Specifications

62 Shaping sound
of the multiplier, a positive signal is output in graph C. Mak ing either sign of
the cosine wave positive like this doubles the frequency. In graph D an absence
of negative square roots produces a broken sequence of positive pulses, and the
effect of the s quare root opera tion is to change the cosine curve to a parabolic
(circular) curve (notice it is more r ounded).
Curved envelopes
We frequently wish to create a curve from a rising or falling control signal in
the range 0.0 to 1.0. Taking the square, third, fourth or higher powers produces
increasingly steep curves, the class of parabolic curves. The quartic e nvelope is
frequently used a s a cheap approximation to natural decay curves. Similarly,
taking successive s quare roots of a normalised signal will bend the curve the
other way
1
. In Fig. 6.11 thr e e identical line segments are generated each of
vline~
1 0 0, 0 $1 0
vline~
*~
tabwrite~ a
tabwrite~ b
a b
120
1 0 0, 0 $1 0
vline~
*~
1 0 0, 0 $1 0
t f f f
t f b
send makegraph
receive makegraph receive makegraph
tabwrite~ c
receive makegraph
*~
squared envelope quartic envelopelinear envelope
c
fig 6.11: Linear, squared and quartic decays
length 120ms. At the same time all
tabwrite~
objects are triggered so the graphs
are synchronised. All curves take the same amount of time to reach zero, but
as more squaring operations are added, raising the input to higher powers, the
faster the curve decays dur ing its initial stage.
SECTION 6.2
Periodic functions
A periodic function is bounded in range for an infinite domain. In other
words, no matter how big the input value it comes back to the place it started
from and repeats that range in a loop.
1
See McCartney for other identities useful in making efficient natural envelopes.