, the higher frequencies run back and forth 
> faster than the lower ones.
>
> You wouldn't see a significant effect like this in winds because the 
> waves are longitudinal waves in air and therefore have negligible 
> dispersion.  Additionally, driven systems such as winds excite 
> coherent waves, so there can be no speeding up of specific harmonics 
> over many cycles.
However, the end-impedance would allow for a similar effect, such that 
the resonance frequency of the overtones would not match up exactly with 
the integer multiples frequency-wise form the base frequency. To 
illustrate the impedance effect on a wind instrument... learn how to 
bend the tone by fractional opening or closing the holes. With a little 
training to get it.
> Other percussive instruments such as stricken bars are just an extreme 
> extension of the string phenomenon, although more complicated because 
> of the qualitatively different kinds of modes that can be excited. 
The long elevator wires of Mimer laven comes to mind. Very cool sound.

Cheers,
Magnus