John Cage was an American composer
and music theorist that has shaped
music in the 20th century in many
different ways. He was a pioneer,
has been a pioneer in indeterminacy
music, electroacoustic music and
non-standard use of music instruments.
He has been a figure that has lived
within a wider framework of the evolution
of modern art in the 20th century, being
instrumental also in dance, for instance
he was the lifetime partner of Merce
Cunningham who was a very famous
and influential dancer and choreographer
of the last century.
I want to discuss here a particular piece
of John Cage, that is based on
indeterminacy and randomness. It is
called "Music of Changes", it is a piece
for piano - actually it is a long
collection of pieces for piano
written for David Tudor who was a pianist
and friend of John Cage and who has
premiered many of his compositions.
Now, the process of composition of
this piece is based on decisions that
are made using a process that uses
the "I Ching", this Chinese text
of divination - very old text of
divination - that is mapped onto
all the musical parameters of this piece.
You can hear it in the PowerPoint
associated with this video, or you
can look for it on YouTube.
Let's see how this composition
comes about from the use of this
I Ching for the mapping and decision-
making in the composition process.
So the I Ching is a text that describes
combinations of 64 hexagrams -
hexagrams, you can see this also
in the Notebook that is associated
with this video, are 6-line figures
of either "yin", broken lines or "yang",
solid lines and the commentaries that
are associated to particular combinations
of these hexagrams. There are two main
methods for building up lines of an
hexagram, either by using 50 yarrow
sticks or three coins and the process
is also kind of - it's a more complex
process than just extracting a
particular number from the yarrow
sticks or the coins. Some lines
are designated as old lines, that means
that then they are changed to create
a different hexagram, and then as I
was saying, the text that is associated
to a combination of hexagrams is
what is used for divination. So it is
kind of an oracle that comes
from the randomness of the choice,
that comes from the process
of extracting and creating these
hexagrams.
So the hexagrams are here, on this slide
you can see them, and here what John Cage
did for this particular piece is employing
the I Ching-derived chance operation to
create charts for the various musical
parameters. So, there is a chart
for tempo, there is a chart for dynamics,
one for sounds, one for silence, one for
durations or superpositions
of different sounds. And with these charts
he was able to create a composition with
a very conventional manner of notation,
that means he actually wrote music
using the traditional notation system
of Western classical music, but all these
elements were derived from a chance choice
through this I Ching system.
You will see in the Notebook that I have
written a software version of the I Ching
divination system that is then used
to demonstrate how using this system
we can actually compose music in
the style of Music of Change.
So here are some of the notes from the
original Cage notebooks, where he lists
different hexagrams and different
parameters, and this is a way of mnemonic
or mapping these parameters into
the score. The actual procedure for
mapping is here, I mean is described
in this slide, there are 8 charts
for sound and silences, 8 charts
for durations, 8 charts with amplitudes
and then a single chart for tempo and
contrapuntal layers. So each chart has
8 rows and 8 columns, like you see here,
and then there are some pre-compositional
decisions that you make, so the
sounds chart is only single pitches
intervals, aggregates and constellations
or more rhythmic combinations of notes,
Cage uses all the twelve tones of
the equal temperament system and
makes also similar decisions for rhythm.
So this is to say that it is
through that that this
composition is firmly founded on
random choices that come from
the randomness of the generation
of the hexagrams but it also indicates
how important the role of the composer
is here, in harnessing this randomness in
a coherent aesthetic - musical aesthetic.
So it's not just that we throw dices
and we put numbers or notes on a score,
there is a framework that is built around
the process and makes it complex and
interesting. So these are two examples
of actual scores of these charts,
the translation of the charts, into
scores where we see here sounds,
so notes, and combinations of notes,
and here is for rhythm for instance,
these are different rhythmic figurations
that Cage uses in his composition.