[sdiy] Generating acyclic waveforms?

[Magnus Danielson]

Ian Fritz wrote:
> 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.
Probably. I just haven't read them, I haven't had time to look at your 
list of publications.
>> 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. 
That is much more specific than your previous answer. This is more of 
the lines of things I can accept, as you give sufficient hints about the 
mechanisms.

When time arise, I would love to dig into that field more, but currently 
my attention is on other things.

Cheers,
Magnus