Music and Math: The Genius of Beethoven

The title of this video really struck my interest. I was envisioning it as something exciting and revelatory, a heretofore undiscovered secret of the music of this great artist. 
It’s also a TED talk, which means it will be fun and entertaining. It also means I shouldn’t have expected it to be on such a level of detail as I’d anticipated.
So there was at least some disappointment on that level, but it was balanced by an excitement to share what was here with other people, namely a friend of mine to whom I’d tried to explain Schoenberg’s twelve-tone idea (in Chinese). While I did explain the idea of consonant and dissonant chords as sounds that “work together” because of their relation to one another on the keyboard (really just a visual expression of that relationship), I did NOT express it in terms of their actual frequencies, which is what’s shown here. 
Having played a bit of this first page of this piece (poorly and slowly), I was familiar with the

consonance and dissonances, and therefore, this little snippet didn’t really offer much new to me, except the visualization of the frequencies, which was kind of cool.

So, while this little snippet likely doesn’t turn on any light bulbs for musicians or music people, it accomplishes a few things. 
  1. It uses an almost ridiculously famous first movement of a sonata (the whole of which is beautiful, not just this opening movement) to express the underlying logic of why music sounds “good” or “sad” or “happy.”
  2. It expresses that logic not only in terms of degrees on a keyboard, but with their actual frequencies. This gives not only a cool visual aid to be able to “see” consonance and dissonance as ideas, but explains (by extension, I guess) the pattern of black and white keys on the keyboard, and the idea of half steps, whole steps, and intervals.
  3. It shows that while music may seem overwhelmingly complicated on a large scale to anyone trying to learn music theory and write it (and overwhelmingly simple to those who think it’s just random notes picked out because they “sound good”), it shows that even simple patterns of three notes here (broken chords), when used effectively, can create wondrous beauty. Beethoven, among many others, was a master at manipulating harmonies and turning a simple little pattern (a “motif”) every which way to get everything he could out of it. It is this inventiveness, different from Mozart or Haydn, that makes Beethoven’s music so fascinating to both amateur and pro alike.


As a side note, I also found it interesting that for a piece like this that’s so well-known, it is more challenging than it looks. My piano teacher (who’s played Gaspard and the like at recitals) claims she could play the notes of this sonata (make the sounds) in elementary school, but says that to this day she still can’t play the piece from the standpoint of interpreting it logically and with enough direction as it requires. I found that fascinating.
I also posted this because I have another Tuesday post at the ready (for quite a while) that is kind of the exact opposite of this that I will be sharing soon, and I thought they would work nicely as opposites. We will also be getting around to more Beethoven soon. 



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