The "pitches" or "tones" of random noise can be plotted
on a graph like this:
Musical tones present a different image. For example, the melodic motion of this chant (excerpt):
can be plotted in this manner:
In this example, the prominence of melodic motion from the tone c to G, c to a, c to b, and c to itself is shown in the magenta rectangles. The frequency of tonal movement between the notes a and G is also a feature of this antiphon.
These tonal movements are easily observed in the notation of this chant (see the excerpt provided above) and one might wonder why a scatter plot has been used to demonstrate what we can easily notice on our own.
Some Benefits: In computer-assisted methods of analysis, digital transcriptions can be analyzed quickly, and they can be combined together. For instance, the melodic motion of the chants in an entire manuscript can be plotted on the same graph, thus potentially revealing melodic tendencies (such as a preference for the note c over b) in whole manuscripts or repertories.
See more analysis and description here.