Most of the time, the things that the reddit community find on the web are ho-hum, but sometimes they can be absolutely extraordinary! Case in point, this video, appropriately posted in the math subreddit, shows a cool logarithmic spiral visualization of one of the most famous pieces by 19th century Hungarian composer Franz Liszt, the beautiful “Hungarian Rhapsody #2″. I’ll let the video’s creater explain his motivation behind the project:

In a piano, notes repeat every 12 semitones (or keys, both black and white), and each whole interval doubles the frequency of these notes. Together, these notes form what we call a pitch class.

It occurred me that the shape of a spiral has all the correct properties to represent this relation between notes. So I wondered, how would piano music look like if it was represented as a spiral of keys?

In this representation, the notes with lower frequencies are in the center of the spiral, starting with A0 (as in the piano). Each radial block of keys represents a single pitch class, so octaves (when two adjacent notes of the same pitch class are played togeter) look like a pair of keys being pressed radially

For the musically and mathematically disinclined, it’s a cool plot that shows interesting patterns based on the similarities between the structure of a piano and a logarithmic spiral! Enough talk, check out the cool result: