[sdiy] Generating acyclic waveforms?

[Ian Fritz]

At 07:06 PM 3/21/2010, Magnus Danielson wrote:

>>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...


No. The played notes have harmonic spectra, because they are periodic.  (In 
mathematical terms this is known as "Fourier's theorem").  You are perhaps 
thinking of the resonances of the impedance curves, which are affected by a 
number of parameters, including the shape of the bore and end effects.  The 
art of making instruments is to try to get the two spectra to match 
reasonably well.  This is *extensively* discussed in Benade's book 
"Fundamentals of Musical Acoustics", chapters 20-23.

Ian