Math Mutation 54: Mozart Rolls The Dice
I bet there are many of you out there who, like me, learned to
program computers as a teenager, and were fascinated when you first
figured out how to make sounds come out of the speakers. If you're
like me, you wrote short programs to randomly generate and play
musical tones, hoping that if you ran them enough times, eventually
you would produce a brilliant melody that would make you the next
David Bowie. And after a while, you probably realized that randomly
producing *good* music was a lot harder than it first looked. It's
kind of like the monkeys-writing-shakespeare theory: maybe it would
eventually happen, but it would take a looong time.
Surprisingly, back in the classical days of the late 1700s, long
before the days of computers, creating classical music through random
rolls of the dice was a bit of a fad in Europe. Well-known composers
including Haydn and Mozart published systems where one could roll dice
to determine how to put together a large number of possible measures,
and thus randomly produce a piece of classical music. They would
supply a large set of pre-written musical fragments, combined with
tables that showed which one to insert at which point based on rolls
of a pair of dice. There are some questions about how seriously the
great composers took such music though-- Haydn titled his published
system the "Philharmonic Joke", and Mozart published his anonymously.
In fact, there is still some controversy as to whether Mozart really
created his random music-creation system-- the Wikipedia entry and
another website in the show notes seem to disagree as to whether he
was truly the author.
In those days when great music was being deliberately created, why
did composers feel a need to publish systems that would let people
randomly come up with a musical composition? One interesting theory
is that in those times and places, it became commonly expected that
educated classes would be able to compose short pieces of music, just
like they were expected to be able to write letters or make speeches.
But needless to say, the majority of pieces created by typical people
were pretty bad. By using Mozart's or Haydn's system to choose a
proper set of prefabricated measures, they could at least have a shot
at getting something listenable. Think of it as using clip art in a
presentation instead of trying to draw everything yourself. And if
the dice-roller had a little bit of talent, they could use the
randomly strung-together measures as the kernel of a larger piece they
completed themselves.
In the mid 20th century, these ideas of randomly created music
were revived by avant-garde composers such as John Cage. I'll
probably talk about him in more detail in another podcast-- he's quite
a colorful character. Most likely, you heard of him due to his piece
"4 minutes 33 seconds", a piece of so-called music which is entirely
silent. Supposedly the true music in that one consists of the random
enviromental sounds that surround you; personally, I think Cage was
just lazy that day. But I'm digressing.
In general I have yet to hear a piece of music created by
dice-rolling that I really enjoy. Even some Cage fans I've spoken to
admitted that his best supposedly random-generated pieces aren't truly
random-- while randomness might help inspire a starting point or
escape a bout of musical writer's block, it's the inspiration and
deliberate creations of the composer that create truly great music.
That's probably one reason why these musical dice games eventually
fell out of favor in the classical period, and why even 20th-century
randomly generated music isn't widely discussed outside snooty art
circles.
And this has been your math mutation for today.
References:
Article on
Mozart's Dice Game
Detailed
Rules of Mozart's Dice Game
John Cage at
Wikipedia
Mozart's
Dice Game at Wikipedia