Harmonics question

[Stopp,Gene]

>
>I understand that a square wave is made up of sine waves, but what are
the
>exact frequencies that the harmonics oscillate at?  For example, if you
>have a square wave at 130Hz are all the harmonics octaves up and down
from it?
>

Hey, I can answer that....

For any waveform other than a sine, there will be harmonics that are
higher in frequency than the fundamental, and none lower. Which
harmonics are present and what amplitude they have in relation to the
fundamental are determined many factors, such as the right/left
symmetry, positive/negative symmetry, sharp edges, etc. In the case of a
perfect square wave (i.e. infinite rise and fall slopes) there will only
be odd harmonics, with decreasing amplitude as you go up in harmonic
number. There is a standard harmonic series where the first harmonic is
the fundamental, the second is an octave up, the third is an octave and
a fifth up, the fourth is two octaves up, and so. Due to a square wave's
symmetry both right/left and up/down, there are no even harmonics - that
is, the second, fourth, sixth, eighth, etc. are entirely missing, and
the odd harmonics - that is, the first, third, fifth, etc. are all there
in decreasing amounts as you go up.

The odd-only harmonic series of a square wave causes it to have a
"hollow" sound. In contrast, a sawtooth waveform with its "full" sound
has all harmonics, even and odd, and you will notice that a sawtooth is
not a "mirror-image" symmetric waveform like the square. A triangle wave
does have this symmetry, and so once again has only odd harmonics, but
since it is much closer in shape to a sine wave, the harmonic
intensities are drastically reduced compared to a square.

This is just a quickie explanation off the top of my head. There are
much more in-depth explanations, and one I can think of is an article in
an old Electronotes that has all the math.

 - Gene