### FM Voice

FM voice synthesis [39] can be viewed as compressed modeling of spectral formants. Figure G.8 shows the general idea. This kind of spectral approximation was used by John Chowning and others at CCRMA in the 1980s and beyond to develop convincing voices using FM. Another nice example was the FM piano developed by John Chowning and David Bristow [41].

A basic FM operator, consisting of two sinusoidal oscillators (a ``modulator'' and a ``carrier'' oscillator, as written in Eq. (G.2)), can synthesize a useful approximation to a formant group in a harmonic line spectrum. In this technique, the carrier frequency is set near the formant center frequency, rounded to the nearest harmonic frequency, and the modulating frequency is set to the desired pitch (e.g., of a sung voice [39]). The modulation index is set to give the desired bandwidth for the formant group. For the singing voice, three or more formant groups yields a sung vowel sound. Thus, a sung vowel can be synthesized using only six sinusoidal oscillators using FM. In straight additive synthesis, a bound on the number of oscillators needed is given by the upper band-limit divided by the fundamental frequency, which could be, for a strongly projecting deep male voice, on the order of kHz divided by 100 Hz, or 200 oscillators.

Today, FM synthesis is still a powerful spectral modeling technique in which ``formant harmonic groups'' are approximated by the spectrum of an elementary FM oscillator pair. This remains a valuable tool in environments where memory access is limited, such as in VLSI chips used in hand-held devices, as it requires less memory than wavetable synthesisG.8.4).

In the context of audio coding, FM synthesis can be considered a ``lossy compression method'' for additive synthesis.