A synthetic timbre sounds more pleasant if the shape of the waveform
subtly changes over time as its various harmonics fade in and out.
To put it another way, a periodic waveform does not sound as interesting
as a quasi-periodic waveform.
The most popular way to generate a quasi-periodic waveform with
analogue electronics is to use pulsewidth modulation, or PWM for
short, which generates a pulse waveform that has a varying duty
cycle. While this technique works well in analogue electronics,
there is another type of modulation that is ideally suited to virtual
synthesisers which use lookup tables in place of tangible oscillators.
Waveforms can be looked at in several ways, such as shapes or
harmonics. Once a waveform has been digitised, however, it can be
seen in yet another way: as a series of numbers. This is where
virtual synthesisers come into their element: because they run on
computers, they are great at performing simple calculations on
numbers. It is trivially easy for a computer program to take two
waveforms and multiply them together or subtract one from the other.
How phase offset modulation works is to take a lookup table, and
generate two instances of its waveform at the same frequency. One
of them should be further ahead or behind in its cycle, making the
two waveforms slightly out of sync with each other. Either the
values of the waveforms are multiplied together, or the value of one
of them is subtracted from the other one.
This process generates an entirely new waveform with a drastically
different shape. For example, one ramp wave subtracted from another
will create a pulse wave, with the amount of offset (the difference
between the two waveforms' starting points) dictating its duty cycle.
If you slowly change the offset amount, you get pulsewidth modulation.
Using this technique, not only can you achieve pulsewidth modulation
using a ramp wave, you can also create a comparable effect using any
other periodic waveform, creating an entirely new quasi-periodic
waveform.
So far, the only instrument I know of which uses phase offset
modulation is SubTractor, part of the Reason virtual studio by
Propellerhead Software. It seems like a rather elegant solution to
the problem of digitally creating quasi-periodic waveforms using
very little processing power. Hopefully more synthesisers will
employ this technique in the future, as analogue hardware is
increasingly being replaced by more convenient software alternatives. | 
