Phase Art: The picture above is of the Wikipedia 3:2 phase modulation example 1 and corresponding comparison with frequency modulation as displayed by an oscilloscope in X-Y mode.2 This is a mode typically used for testing phase relationships between signals and is well known as the method for displaying Lissajous curves – a sine wave on the X axis and a cosine wave on the Y creates a perfect circle, for example.
What I hadn’t realized is that a phase modulated signal against the same (unmodulated) reference frequency could create the kinds of shapes above. (The frequency modulated signal against the same unmodulated reference frequency produces a rotating oval.3) In this case the phase and (linear) frequency modulated signals are presented simultaneously, resulting in the bands of lines that look something like a staff in music notation.
In this case 750:500 Hz ↩
Playing with the linear frequency index (the degree to which it approaches exponential frequency modulation) alters the number of lines present and their proximity. The more exponential the curve, the more one approaches familiar Lissajous territory. ↩