Fons Adriaensen wrote:
On Sat, Jul 09, 2011 at 09:41:04PM -0400, Marc Lavallée wrote:
If you could help me understand spherical harmonics, I'd be a "MAG
fanboy" in no time. The best didactic resource I found is a very
strange article titled "Notes on Basic Ideas of Spherical Harmonics".
It's so good that I barely understand 10% of it.
What you probably need is some intuitive understanding of them.
I've tried it many times, and the following seems to work well
with most people interested in the subject.
You are probably familiar with the fact that a cyclic waveform,
e.g. a square wave, corresponds to an harmonic line spectrum:
if the fundamental frequency is F, the waveform is the sum of
a number of sine/cosine waves with frequencies k * F, with k
an integer.
The square wave is exactly the oddest example for musical or acoustical
purposes which I could imagine!!
Firstly, there are serious problems to sample this. (You would need very
high sample frequencies, and just to receive some form of approximation.)
Secondly, any amplifier or any loudspeaker would have "seious" problems
to reproduce this. Thirdly, I don't know how a square wave sounds...
:-) (ok, this was a joke...)
As a violinist, my choice would be the sawtooth wave, just for
demonstrational purposes.
Now some cite from the little accurate Wikipedia:
http://en.wikipedia.org/wiki/Square_wave
A square wave is a kind of non-sinusoidal waveform
<http://en.wikipedia.org/wiki/Non-sinusoidal_waveform>, most typically
encountered in electronics <http://en.wikipedia.org/wiki/Electronics>
and signal processing
<http://en.wikipedia.org/wiki/Signal_processing>. An ideal square wave
alternates regularly and instantaneously between two levels. Its
stochastic counterpart is a two-state trajectory
<http://en.wikipedia.org/wiki/Two-state_trajectory>.
And this is not about acoustics, unless you talk about synthesizers.
The rest you wrote is probably right, although I didn't have time to
reflect about this. ;-)
I don't want to annoy anybody or you, but don't explain acoustics via
square waves...
Best,
Stefan
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