A Few of My Favorite Sigmoids (2018)

You take a damped sine wave, where its amplitude gradually moves towards zero, of some frequency and you pass it through the particular sigmoid function. Just like you can play a sine wave, you can play the resulting tone.

If you look at his code, you can see how he wrote it:

  fn gen_audio(len: usize) -> Vec<f32> {
      //(0..len).map(|i| ((i as f32).powi(2) * 1e-7).sin()).collect()
      let f = 440.0;
      let d = f / 44_100.0 * 2.0 * std::f64::consts::PI;
      (0..len).map(|i| {
          let i = i as f64;
          let amp = 100.0 * (i * -4e-5).exp();
          let tone = (i * d).sin() * amp;
          tone.max(-1.0).min(1.0) as f32
          //erf7(tone as f32)
          //(tone / (1.0 + tone * tone).sqrt()) as f32
          //tone.tanh() as f32
      }).collect()
  }