[sdiy] Generating acyclic waveforms?

[cheater cheater]

It happens in all accoustic instruments to some degree. No accoustic
instrument adheres to the ideal string and generally ideal resonator
equations. Even wind instruments have that, because even if the air
can generate a perfect resonator, the instrument's body will have that
effect and, by leeching the accoustic power from the resonator, will
generate even more anharmonic content.

D.

On Sun, Mar 21, 2010 at 22:19, Tom Wiltshire <tom at electricdruid.net> 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.
>
> Thanks,
> Tom
>
>
>
> On 21 Mar 2010, at 16:58, cheater cheater wrote:
>
>> Most people here know that in piano timbre the partials are sine waves
>> that are not spaced like in synth waveforms. That is, in the
>> synthesizer, if the note's fundamental frequency is F, then harmonics
>> will be at 1F, 2F, 3F, 4F etc. In a stretched-harmonic waveform, the
>> frequencies will for example be of the form 1sF, 2sF, 3sF, 4sF, and so
>> on, where s is the stretching factor. For s=1 we have the usual
>> harmonic series. For s which is not an integer and not a specially
>> chosen rational number, we have a probability of 100% of generating an
>> acyclic waveform. Of course, the spacing of harmonics in the piano is
>> more complex than that, but this is the first approximation.
>
>