[sdiy] Generating acyclic waveforms?

[Ian Fritz]

At 08:18 PM 3/21/2010, Magnus Danielson wrote:

>  I also think you might have missed the finer details that occurs in 
> acoustical resonators such as used in crystal oscillators,

Then you might want to look up my dozens of publications in the field.


>where fundamental frequency and overtones is known to be non-harmonic due 
>to among other things impedances, and that also many modes of oscillation 
>occurs.
>It is not entirely impossible, that similar effects do haunt air-resonant 
>open-ended resonators such as wind instruments, which is what I proposed 
>passingly. If you do not match the impedance carefully, the resonances 
>will not match up harmonically and the produces waveform will be periodic 
>at a frequency much lower than the fundamental, but not have the usual 
>relationships to the fundamental tone, as you then point out.

There is a concise discussion of all this in Fletcher and Rossing, "Physics 
of Musical Instruments" Ch. 5. They write:

"Sustained tones from real musical instruments do, however, have precisely 
repeating waveforms, and so their their individual modes must be somehow 
locked into precise frequency and phase relationships despite the 
inharmonicities of the natural resonances."

Yes there are situations where driven nonlinear systems give non-harmonic 
responses, such as the chaos generators I have been working on for the past 
several years, wolf tones in cellos, etc.  There was even a paper a while 
back that demonstrated the period doubling route to chaos in a model clarinet.

But the original question was whether wind instruments have stretched 
harmonic spectra, and the answer is still emphatically no, because they are 
practically always in the phase locked regime, as widely discussed in the 
many books and publications on the subject.

Ian