[sdiy] Harmonics Question

[Magnus Danielson]

On 11/03/2011 04:51 AM, Kyle Stephens wrote:
> This has always been rather unclear to me: are harmonics measured in integers because that's an "easy" metric to employ, or do they occur naturally in integer multiples? Did the phenomenon or its measurement come first?
>
> For some reason that seems overly "convenient" to me, or is it just a lucky happenstance? Though obviously other things in nature occur in whole numbers (at least I think I have "2" arms).

In one-dimensional resonance systems (strings, pipes etc) you would get 
good integer relations if using simplifying assumptions. However, the 
end impedance might be different between different frequencies, so 
over-tones might experience a different tuning and hence they would not 
form integer multiples to the fundamental resonance.

Effort is made in instruments design to tune-up them to integer 
relationshhip since it does sound better. Also, frequency shifters can 
be used to create a particula effect which occurs when they do not line 
up properly.

> Follow up question: just how do vacuum tubes tend to produce predominantly even harmonics, and likewise why do transistors rock the odd harmonics?

Recall that non-linear functions changing sign on through-zero will 
deliver prodominantly odd harmonics and non-linear functions not 
changing sign on through-zero (typically mirror-like) will deliver 
pro-dominantly even harmonics. Non-linear devices like tunnel-diodes 
will dynamically provide all these responses with both signs, but I have 
not seen anyone else to a CV-waveshaper with them.

Cheers,
Magnus