Mathematics & Music

06 April, 2014

The common denominator behind all music.



By Terence Peterson




If there is one thing to take away from this article, it is that mathematics and art are not as opposed as oil and water, for they share a primary purpose: expression.


Maximalism - Lubomyr Melnyk - Piano




Lubomyr Melnyk is the fastest recorded pianist; he can play up to 19 notes per second, continuously.  The sound of his fingers flying across the keyboard evokes the feel of some gigantic ticking machine made up of so many moving parts that one can't truly hear all of them as separate.  In line with this, he refers to his personally developed musical style as "continuous music" because his pieces are unbroken streams of sound; with no pauses, no phrases, the quality of the music as a unified whole is intended to bring the listener peace.  There is a powerful duality at work in Melnyk's philosophy.  He reaches towards thegreatest possible quantity of notes to express above all the unity, the holisticone-ness of all existence.  But don't take my word for how cool this guy is; check the video.  There's an interview in the middle, sandwiched by two stunning performances!






Counting - Philip Glass - Violin



Philip Glass


You can't have a conversation about the history of minimalism without mentioning this guy.  One of the greatest influences among contemporary composers, his spare, rhythmically driving harmonies often evoke a deep sense of wonder.  In the video Tim Fain, a truly virtuosic interpreter of new and old music, performs a concise excerpt of what could be considered Glass' magnum opus, the 1976 opera Einstein on the Beach.  A plotless, abstract exploration into the mind of the man whose discoveries both revolutionized our understanding of the universe and resulted in the creation of the atom bomb, the four hour opera makes a point of expanding miniscule (one could say atomic) melodies one note at a time, effectively counting up, and collapsing them back to the single repeated note, effectively counting down.  The effect can be almost claustrophobic; as the process becomes apparent long before it is finished winding up and back down, the listener is trapped in the omniscient sense of knowing already what is yet to come.  On the other hand, there is something inexplicably relatable and pleasing about the oscillation found in Philip Glass' works, and this piece is no exception.





Expressions - Bach - Violin




For the uninitiated, the common image of Johann Sebastian Bach is often that of the stodgy old classical composer from three centuries ago whose music was special for being beholden, further that most other composers were willing to commit, to all these mathematical and harmonic rules, of counterpoint, voice leading, etc. One might think that choosing every note on the basis of some rule or another could be… restricting, to say the least.  Certainly there are many artists in the modern era, especially since the Romantic century, who specifically aim to break all the rules.  And yet this piece, the Ciaccona that serves as the finale of Bach's Partita No. 2 for solo violin, is a monumental tour de freedom.  What makes the Ciaccona so incredible is the way it seems to draw on an infinite well of expression, taking simple ideas and restructuring, and re-voicing them until it seems they can truly no longer be expounded upon.





Karlheinz Stockhausen - Electronic Music




Gesang der Jünglinge, or Song of Youth, is among Stockhausen's earliest works, and demonstrates quite effectively his progressive tendencies.  He had a lot of unusual and unprecedented ideas about music, but also about most things.  This piece, bordering on musique concrète, takes computer-generated tones and odd, deliberately artificial timbres and combines them with processed recordings of children's voices to create what can only be called unusual.  But fun, if you're into the weird stuff!