Jean-Claude Risset observed (1964-1969), based on spectrum analysis of brass tones , that the bandwidth of a brass instrument tone was roughly proportional to its overall amplitude. In other words, the spectrum brightened with amplitude. This observation inspired John Chowning's FM brass synthesis technique (starting in 1970). For FM brass, the FM index is made proportional to carrier amplitude, thus yielding a dynamic brightness variation with amplitude that sounds consistently ``brassy''. A simple example of an FM brass instrument is shown in Fig.G.6 above. Note how the FM index is proportional to the amplitude envelope (carrier amplitude).
FM Harmonic Amplitudes (Bessel Functions)