Signal Transduction: seeing the music

Looking at the problem with a different perspective often allows us to perceive new insights and patterns. When recording neurons, neuroscientists often convert the electrical signal to sound, which provides an auditory feedback and help him/her to locate the region of interest. For a music, transduction to visual domain or seeing it is fun and interesting.

I've been always fascinated by the repeats and symmetries in the variations, so I wanted to visualize the structures. A simple Google search pointed me to the MIDI files, and I downloaded and import the MIDIs of the variations. Then I cleaned it up and performed simple processing such as converting each note (e.g.: G6) into frequency (e.g.: 1567.98 Hz).

Voilà, the portrait of the famous aria:
aria time/frequency plot
Here's a version with log scale:
aria time/frequency plot log

A beautiful symmetry lies in the variation 14:
variation 14 time/frequency plot
variation 14 time/frequency plot log

In variation 17, the repeated increases and decreases become apparent and linear in the log plot:
variation 17 time/frequency plot
variation 17 time/frequency plot log

The alternating trills in the 28th variation almost form solid lines. Now with visual aids, the progression of the trills become apparent:
variation 28 time/frequency plot
variation 28 time/frequency plot log

The fiery arpeggios in the 29th variations:
variation 29 time/frequency plot
variation 29 time/frequency plot log