Q About Phasers Vs. Flangers

[Mark Hammer]

At faster speeds (e.g., >0.8hz or so), perceptual differences between flangers and phasers tend to disappear.  I suspect this is largely due to both sweeping over their entire range quickly enough that we tend not to pay attention to how and where they sweep.  They tend to pull apart, perceptually, when the sweep is slow.  A big part of that is the manner in which audible notches increase as the sweep descends.  I like to describe this as the audio signal becoming "infected" with notches, as the delay time goes from absolute minimum to its maximum.  Although the sweep ratio of minimum to maximum delay is important, it is the minimum delay time that plays a huge role in the dramatic quality of a good flanger.  If the minimum delay time is very short, notches created at that delay are either well above audibility or the spectral content of the source material, or else simply difficult to hear/notice because there may be frequency content "up there", but it's such low amplitude, relative to the rest of the signal, that we simply don't perceive those notches.  Whatever the case, as the sweep descends, more and more of the signal is amenable to audible notches, and more notches are created. 

One of the more common flangers, the Boss BF-2, does not sweep to anything shorter than 1msec, such that there are always audible notches at every point in the sweep cycle.  It never achieves that "infection" quality as more desirable flangers do.  According to the experts, one needs to have a longest-to-shortest delay time ratio of about 35:1 or greater for "dramatic" slow flanging.  The BF-2 is around 13:1.  That said, if one has a preference for using flangers like a chorus or ersatz slow Leslie, you don't want a very wide sweep range, so the BF-2 is just fine.  Similarly, if you listen to the always-phased sound of Donald Fagen's P90-modulated Rhodes, the sweep speed is jiggly-but-not-bubbly, and the sweep width is actually pretty shallow.  The WIDE range is for very slow sweeps.

Okay, put that on hold for the moment.  Let us say that we have a 10-stage phaser, yielding 5 notches.  As has been noted by others, the spacing of the notches will be different than a flanger, yielding a different tonal quality.  The shape of the sweep can be made equal between phaser and flanger.  Assuming we are able to get the lowest notch produced up into the inaudible range, as it starts to descend in the sweep, making more of the notches audible, I suspect there will be a certain tonal similarity between phaser and flanger.  But as it sweeps further in a downward direction, making all notches audible, it would kind of runout of drama, relative to a flanger, where the number of notches produced by time delay just keep getting larger and larger.

In some respects, and in theory, one could force a flanger to sound more like a phaser by severely lowpass filtering the delay signal, such that the number of notches created and audible at, say, a third of the downward sweep, are pretty much the same number as when one reaches the bottom of the sweep (i.e., longest delay time).  I leave it to you empiricists to do that experiment and tell me if I'm right or totally wrong.

All of this is based on a perceptual analysis of the two effect types, and what each nudges to pay attention to.

[Steben]

Thx for the addition Mark.
Thing is, my question was completely theoretical. Phasers become huge and impractical at a certain point where a single delay line does the job.
However .... afaik phasers where the first compact effects to mimick rotary ... where freq split delay lines are the elaborate approach. That is intriguing and confusing.
Being freq-based, a phaser gives larger "delay" on lower freqs and this becomes shorter as freq goes up. That is a bit what a rotary system does.

[puretube]

...
Being freq-based, a phaser gives larger "delay" on lower freqs and this becomes shorter as freq goes up. That is a bit what a rotary system does.

Swap the position of the "phasing" R & C, and its the other way round.
(But you sit there with the "floating" (i.e.: not: "to ground") variable resistor problem - which can be solved, though ...).

[Digital Larry]

One thing about flangers is that the notches are always going to be harmonically related.  So in the case where you have something like a single guitar note, with or without distortion, those notches can quite easily sweep through all frequencies with energy in them at once, making the note "disappear" for a moment.  This is a bit different than a TZF where the cancellation is complete for all signals because it simply amounts to a phase inversion.

DL

[puretube]

Phasing it to death:
When NYQUIST played with his 736-stage (!) Phaser - 93 (!) years ago:
190ms delay (with inductors!)
Unmodulated, however ...
https://worldwide.espacenet.com/publicationDetails/originalDocument?CC=US&NR=1726578A&KC=A&FT=D&ND=4&date=19290903&DB=EPODOC&locale=en_EP

Ununderstandable!

(I would have loved to play with a BIG LFO-modulated hi-current coil near all those inductors, and mix the phaseshifted output with the dry signal ...).

In contrast thereto:
Early modulated delay (ideal for Flangers) from 107 years ago.
(Again it served to mangle communication)
https://worldwide.espacenet.com/publicationDetails/originalDocument?CC=US&NR=1325574A&KC=A&FT=D&ND=7&date=19191223&DB=EPODOC&locale=en_EP

(Again: just mix it with the dry signal).

It`s all about secrecy!

[Rob Strand]

As I said before, if you listen to the unmixed signal from a flanger and a phaser there is clearly a difference in the sound.   The unmixed signal has *no notches*.  So focusing on notches isn't the whole picture.

I found some samples of the Sobbat PB-2 Phasebreaker II.  This unit has a switch for vibrato mode which I'm fairly sure disconnects the dry signal from the mixer.   For the sake of this argument it would be nice if it did or if that could be confirmed.  To me it's not a big deal as the vibrato mode is representative of listening to a phaser with the dry signal removed from the output mixer.

Phaser:

Sobbat PB-2 Phase Breaker II
https://www.youtube.com/watch?v=xwo8gdab34c

4 -stage ?, 3 modes

time   Mode      Comment
0:00   Phase       vintage, no feedback
1:33   Phase 2      small amount of feedback
2:30   Vibrato      no clean mix

Sobbat PB-2 and MXR Phase 90 (1974 script, bud box )
https://www.youtube.com/watch?v=EpOIl4Zzxno

1:44 Vibrato mode.

There is phaser clearly a phaser-ish characteristic in Vibrato mode.
Vibrato mode is less pronounced than phaser mode.
What's missing is the notches.   The missing character is very similar to when you dial-up notch on a parametric equalizer.

A Flanger with the dry signal removed is very much like this:

Boss Vibrato VB2/VB2W
Waza run-down
https://www.youtube.com/watch?v=b3ldgDN179Q
Sounds at 2:19

It's fairly clear the unmixed sound of the phaser has a phaser characteristic.  The vibrato/flanger sounds very much like a tape machine with a slipping belt.   

So why's that?

For a flanger the perceived pitch is,

            p  = w * [1 - (d td / dt) ]

where (d td / dt)  = the rate of change of the delay.   Basically modulation of the delay.

w = angular frequency [rad/sec].
Just think of that as the *signal* frequency, w is related to frequency from w = 2* pi * f .

The important thing here is all signal frequencies are pitch shifted by the same (relative) amount.  So
if the pitch shift is one semitone at 100Hz it shifts one semitone at 1kHz.   The pitch of the
entire signal is shifted up and down in a way which preserves the relative tuning, like a tape.


For a phaser the perceived pitch is,

             p = w * [1 - (Tg/Tg0) * (d Tg0 / dt) ]

The group delay for a phaser is plotted back in Reply #18.
Tg0 is the group delay at DC (the intercept on the axis at frequency 0)
Tg is the group delay at the signal frequency w.

Look at the group delay graph and you can see at low frequencies Tg is approximately the same as Tg0.
In this case Tg/Tg0 = 1 the pitch shift is,

             p = w * [1 - (d Tg0 / dt) ]

Virtually the same as the flanger.

But at higher frequencies  Tg drops off and the amount of pitch shift becomes less and less.

If you have trouble with the idea of group delay just think of it as the effective delay
which is stretching or contracting the signal due to the phase-shift of the allpass filter.
We can relate it back to a phaser circuit as follows:
- When we build a phaser we modulate say a resistor value using the LFO.
- The modulation of the resistor value modulates the frequency of the allpass filter.
   f0 = 1/(2*pi*RC)   ;or w0 = 1/RC.
- The w0 value and the number of allpass stages sets the DC group delay Tg0.
   It shouldn't be too hard to accept that when the all-pass filter is set to a low frequency
   the amount of phase shift is more and that produces a larger delay.
   We can even calculate the group delay. For a basic phaser,
   Tg0 = n * 2 / w0 = n * 2 / (2*pi*f0).    where n is the number of first order stages.
   (you can see this in the group delay plot in reply #18)
- Modulating the resistance modulates f0 and that modulates the group delay Tg0 (and Tg).
- w0 and number of stages also set to total phase shift and the notch locations.

IMHO the difference between phasers vs flangers is that the phaser has different delays
at different frequencies. A flanger is pure delay whereas a phaser has a dispersive nature.
When the phaser has a small number of stages the group delay is not constant at all over the audio
spectrum - it is very dispersive.

What that means is for a given signal different parts of the signal are shifted by different amounts.
If the pitch shift is one semitone at low frequencies it is not shifted one semitone at higher frequencies.
Well not unless there are so many phaser stages that it looks like a delay.

The point reply #18 is there is enough stages to sound like a flanger (by ear and from experience on a real unit).
We can also see the group delay of the all-pass filter looks like a true delay over a reasonable portion
of the spectrum.

Here's the plots for a 4-stage phaser.    (I left the 2nd-order all-passes in for completeness.)
It's pretty clear from the group delay that it hardy looks like a delay over any part of the guitar spectrum.

We can't ignore the fact the notches don't line up with a flanger (true delay).   That's also part of the sound.  However, as the sound samples above show the notches don't explain everything either.


Schematic:


Group delay:


Frequency response of mixed signal:





Some phasers have unmodulated all-pass sections these don't count for pitch shift.   The extra stages do shift the notches but not in the same way as if they are modulated.   Pitch shifting only applies to modulated allpass stages.    If you listen to a Boss phaser with 12 stages it still sounds quite a bit like a phaser.  That's because only 8 stages are modulated and modulated 8-stages is on the transition where phasers start to sound like flangers.

[ElectricDruid]

For a flanger the perceived pitch is,

            p  = w * [1 - (d td / dt) ]

where (d td / dt)  = the rate of change of the delay.   Basically modulation of the delay.

Where did you find this, Rob, or how did you derive it? It doesn't fit with my own research into this, so I'm curious.

It's a minor point though - I agree with all of your conclusions re flangers vs phasers, and removing the dry signal and looking at just the effect on the wet signal is a very good idea for helping understand the differences between them.

[Rob Strand]

For a flanger the perceived pitch is,

            p  = w * [1 - (d td / dt) ]

where (d td / dt)  = the rate of change of the delay.   Basically modulation of the delay.

Where did you find this, Rob, or how did you derive it? It doesn't fit with my own research into this, so I'm curious.
e differences between them.

I derived it but I thought it was reasonably well known.   You can get different results if you use the control voltage  or the delay *implied*  from the control voltage "now" (as BBD's accumulate the sample delays).  The way I've phrased it is td is the actual delay from when the sample went in to when it came out, doesn't matter what happened in between to get there.

The idea stems from the instantaneous frequency.   The place this appears most in textbooks is under Phase Modulation, see p17.   You take the time derivative of the whole sine argument. Without modulation that's (wt+theta) and the time derivative gives w, the fixed frequency of a sine wave.
https://www.csun.edu/~skatz/katzpage/sdr_project/sdr/FM_and_PM.pdf

For the time delay case you can see J.O.Smith uses the same equation, see equation (10),
https://www.researchgate.net/publication/2568326_Doppler_Simulation_And_The_Leslie

For the phaser I haven't seen the form I posted but it comes from the same process.   The equation doesn't just fall out.  A number of steps are required to massage the equations so the modulated part is the DC group delay.   I did that deliberately so you can see the common thread between group delay and time delay, and also the differences from the frequency dependent Tg(w)/Tg0 factor.

FWIW,  the notch positions are also linked to the group delay.   The phaser notch frequencies deviate from the Flanger notch positions when the group delay isn't flat.  If the allpass filter has zero phase shift at DC then the DC group delay pretty much forces the position of the lowest notch.   That means all phasers with same group delay have approximately the same lowest notch frequency.  You can see that in the plots.   For a 4th order phaser you can see the group delay starting to droop at the notch frequency.  The DC group delay predicts the lowest notch at 0.39*w0 and the actual is 0.41*w0.    So notches and group delay are linked.   Adding fixed all-pass stages is way to shift the notches.

[Rob Strand]

Where did you find this, Rob, or how did you derive it? It doesn't fit with my own research into this, so I'm curious.

OK I think I see where the difference is creeping in.

From here,

https://electricdruid.net/investigations-into-what-a-bbd-chorus-unit-really-does/

Here your derivatives are in terms of clock frequency and not delay so you end-up with different results.  (It's not incorrect, but it is a step along a long chain of similar things.)

For a flanger:
- We start with an LFO waveform.   The shape of that can vary.
- The LFO feeds into the VCO resulting in a clock frequency.
- The clock frequency sets the instantaneous delay time.
- The BBD averages all the delay times to produce a delay.

The whole process of how the LFO waveform translates to a delay affects the shape of d td /dt.   In reply #16 I mentioned shaping affects the final result.  I mean it's no surprise sine modulation sounds different to triangle or exponential waveforms.   Sine is often presented for theory, and in DSP, but triangle and exponential are more common in circuits.   The way the control voltage affect the VCO frequency is something that needs to be factored in, and not all VCOs do the same thing.    Moreover flangers often use transistors to create an exponential current at the input to the VCO.

Phasers can have a similar set of variables.   We could even make a waveform that mimics what's going in a flanger.

All those factors contribute to why one flanger/chorus/phaser sounds different to another.
I guess the point is those factor aren't what makes a flanger sound different to a phaser.
There's something more fundamental separating them.

[Steben]

These analyses enforce my idea a rotary sim with low count stage phaser for the low pass region might work enough. But is not that useful. I mean a 2 stage phaser is not good enough and 4+ stages are just as complex to build as a delay stage.

A 4 to 6 stage phaser is perhaps the most simple rotary sim. Univibes are completely into that game.
They do not have amplitude wobble however to make things complete. Afaik that wobble is mostly percieved in the lower freqs.

[Steben]

One thing that strikes me is the amount of rotary sim tips and hints across the net that can be sumarised as chorus/flanger for high speed and phaser or vibes for low speed.
A fast chorus has a cheap but noticable rotary organ thing. The shine on you crazy Diamond sound definitely has a slow leslie thing. And that is a phase 90.
Thing is, I tend to agree.
But why?

The only thing that pethaps comes to mind is the fact low mid speed accentuates the difference in low and high rotary delays which is suited to a phaser. The high speed accentuates the lfo above the delays, which is suited for chorus style effect.