very simple FM synthesis!

fm.cc

// clang++ -std=c++14 fm.cc && ./a.out | aplay -r44 -f S16_LE
#include <cstdint>
#include <cmath>
#include <cstdio>

using s16 = std::int16_t; // signed 16-bit samples
const auto rate = 1.0 / 44000.0; // 44 kHz
const auto τ = 3.14159265 * 2;

s16 to_sample(double x) { return s16((x<-1?-1:x>1?1:x) * 0x7fff); }

double wave(double t) {               // t in seconds
    const auto ωc = 110.0;            // carrier freq
    const auto ωm = ωc * 4;           // mod freq
    const auto ω3 = ωc * 23;          // op3 freq
    const auto A = 0.5 * exp(-3 * t); // carrier amplitude
    const auto β = 1.8 * exp(-2 * t); // mod amplitude
    const auto γ = 0.3 * exp(-1 * t); // op3 amplitude
    const auto φ = 1.5;               // feedback
    static double op3, opM, opC;      //  ┌───┐
    op3 = sin(ω3*τ*t + φ*op3);        // φ│ ┌───┐γ┌───┐β┌───┐A
    opM = sin(ωm*τ*t + γ*op3);        //  └→│ 3 │→│ M │→│ C │→
    opC = sin(ωc*τ*t + β*opM);        //    └───┘ └───┘ └───┘
    return A*opC;
}

int main() {
    for (int s = 0; rate * s < 2.0; s++) {
        s16 sample = to_sample(wave(rate * s));
        putchar(sample & 0xFF);
        putchar(sample >> 8);
    }
}