[sdiy] Generating acyclic waveforms?

[Jerry Gray-Eskue]

<<"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.">>

<<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.>>

I may be misunderstanding what "stretched harmonic spectra" actually means,
but if we take a sine wave fundamental frequency and a set of harmonics, and
use the fundamental sine wave to frequency shift (+- around zero) the
harmonics we would get a "precisely repeating waveform" with "inharmonics".

Will this class as "stretched harmonic spectra"?

-----Original Message-----
From: synth-diy-bounces at dropmix.xs4all.nl
[mailto:synth-diy-bounces at dropmix.xs4all.nl]On Behalf Of Ian Fritz
Sent: Monday, March 22, 2010 1:28 PM
To: Magnus Danielson
Cc: synth-diy
Subject: Re: [sdiy] Generating acyclic waveforms?


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

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