I understand why FM is preferred for music: noise is mostly amplitude modulated, FM yields much higher fidelity. I also understand why commercial FM signals have a much larger bandwidth than commercial AM signals: the signal spectra of the former are 5-10 times wider than the latter. I also understand the mathematics of FM, Bessel functions 'n all.
What I don't understand is the reason for using a large modulation index >> 1. A modulation index of 1 indicates that the width of the FM modulated spectrum is comparable to the width of the signal spectrum. If the modulation index is >> 1, the width of the FM modulated spectrum is much larger than the width of the signal.
It seems to me that the wider bandwidth doesn't provide any additional information. As a matter of fact, the signal power for a large modulation index is divided up among multiple carriers and sets of sidebands instead of being concentrated in a single carrier and set of sidebands.
Why is a large modulation index used?