The Geometry of Music

One of my favorite phrases I have quoted from people's reviews of my book is from K. Flekkoy, who had this to say at amazon.com: "an imaginative and strangely 'musical' way of imagining superimposed dimensions". I was strongly reminded of that phrase today when I saw the picture at left, which was created by Dmitri Tymoczko of Princeton University. I came across the picture in an article published a few days ago by ScienceDaily.com, click here for the full story.

The article is about three music professors -- Clifton Callender at Florida State University, Ian Quinn at Yale University and Dmitri Tymoczko at Princeton University -- who (to quote from the article) "have devised a new way of analyzing and categorizing music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric."

Their system uses colors and a five-dimensional grid to analyze and portray the differences and similarities between one piece of music and another: "geometrical music theory", as they are calling this new system, provides a rich set of visualization tools that analyze elements like rhythm, melodic density, and chord structure, in a sense boiling a piece of music down to its essence and providing ways of visualizing that essence.

In this picture, the red dot at the center represents a diminished seventh chord, and the other nearby dots are some of the chords we would be most familiar with. As an analysis method, it appears their system is more suited for chordal music, and "Western" sensibilities as opposed to the music of other cultures, but within that context these professors are saying this graphing method might be able to show the differences between the composition style of Lennon versus McCartney, or how classical compositions from centuries past are related to modern-day pieces.

It's All About Connections
Persons familiar with the Imagining the Tenth Dimension project will recognize one of my central themes here: what gives a piece of music its innate power, its emotional and cultural resonances? Thinking of music as being created from interlocking sets of memes that are connected across time and space is an important key, and it appears these three researchers are now providing us with new tools to categorize those musical memes.

Another related fascination for me is the rhythm of language, and how different cultures have their own patterns of pitch, rhythm, and grouping. How does emotion translate into speech in different languages, and are there universal physicalities for communicating sorrow, happiness, fright, (and so on) that transcend language? Might such connections be able to be tracked and coded with a similar visualization tool to the one we're looking at above?

A blog entry at Cosmic Variance talks about the work of researcher Diana Deutsch, who specializes in the psychology of music. There is a real audio interview embedded into that blog entry, listen to the first four minutes or so for a fascinating example of how music and language are so easily intertwined. When we begin to see ourselves as being part of patterns that exist across time and space, this all ties in nicely.

Edit: A few days after I published this entry, Millsley (one of the regular contributors to the tenth dimension forum) posted his latest list of fascinating links that fit into the Everything Fits Together paradigm. This collection of podcasts from WNYC about music as patterns was one of those links.

Enjoy the journey,

Rob Bryanton

Other entries related to this:
Waveforms in the Ten Dimensions
Music and the Dance of Creativity
Song 19 of 26 - Positive Vibes
Song 6 of 26 - Connections
Seeing Eye to Eye