Bessel Functions
Just how do you know how "loud" each of the spectral components of FM synthesis is going to be ? This is very important because the relative strength of a sound's various spectral components, or "partials", is the basis for WHY the sound has the tone color or timbre it has. Sounds that have lots of strong high partials will sound much brighter than sounds that have weak high partials. Two sounds with the same number of partials, at the same frequency, may sound COMPLETELY different to you simply because the relative strength of the partials differs. This is absolutely critical to understand !
With the MODULATING FREQUENCY and INDEX VALUE controlling the Carrier Frequency, how can we predict musical timbre using FM synthesis ? What is controlling how strong or weak a particular partial component of the sound is going to be with FM ? The answer is BESSEL FUNCTIONS.
What are Bessel functions ? A long long time ago....... in a galaxy far far..... away..... oops, wrong story! Named after Friedrich Wilhelm Bessel (1784-1846), a German astronomer and mathematician, Bessel functions are just mathematical formulas and tables that allow us to predict the behavior of a number of physical phenomena, FM Synthesis being one of them.
Perhaps it's easier to think about Bessel Functions, if you can actually SEE THEM ? Press the cow button below:
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