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.