Why is saxophone growling produced by modulation of the sound waves?

[Baluncore]

I don't see how low frequency product generation is any more relevant than high frequency products.

The growling is a sub-harmonic, at a lower frequency than the fundamentals of the two input frequencies.
Harmonics above the fundamental, f⋅n, are generated by amplitude distortion.
Sub-harmonics, below the fundamental, f/n, are generated by energy storage, which can be seen as time distortion.

 

[sophiecentaur]

Sub-harmonics, below the fundamental, f/n, are generated by energy storage,

Calling it "energy storage" seems unnecessary. With any form of modulation there is no distinction between upper or lower sidebands - you put it all in the pot and you get your products out. When the modulator involves a delay then you clearly have to wait for the result until all the products have caught up and that will affect the temporal response (pulse shape etc.). The growl will take time to build up. Our hearing system deals with low frequency sounds a bit differently and the 'tuning' of low strings and organ pipes is less critical. The growl is down there.

I think you may be referring to the way the attack of a note is affected by (or described by) the maximum length of the temporal response of the system.