Why In FM the modulation index is defined as the peak frequency deviation divided by the frequency of the modulating tone, m = Δf / fm. For example, 5 kHz of deviation produced by a 1 kHz tone gives an index of 5. Because it depends on the instantaneous modulating frequency, the index changes as the audio pitch changes, even if deviation stays the same. The related quantity called deviation ratio uses the maximum deviation over the maximum modulating frequency, and it is a fixed number for a given system.
Watch out The choice dividing transmitted bandwidth by modulating frequency looks similar, but bandwidth is a result of modulation (Carson's rule), not part of the definition; amplitude of the modulating signal only matters because it sets the deviation, not directly.
Modulation index = deviation over tone frequency. Deviation on top, always.