Whenever we talk about patterns,
manipulation of patterns and uses
of contrapuntal techniques to modify
a particular pattern, we always go
back to the work of Johann Sebastian Bach,
who was a master of composition and
manipulation - I mean in this particular
aspect of contrapuntal manipulation
of musical ideas - and in particular
there are some influential works that Bach
produced. One is the art of the fugue
and the other one is the musical offering
where he uses all these manipulation
techniques in an amazingly masterful way.
Now, the examples that I want to talk
about in this context are related to
the idea of a canon. For those of you who
are not familiar with what a canon is,
a canon is a piece of music that is based
on a single melodic line, that is played
or sung by a performer,
and then a second performer
enters with the same identical melodic
line but at a different time. So there is
a superposition of two identical lines,
with different starting points in time.
And the combination of these two identical
lines gives rise to harmonic and melodic
effects that generate
the composition itself.
If one is a student in countrapoint that
has to go through training in how to write
canons and canons of very different kinds,
this is not the place for me to go into
all these details, but there are some
very sophisticated canons that
one can write, and one is what is called
a crab canon.
A crab canon is a canon where there is
one melodic line that is sung or played
by one performer,
and the same melodic line is played
but retrograted by the other one.
So you have a single melody that one
performer plays left to right, and the
other one plays right to left at
the same time. And there is a famous
crab canon in the musical offering of
J. S. Bach that you can hear, that you can
listen to in the PowerPoint of this unit.
You can see actually the whole canon as it
is written. As you see, it is written only
in one line, and so the first performer,
the first voice, plays it normally, left
to right, and the second one plays
the score backwards. And this is actually
how these crab canons were written at
the time of J. S. Bach.
The second example is another canon
from the musical offering of J. S. Bach,
it is called the mirror canon. In a mirror
canon, we still have a single melodic
line, that is the principle line of
the canon, but then the response, or
the second performer enters at a
given point of the performance of
the first line, but instead of repeating
the same melodic content, it plays
the same motif, but inverted. So it's
an equilibrium between the original line
and the inverted line that start at
different times. Both a crab and a mirror
canon are demonstrated in the notebook,
where you can actually play with
the structure of it using very few lines
of code, so again it is a demonstration
of how these kind of algorithmic processes
give rise to very interesting
musical structures.