AMFM paths

The amfm path is the most complicated path of all. Here is the function used to generate it:

$$f(t) = (1 + sin(2 \pi a_m t / sr)) * sin(2 \pi f_c t / sr + f_c/f_m * sin(2 \pi f_m t / sr))$$

Never mind if you don't follow the math here. What's significant about this is that it takes the John Chowning's ``classic'' function for frequency modulation:

$$f(t) = sin( 2 \pi f_c t / sr + f_c/f_m * sin(2 \pi f_m t / sr))$$

and applies the amplitude modulation function to it:

$$f(t) = (1 + sin(2 \pi a_m t / sr))$$

There are 3 variables you need to set: a_m, f_c, f_m. Here's how you can do it:

20 40 amfm(am=0.1, fc=0.2, fm=0.3) periods(10)
1000 -1000 amfm(am=0.01, fc=0.02, fm=0.03) range(5000,-5000)

Of course, you can also give the number of periods and the range to this path, as shown above.

Here is a datafile that uses the amfm paths, followed by a plot of the paths.

     output(sound.wav)    # name of the output soundfile
     duration(5)          # duration of the transformation
     initial(1)           # play the initial state for these many seconds
     final(1)             # play the final state for these many seconds

     10 50 amfm(am=0.1,fc=0.2, fm=0.3) # duration in samples
     -500 500 sin                  # amplitude

     40 80 amfm(am=0.01,fc=0.02,fm=0.03) # duration in samples
     10000 -10000 tri              # amplitude
    
     30 60 amfm(am=0.9, fm=0.8, fc=0.7) # duration in samples
     -10000 10000               # amplitude
    
     20 40 amfm(am=0.6, fm=0.5, fc=0.4) # duration in samples
     1000 -1000 sin              # amplitude

The values for am, fm, and fc can by any floating-point number. Values greater than 1 tend to ``noisy'' very fast.