programming with max/msp - Virtual Sound

Chapter 2P - Additive and vector synthesis 2P
When it begins to drop from 0.5 towards 0, the oscillators are no longer in antiphase,
and you hear a sound growing progressively in amplitude until the two
oscillators are completely in phase and their summed amplitude ranges between
-2 and 2. 4 Try using phase values larger than 1, and note that whenever the
phase is equal to an integer, the sound reaches its maximum amplitude, and
whenever the phase is exactly halfway between two integer values (such as 1.5,
2.5, 3.5, etc.), the sound is cancelled out. Phase values larger than 1 (larger than
360 degrees) cause the cycle to wrap around, beginning anew, as we explained
in the box dedicated to phase in Section 2.1T. Of course, all of these observations
hold true only if the two generators share exactly the same frequency.
If they don’t, the ratio between the phases of the two oscillators would vary
continuously, giving rise in the case that frequencies are only slightly different
(for example 440 and 441 Hz), to the phenomenon of beats that will be covered
in Section 2.2.
Let’s look at another possibility for the right inlet of cycle~ (as shown in
Figure 2.4).
Fig. 2.4 Oscillator controlled by a phasor~
Here we have a cycle~ set to 0 Hz, since it has neither an argument nor has it
received a numeric message on its left inlet. The phase of this cycle~ is set to
be modified by a phasor~, which in the figure also has a frequency of 0 Hz, so
to remain still. Looking at the oscilloscopes, we see that the phasor~ generates
a stream of zero-valued samples, which implies that it is frozen at the beginning
of its cycle, and cycle~ generates a stream of ones, which means that it too
is frozen at the beginning of its cycle. It is important to stress that the cycle of
a waveform generated by cycle~ begins with the value 1; cycle~ generates
a cosine wave, as we pointed out in Section 1.1, which explains why the cycle
starts at 1, its maximum positive value. 5 This is not a general rule: phasor~, for
example, begins its cycle at 0.
4 The resulting wave oscillates between -2 and 2 because it is the sum of two cosine waves (more
on this shortly) that oscillate between -1 and 1 and are perfectly in phase
5 For a definition of the cosine function, see theory sections 1.2 and 2.1.
from “Electronic Music and Sound Design” Vol. 1 by Alessandro Cipriani and Maurizio Giri
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