[sdiy] Harmonics Question

[Harry Bissell]

Not quite. On a vibrating string you will always get harmonics, but they could be damped
easily by the width of your fat finger, or go outside the human hearing range. The obvious
choices like 1/2 the string length (2nd harmonic) have the highest amplitude and lowest frequency.

High enough harmonics can be dampled bu the media (string) itself.

I'll avoid talking about vibrating columns of air (someone else will undoubtedly be an expert...

Strings have ~integer~ harmonics only if they are perfect strings, that have mass and tension, but do not
have stiffness.  Most texts try to illustrate this by modeling a sting as a series of weights (balls) connected with
links like a bead chain. Stiffness makes the harmonics sharp (higher) in frequency than the integer value.

Bell ~harmonics~ are usually non or more complex integers because they are two dimensional vibrating systems
rather than one dimensional...

The odd-even harmonic question is different.  Waves that are symmetric around 'zero' such as sine, triangle
and square have only odd harmonics (sine has only fundamental or 1st harmonic, one is an odd number). Asymmetric
waves like sawtooth and pulse (not 50% duty) have a mix of odd and even harmonics.

Transistor amplifiers usually clip symmetrically on positive and negative peaks, thus odd harmonic distortion.
Tube amps more often rely on different bias schemes like "class A" which overload asymmetrically, causing some
even harmonic distortion (as well as odd)

Why they sound more ~phat~ to some is a mystery.  A tube amp and transistor amp could in theory sound identical !

H^) harry



----- Original Message -----
From: David G Dixon <dixon at mail.ubc.ca>
To: 'Kyle Stephens' <lightburnx at yahoo.com>, synth-diy at dropmix.xs4all.nl
Sent: Thu, 03 Nov 2011 01:26:24 -0400 (EDT)
Subject: Re: [sdiy] Harmonics Question

> 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).

Pick up yer guitar and play some harmonics (pick a string while just
touching it at the 12th fret (first harmonic), 7th fret (second harmonic)
and 5th fret (third harmonic), and you'll have your answer.  Each harmonic
divides the string into an integer value of equal vibrating sections
separated by non-vibrating nodes.  If you touch the string in a place where
it is not divided into a relatively small integer of equal lengths, you
won't get a harmonic.

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-- 
Harry Bissell & Nora Abdullah 4eva