Another kind of Phasing

[Haible Juergen]

Hi !

I didn't dare to write "new kind", but it was new to me at least.
Spend most of the hollidays to make a usable FX device out of
my frequency shifter pcbs - building the front panel, and wiring
everything together is always the hardest part for me. But now
my FS-1 has a nice enclosure, a built-in mic preamp, a second
input channel, two separate output channels with selectable up/down
and individual dry/wet mix for stereo output or for a delay loop.
Then I could start experimenting.

Not the most spectacular, but the most interesting thing I found
was this "other" kind of phasing that occurs when I mix the dry signal
and a very slightly ( 0.1 ... 0.5 Hz) frequency shifted signal at equal
level.
It sounds similar as phasing, only different.
Most pleasant it is when I use 0.2Hz Upshift in one channel, and
0.2Hz Downshift in the other channel. (Each side mixed with the dry
signal, as above.)

Now this made me think of different kinds of phasing / flanging / chorus
and pitch shifter effects, and find a fitting place for "Frequency Shift
Phasing"
then.

The *delay* based (BBD or digital) effects like Chorus or Pitch Shifter
will produce a certain *percentage* of frequency shift for each
harmonic, while 
the Frequency Shifter produces a certain *offset* of frequency for each
harmonic. That's why a Frequency Shifter is generally considered useful
for producing non-harmonic spectra, while a a Pitch Shifter will produce
harmonic outputs (with harmonic input). This is all well known.

But this is only *one* way to look at it. When we produce very *small*
amounts
of shift, either with a Frequency Shifter (FS) or a Pitch Shifter (PS),
and then 
mix the input and output signals in order to get a beating "chorus"
effect, the Frequency shifter has its own benefits.
Consider a FS and a PS, both set in a way that the *fundamental* of some
audio signal (say, 100Hz) is shifted by 0.2Hz.
So we will have the following frequencies for the harmonics:

Number  Original     PS        FS      

1       100Hz        100.2Hz   100.2Hz
2       200Hz        200.4Hz   200.2Hz
3       300Hz        300.6Hz   300.2Hz
4       400Hz        400.8Hz   400.2Hz
...
10     1000Hz       1002.0Hz  1000.2Hz

And so on - you get the idea.
Now of course the FS signal is not *exactly* harmonic anymore, but
the error is small and you won't hear it.
But now look at the *beat* frequencies, when you mix the processed
signal and the original signal! In the PS case, every harmonic of
increasing
number will have an increasing beat rate. This produces the typical
swirling, and slightly detuned, "chorus" sound. In the FS case, however,
all harmonics will have the same beat rate of 0.2Hz with their orignal
counterpart. You get a slow homogenous modulation over the *whole*
sound, similar to what we know from phasing.
This would (I hope) explain the sound I found by experimenation.

Now there is some logical link between Pitch Shift (static shift), 
Chorus (periodically varying shift - your BBD or wat else has a finite
maximum delay, then you have to reverse ..) and Flanging (same as
Chorus, but
smaller delays involved), which is also well known.

Telling from the *sound*, there should be a similar link between
Frequency
Shift (static) and Phasing (approximation of a static frequency shift
???),
but from the Maths it is not quite clear at first.

Of course there would be other possible descriptions of this process.
In the FS, the audio signal is split into two paths that have a 90degree
phase relation for (almost) all frequencies. This is done with - guess
what - "Phaser" circuits, only that these allpass filters are fixed, and
the
movement comes by "scanning" the two outputs with a quadrature
modulation signal of 0.2Hz (in our example). So there is a certain
relation.
(But I'd rather have phasing explained with FS, and not the other way
round
 (;->) )

Speaking of "scanning": The 4-quadrant modulation implemented in the FS
is surely more than scanning, but you can think of it as sucessive
scanning
of 4 signals with 0, 90, 180 and 270degree phase shift.
Reminds me of the Hammond Scanner Vibrato, where a chorus effect is
produced by scanning a delay line / low pass filter.
Another project that waits for analysis, and cloning.

Hope you found this interesting. I feel I have an *idea* what's going on
in
these devices, but not the full picture yet. Any contributions highly
welcome.

JH.