I had this idea that music and
mathematics are deeply linked one with another. What if the masterminds of the
chess board were composing music? Mathematics in music is nothing new.
Many composers were dealing with the question of how formulas and notes could
be combined. In fact, there are many equations hidden or evident in a song,
starting with the measures. It could be three quarter or four quarter – as a
classical way – or anything else you like, if you’re only able to count and play it.
There have been attempts to divide music in measures like three PI over four
hundred fifty six times twenty three divided by two thousand three hundred
forty five point seven eight nine times five point three two one, but this cannot
be played even by highly trained musicians. Anyway, this isn’t blurring out
the fact that the value of all the notes in the measure must not exceed the
measure itself in total – or in other words: one cannot override the logic of
mathematical equations. There are 12 notes forming an octave. In general, the
weighting of each one is quite different in each musical piece. Schönberg, however,
tried a different approach. Normally, in a song – let’s say in C major – notes like
A and G and C are played more often than C sharp and G sharp. Not so in Schönberg’s
compositions. Although this is a mathematical rule and our ears can get
used to this kind of music most of the people do not prefer it over popular
music. The same is true for another approach:
Mathematical musicians have composed pieces the notes of which are completely
random. Take a look at “the world’s ugliest music” composed by Scott Rickard. I
can’t really tell that this kind of music is ugly, but somehow it is very
difficult to feel attached to it. In chess nothing is random. Players are
planning multiple steps ahead and include several alternatives, lurking for
the opponent’s mistakes. And then: Checkmate, the game is over. A chessboard
is very structured. It is completely symmetric. A chessboard is pure
mathematics. It’s not about equality since each figure has individual
features the player has to know, to respect and to use each of them for its
best. Professional chess is played by masterminds. Can a chess game be
transferred into music? I wanted to try an experiment. Unfortunately, I don’t have
any genius chess player composers in my circle of friends. So I studied a chess
match which took place in Sevilla in 1987, more than 30 years ago. It was
played in the exact way that I’m reconstructing in a one-minute musical
piece by Anatoly Karpov and Garry Kasparov. Both are multiple world champions.
In 1987, Kasparov defended his title against Karpov only a few moves ahead.
Here’s the setup of the experiment: A chess board has eight times eight fields.
Eight also is an octave, let’s say from C to C, leaving out the flats and sharps. We
can decide later to transpose to a different key, but for now, let’s stick to
the white keys which at the same time is the Aeolian mode in C. We have another
premise: Lines 1 & 8 mark one-eighth notes, 2 & 7 quarter notes, 3 & 6 half notes, 4 & 5 whole notes. If the succeeding node is the same, for
example, G succeeds G, the value of the next G is put into half, the other half
is a pause.For example, here two Gs succeed each other, so the second G has
half the value, so the succeeding G is half of the value
that it normally would be, the other half is a pause. I do not know where this is
going, but I’m expecting awesome things to happen.
Let’s continue. There are white and black figures. White is an acoustic guitar,
black is a bass guitar. So we have Kasparov on the acoustic guitar and
Karpov on the bass guitar. Isn’t that great? To make the sound of the music
more complex I will add two more guitars that double the voices in a fugish
style. I still do not know where this is leading us to. The song has a sudden ending in the midst of time, such as the game ends unexpectedly with no king in sudden
danger. Obviously, this gentleman had enough
brain power to realize he was beaten. I do not. Could you please explain this to me
like I’m a four-year old? All right. Let’s compose some music. The
next minute you will feel the spirit of a chess game that took place more than 30
years ago. I can see the two chess players in front of each other,
and I can feel the silence of the audience. Hold your breath.