# Another kind of Phasing

Magnus Danielson magnus at analogue.org
Wed Jan 14 21:42:15 CET 1998

```>>>>> "HJ" == Haible Juergen <Juergen.Haible at nbgm.siemens.de> writes:

HJ> Hi !

Hi Juergen!

(Sorry all for lack of propper removal of quotation)

[Stuff removed]

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

About here I went thinking "Oh, Lesley Speakers..."

HJ> So we will have the following frequencies for the harmonics:

HJ> Number  Original     PS        FS

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

HJ> And so on - you get the idea.

Constant shift.

This is similar to the Lesley dual doppler effect where you would have
an table close to this:

Number	Original	Horn1	Horn2
1	100		99.8	100.2
2	200		199.8	200.2
3	300		299.8	300.2

And so on...

Horn1 - moving away from you
Horn2 - moving towards you

This is shifting...

The Lesley speaker causes two instances of the sound which is being
frequency shifted with a low frequency (the rotation speed of the
horns) and those two instances are modulated with 180 degree
difference. The frequency shifting of an Lesley is done througth the
doppler effect. An Lesley cabinet allso causes an amplitude modulation
due to the directivity of the horns.

So, in a since does the "diffrent Phasing effect" becomes related to
the Lesley effect, at least as it looks in theory to me.

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

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

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

Phasers create a "comb filter" which is a lot of zero's all over and
shifts this (an 30-band RTA shows this well) all around the place.
An similar thing will happend to the others - the changes in relation
of various harmonics in the sound AND the way that they changes migth
probably better explain how we preceive them rather than the actual
frequency changes.

Just the sligthly shifted or sligthly phase-modulated sound isn't very
interesting.

This doesn't mean that the way and various methods by which you can
asheive such effects becomes unintresting, rather the opposite. It is
not allways the same old effect over and over again.

Now, start playing with feedback and you get yeat more interesting
effects (as with the EH SmallStone for example).

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

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

The Hammond Scanner Vibrato where Hammonds attempt to get the Lesley
effect without the Lesley cabinets, this was not such a great thing so
Hammond ended up bying the Lesley company to get the right effect
along with their organs... (if I recall things rigth, I am sure
someone will correct me if I am not right).

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

Well Juergen, at least I find this an interesting thing. I hope there
is a few more that feels the same way...

Hmm... maybe it is time to get that Eventide Harmonizer up running again...

Cheers,
Magnus

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