a single struc-
tural unit, half
of them mobile
and half of them
immobile. Mo-
bile meant that once
any of the
elements in
a chart was used
it disappeared
to be replaced
by a new one.
Immobile meant
that though an el-
ement in a
chart had been used,
it remained to
be used again.
At each unit
structural point,
a chance oper-
ation deter-
mined which of the
charts, numbers one,
three, five, and sev-
en or numbers
two, four, six, and
eight, were mobile
and which of the
charts were immo-
bile—not changing.
¶The structure, there-
fore, was in these
respects useful.
Furthermore, it
determined the
beginning and
ending of the
composition-
al process. But
this process, had
it in the end
brought about a
division of
parts the time-lengths
of which were pro-
portional to
the origi-
nal series of
numbers, would have
been extraordi-
nary. And the
presence of the
mind as a rul-
ing factor, e-
ven by such an
extraordina-
ry eventu-
ality, would
not have been es-
tablished. For what
happened came a-
bout only through
the tossing of
coins. ¶It be-
came clear, therefore,
I repeat, that
structure was not
necessary.
And, in Musicfor Piano, and subsequent pieces, indeed, structure is no longer a part of the compo- sition means. The view taken is not of an ac- tivity the purpose of which is to inte- grate the oppo- sites, but rather of an activ- ity charac- terized by process and es- sentially
purposeless. The
mind, though stripped
of its right to
control, is still
present. What does
it do, having
nothing to do?
And what happens
to a piece of
music when it
is purposeless-
ly made? ¶What hap-
pens, for instance,
to silence? That
is, how does the
mind’s perception
of it change? For-
merly, silence
was the time lapse
between sounds, use-
ful towards a va-
riety of
ends, among them
that of tasteful
arrangement, where
by separat-
ing two sounds or
two groups of sounds
their differen-
ces or rela-
tionships might re-
ceive emphasis;
or that of ex-
pressivity,
where silences
in a musi-
cal discourse might
provide pause or
punctuation;
or again, that
of architec-
ture, where the in-
troduction or
interruption
of silence might
give defini-
tion either to
a predeter-
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