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

[Jerry Gray-Eskue]

That explains its tonal qualities as it is markedly a "purer" sound than a
ramp, but far short of the "purity" of a sine wave.

Aaron, thanks for clearing up addition / multiplication of sine waves for
me.

Regards,

Jerry

-----Original Message-----
From: synth-diy-bounces at dropmix.xs4all.nl
[mailto:synth-diy-bounces at dropmix.xs4all.nl]On Behalf Of Tom Wiltshire
Sent: Wednesday, June 03, 2009 12:23 PM
To: Aaron Lanterman
Cc: sdiy DIY
Subject: Re: [sdiy] Harmonic content of the "sigmoid" half-sine wave



On 3 Jun 2009, at 17:36, Aaron Lanterman wrote:
>
>> So is the suggested fundamental not there, or is it created by the
>> total interaction of the original sine waves, their least common
>> fundamental frequency, ( even though not present in the generation
>> of the waveform ) and represented by the resulting wave form?
>
> That can happen, but in the case of the particular "sigmoid" we
> were discussing the fundamentally really is there. The Fourier
> coefficient a_1 is nonzero.

Aaron is dead right about the Sigmoid, but I think Jerry was talking
about my  'pulse' examples. Sorry, I was sidetracking this
conversation there...

I've made the following sigmoid:

http://www.electricdruid.com/Sigmoid.png

This was done by creating a standard ramp wave with 64 harmonics
(where each harmonics amplitude is 1/h) and then boosting the level
of the fundamental to 1.6 rather than 1. This can alternatvely be
seen as scaling the other harmonics down a little bit. Either way,
the sigmoid is a ramp with the harmonics backed off a little bit.

Regards,
Tom


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