Specifications

74 Pure Data essentials
1.0, is fed to the left channel multiplier, while its co mplement (obtained by
subtracting it from 1.0) governs the right side. With a control signal of 0.5 both
sides are multiplied by 0.5. If the control signal moves to 0.75 then the opposing
side will be 0.25. When the control signal reaches 1.0 the co mplement will be
0.0, so one side of the stereo image will be completely silent.
Square root panner
inlet~ signal inlet control
sig~
*~ *~
outlet~ left outlet~ right
lop~ 1
sqrt~
sig~ 1
-~
sqrt~
fig 7.8: root law panner
The problem with simple linear panning is that when
a signal of amplitude 1.0 is divided in half and sent
to two loudspeakers, so each receives an amplitude
of 0.5, the r e sult is quieter than sending an ampli-
tude of 1 .0 to only one speaker. This doesn’t seem
intuitive to begin with, but remember loudness is a
consequence of sound power level, which is the square
of amplitude. Let’s say our amplitude of 1.0 repre-
sents a current of 1 0A. In one loudspeaker we get
a power of 10
2
= 100W. Now we send it to equally
amongst two speakers, each receiving a curre nt of 5A. The power from each
sp e aker is therefore 5
2
= 25W and the sum of them both is only 50W. The real
loudness has halved! To r e medy this we can modify the curve used to multiply
each channel, g iving it a new taper. Taking the squar e root of the control signal
for one channel and the square root of the complement of the control signal
for the other, gives panning that follows an equal power law. This ha s a 3dB
amplitude increase in the center positio n.
Cosine panner
inlet~ signal
inlet control
sig~
*~ *~
cos~
-~ 0.25
*~ 0.25
outlet~ left outlet~ right
lop~ 1
cos~
-~ 0.25
fig 7.9: cos-sin law pan-
ner
While the square root law panner gives a correct am-
plitude r e ductio n for centre position it has a problem
of its own. The curve of
√
A is perpendicular to the x
axis as it approaches it, so when adjusting the panning
close to one side the image suddenly disappears com-
pletely from the other . An alternative taper follows the
sine-cosine law. T his also gives a smaller amplitude re-
duction in the centre position, but it approaches the
edges of the image smoothly, at 45 degrees. The cosine
panner is not only better in this regard but slightly
cheaper in CPU cycles since it’s easier to compute a
cosine than a square root. It also mimics the pla c e-
ment of the source on a circle around the listener and is nice for classical music
as an orchestra is g e nerally arranged in a semicircle, however some engineers and
producers prefer the root law panner because it has a nicer response around the
center position and signals are rarely panned hard left o r right.
Fig. 7.10 shows the taper of each panning law. You can see tha t the linear
method is 3dB lower than the others in the centre position and that the root
and cosine laws have different approaches at the edge of the image.