What fascinates me about this article and video is the relationship of music and chords to the mobius strip (an abstraction of the surface of a torus) and music notes to the torus. I’m not the hottest in math (I have to work at – perhaps because I had so few good teachers in it) but it reminds of the relationship in Calculus of the derivative to the integral. I’ve had many discussions with GW Hardin about relationship of tones to the Rodin coil, Solfeggio frequencies and the apparent musical nature of the structure of the universe. This seems to also support that insight as the surface he is showing is a torus. I don’t know if you see what I see in this but I think you will enjoy the video either way. CLICK ON THE IMAGE TO PLAY BELOW… -Bill
Mathematical Impressions: Making Music With a Möbius Strip
The connections between mathematics and music are many. For example, the differential equations of vibrating strings and surfaces help us understand harmonics and tuning systems, rhythm analysis tells us the ways a measure can be divided into beats, and the study of symmetry relates to the translations in time and pitch that occur in a fugue or canon.
This video explores a less well-known connection. It turns out that musical chords naturally inhabit various topological spaces, which show all the possible paths that a composer can use to move between chords. Surprisingly, the space of two-note chords is a Möbius strip, and the space of three-note chords is a kind of twisted triangular torus.
For a thorough presentation of the ideas introduced here, suitable for both mathematicians and musicians, see “A Geometry of Music” by Dmitri Tymoczko.
The “Umbilic Torus” sculpture shown at the end of the video was created by Helaman Ferguson.