Researchers map the math in music

Below left: The figure shows how geometrical music theory represents four-note chord-types - the collections of notes form a tetrahedron, with the colors indicating the spacing between the individual notes in a sequence. In the blue spheres, the notes are clustered, in the warmer colors, they are farther apart. The red ball at the top of the pyramid is the diminished seventh chord, a popular 19th-century chord. Near it are all the most familiar chords of Western music. Image: Dmitri Tymoczko -   - The connection between music and mathematics has fascinated scholars for centuries. More than 2000 years ago Pythagoras reportedly discovered that pleasing musical intervals could be described using simple ratios. And the so-called musica universalis or "music of the spheres" emerged in the Middle Ages as the philosophical idea that the proportions in the movements of the celestial bodies - the sun, moon and planets - could be viewed as a form of music, inaudible but perfectly harmonious.