9.
Make it swing with smooth time...
So
far we played around with musical items that were set on
striated
time,
i.e. with a regular beat imposed by the time base (metronome, see §4.3).
Indeed it was possible to change the metronome setting (although not in the
middle of an item) and the time setting algorithm provided for infinite
flexibility with sound-objects relocated or truncated on the basis of
individual properties. However it seemed impossible to program an
accelerando
or some non-metric time-pattern like the typical elongated third beat in
Saturday evening's waltz.
With
smooth
time
you will be able to combine "plasticity" with accuracy. Suppose for instance
that you want BP2 to play
do5
re5 mi5 fa5 - la5 si5 do6_ mi6
(in
which '-' is a silence and '_' is the prolongation of do6) with the following
time-pattern:
Fig.27
Time-pattern with irregular beats "t1",
"t2", etc. are
time-objects,
somehow similar to
sound-objects
except that they do not contain any sound-generating code. Here the piece is
divided in two sections, namely "t1" and "t2", each of them lasting five beats
with different
physical
durations
.
Let us assume that "t1" is a "normal duration" yielding five beats in 2.5
seconds, therefore we will set mm = 120. Here the metronome does not construct
a regular pattern of
time
strea
ks.
It only serves as a time reference. This case is referred as
measured
smooth time.
The second section "t2" is also five beats but it lasts 3.75 seconds, i.e. 1.5
times the first section. When specifying time-patterns each duration will be
written as an integer ratio. We will therefore write:
t1
= 1/1 t2 = 3/2
(We
could write t2 = 150/100 or any equivalent ratio as well.) This statement
contains three pieces of information: (1) t2 is 1.5 times longer than t1, (2)
the default duration of t1 is one metronome beat, (3) the default duration of
t2 is 3/2 metronome beats. Of course, (3) may be deducted from (1) and (2).
Let
us now look at subdivisions. "t1" contains three subdivisions labelled "t1",
"t3" and "t4". Of course, the new "t1" has been resized so that the three
subdivisions fit exactly in the first section. Only ratios are important at
this stage. You may measure that t3 is 1.33 times longer than t1, and t4 is
two times shorter. Therefore we will write
t3
= 4/3 t4 = 1/2
(or
equivalent integer ratios). The second section is subdivided as "t3" and "t1"
in which the ratio between t3 and t1 is 1.33 as expected.
So
far we have been able to define the
hierarchy
of time-span intervals
as a
tree
structure.
Let us now look at the note sequence itself. Time-object "t1" is subdivided
as "do5" and "re5" with equal durations because all sound-objects belonging to
"-mi.Frenchnotes" have identical time references -- corresponding to ratios
1/1. "t3" is subdivided in a similar way, as well as "t4" which contains '-'
(a silence) and "la5". The last part "t3 t1" is an interesting case since the
time-span of "do6" is partly a subdivision of "t3" and of "t1". This indicates
that the hierarchy of time-span intervals is not always a tree structure --
here it is called a
join-semilattice.