[sdiy] Harmonic content of the "sigmoid" half-sine wave

[Forbes, William ALGLSG-LXES]

> -----Original Message-----
> From: synth-diy-bounces at dropmix.xs4all.nl 
> [mailto:synth-diy-bounces at dropmix.xs4all.nl] On Behalf Of 
> Aaron Lanterman
> Sent: 03 June 2009 17:42
> To: sdiy DIY
> Subject: Re: [sdiy] Harmonic content of the "sigmoid" half-sine wave
> 
> 
> On Jun 3, 2009, at 12:15 PM, Scott Nordlund wrote:
> 
> >>  think you need some sort of nonlinearity for the 
> difference tones  
> >> to come out.    The ear (and/or brain) isn't necessarily 
> perfectly  
> >> linear though.
> 
> This is true... some multiplicative tyoe mixing can occur in 
> the brain. It's a very very subtle effect, though. Ian Fritz 
> has posted about this in the past.
>

Note:
sin(a) + sin(b) = 2 * ( sin( (a+b)/2 ) * cos( (a-b)/2 ) )

and:
sin(a) * sin(b) = -( cos(a+b) + cos(a-b) )/2
 
Thus what happens when we hear the beat frequency between two
frequencies?

If I play 19khz and 20kHz tone I don't hear the 1kHz until distortion
causes
the multiplication terms to be generated.
My ears don't work at 19kHz so I hear nothing when the system is linear.
But I can quite easily hear the 1kHz when the system is non-linear.

Yet I can quite easily hear a beat frequency when tuning a guitar.

<snip>

> 
> - Aaron
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Bill Forbes.