Pan law contradiction(?)

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Unaspected
KVRAF
3177 posts since 4 May, 2012

Post Wed Nov 23, 2022 7:35 pm

The equal power crossfade that is used keeps the signal level so that there is no dip when both speakers receive the signal equally. Essentially giving the centre signal a multiplier of 0.707 in both channels; rather than 0.5, that would result from a linear fade. You can use functions other than sine, and they will sound different when modulated - the perceived motion will change.

In addition to this, a stereo pan that accounts for signal loss in one speaker when hard panned, might increase the other by +3dB using the same type of control curve. This gain is not compensated for on the channel that is already being attenuated - as far as I recall. It's been a little while since I last looked at this but as I know I have a picture of the control curves somewhere, I thought it might be beneficial to the thread. Hopefully they'll help - or just be something pretty to look at.

losangeles
KVRist
Topic Starter
87 posts since 5 Nov, 2022

Post Thu Nov 24, 2022 6:13 am

camsr wrote: Tue Nov 22, 2022 9:07 am
losangeles wrote: Tue Nov 22, 2022 8:55 am By simply panning a true stereo signal hard L or R, wouldn’t just the respective channel’s original signal pass through (at +3dB, or whatever pan law is employed)?
Yes, however if it's a mix pan (here meaning not a hard pan, some L or R still remains on the L or R) stereo correlation remains a variable and what I said above holds true. I always approach mixing stereo as mixing 2 discrete channels, whether the said audio signal between the 2 channels is stereo correlated (true stereo) or not (different sounds hard panned).
Is it true to say your above argument only holds if we’re considering low frequencies? Because (by my potentially flawed reasoning, at least) if we have a mix pan with a stereo track that’s somewhat correlated (but with inverted polarity on one channel), then after the respective channels’ signals pumping through the speakers, we’re relying on cancellation effects in the air for the “dropouts.” So, if the two channels have equal amplitudes, full cancellation would occur (again, at suitable frequencies). If the channels have different amplitudes, then I’d think panning in the direction of the quieter channel would tend the perceived signal to zero (making the louder channel louder would not). As I understand it, higher frequencies are better treated as uncorrelated in such situations due to relative wavelength:inter-ear distances.

What you say could also be true at the true ‘sweet spot’ between stereo speakers, but again doesn’t seem like a probably practical outcome for humans listening with two ears.

camsr
KVRAF
7252 posts since 17 Feb, 2005

Post Thu Nov 24, 2022 12:12 pm

Stop thinking about pan laws and just mix stereo. Use a plugin like Fruity Stereo Shaper (if you have FL Studio) and you can mix any stereo you want, with the added bonus of having 4 knobs versus 1 to do any type of mixing required. I know I know, people only have 2 hands, 4 knobs is cumbersome, but most stereo mixing tasks do not require hands-on modulation. I have never mixed more than 2 channels but that's why plugins are awesome, just connect a modulation source and have the DAW do the work for you! Then it's only about setting up automation tracks!

losangeles
KVRist
Topic Starter
87 posts since 5 Nov, 2022

Post Thu Nov 24, 2022 1:07 pm

camsr wrote: Thu Nov 24, 2022 12:12 pm Stop thinking about pan laws and just mix stereo. Use a plugin like Fruity Stereo Shaper (if you have FL Studio) and you can mix any stereo you want, with the added bonus of having 4 knobs versus 1 to do any type of mixing required. I know I know, people only have 2 hands, 4 knobs is cumbersome, but most stereo mixing tasks do not require hands-on modulation. I have never mixed more than 2 channels but that's why plugins are awesome, just connect a modulation source and have the DAW do the work for you! Then it's only about setting up automation tracks!

Yeah, probably about time for a comment like that. Although I am a nut for theory, I’m pretty sure we’ve covered it all to the point where I have a sufficient qualitative (and even partially quantitative) understanding. Thanks again, happy thanksgiving!

camsr
KVRAF
7252 posts since 17 Feb, 2005

Post Thu Nov 24, 2022 1:34 pm

losangeles wrote: Thu Nov 24, 2022 1:07 pm
Yeah, probably about time for a comment like that. Although I am a nut for theory, I’m pretty sure we’ve covered it all to the point where I have a sufficient qualitative (and even partially quantitative) understanding. Thanks again, happy thanksgiving!
Speaking quantitatively, a +6db pan knob keeps the mid signal stable, and a 0db pan knob keeps one channel from exceeding a set gain. +3db is kind of in the middle.

losangeles
KVRist
Topic Starter
87 posts since 5 Nov, 2022

Post Thu Nov 24, 2022 3:16 pm

camsr wrote: Thu Nov 24, 2022 1:34 pm
losangeles wrote: Thu Nov 24, 2022 1:07 pm
Yeah, probably about time for a comment like that. Although I am a nut for theory, I’m pretty sure we’ve covered it all to the point where I have a sufficient qualitative (and even partially quantitative) understanding. Thanks again, happy thanksgiving!
Speaking quantitatively, a +6db pan knob keeps the mid signal stable, and a 0db pan knob keeps one channel from exceeding a set gain. +3db is kind of in the middle.
Aha! Yes, now everything clicks perfectly. So now, I’m fairly confident in saying Live’s “Pan Law” quoted above is actually a stereo balance law: a true constant power pan law would have per-channel attenuation at C position, but what is described has 0dB attenuation at C. There is still a +3dB boost at either fully panned extreme, however. This is consistent with the ‘middle-road’ alternative you mention.

All of this over a misnomer… won’t complain given how much I learned, though 👍

camsr
KVRAF
7252 posts since 17 Feb, 2005

Post Sat Nov 26, 2022 3:09 pm

A decided correlation cannot be kept while panning unless there is a crossfeed mix, which is what I meant by using 4 knobs.

Anything beyond the mixing board and speakers (the stuff in the air) is of no relevance concerning pan laws.

camsr
KVRAF
7252 posts since 17 Feb, 2005

Post Sat Nov 26, 2022 3:17 pm

Unaspected wrote: Wed Nov 23, 2022 7:35 pm The equal power crossfade that is used keeps the signal level so that there is no dip when both speakers receive the signal equally.
A crossfade is not a pan.

Unaspected
KVRAF
3177 posts since 4 May, 2012

Post Sat Nov 26, 2022 9:07 pm

camsr wrote: Sat Nov 26, 2022 3:17 pm
Unaspected wrote: Wed Nov 23, 2022 7:35 pm The equal power crossfade that is used keeps the signal level so that there is no dip when both speakers receive the signal equally.
A crossfade is not a pan.
Same principal applies only we have the signal fading between channels, each with their own loudspeaker.

The crossfade mixes down two signals to one channel; whilst the pan mixes up one signal to two channels. A stereo pan is slightly more complex but the method is essentially the same.

losangeles
KVRist
Topic Starter
87 posts since 5 Nov, 2022

Post Sun Nov 27, 2022 11:50 am

mystran wrote: Tue Nov 22, 2022 3:45 pm
losangeles wrote: Tue Nov 22, 2022 10:55 am When you say “interaural phase difference,” do you mean ‘beating?’
Interaural phase difference is the technical term. It's really the difference in arrival time that the brain wants, but unless there's some clear transient event, we need to estimate this from the phase difference.

If we assume the ear to ear distance is about 20 cm and the sound propagation path goes around a spherical head, then the maximum path length difference is approximately 10cm*(1+pi/2) or 25cm which gives a maximum time difference of about 0.7ms. To fully disambiguate we require that the wavelength is twice this much, which gives us a maximum frequency of about 700Hz, but if we can correctly guess which signal arrived first (say from intensity difference) then one wavelength is enough and we get a maximum frequency of about 1400Hz. Beyond that there might be multiple cycles and we can't really tell how many.

When I was writing this post, I just Googled "ear to ear distance" and calculated the rest, but it's probably not a pure coincidence that my estimate arrived at roughly the same 700-1400Hz range that hugoderwolf gave earlier. :)

I have since answered my original inquiry the thread pertains to. However, I was recently reading more into psychoacoustics and this prior post of yours came to mind. When designing stereo widening techniques, we are attempting to accentuate perceived width effects. However, for such cases (e.g. using pan as an artificial means of inducing IID) doesn’t this also assume an ideal stereo arrangement? For instance, the listener would have to be at the sweet spot of a two-output setup for such effects to fully manifest. Same for ITD-based effects such as Haas, etc.., right?

Also, with certain widening effects such as wideners which simply increase the level of the “sides” signal.. I can’t seem to understand how these increase width. I could see that they change the depth (the louder periphery sounds appear closer), but not in a different direction relative to the saggital land.

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mystran
KVRAF
7332 posts since 12 Feb, 2006 from Helsinki, Finland

Post Sun Nov 27, 2022 12:46 pm

Usually you'd assume the listener is at least close to the sweet spot, but with stereo speaker setups one should typically expect listening conditions to vary, so things like ITD panning are going to be rather unpredictable.
losangeles wrote: Sun Nov 27, 2022 11:50 am Also, with certain widening effects such as wideners which simply increase the level of the “sides” signal.. I can’t seem to understand how these increase width. I could see that they change the depth (the louder periphery sounds appear closer), but not in a different direction relative to the saggital land.
The perceived "width" is mostly a function of how correlated the left and right signals are. If we think of the left and right channels as an orthogonal basis (ie. the two directions are at right angle with respect to each other), then we can rotate this "stereo field" by 45 degrees and obtain a mid-side representation, where the M channel is (L+R)/sqrt(2) and the S is (L-R)/sqrt(2). The M channel then contains the correlated part while the S channel contains the anti-correlated part. By adjusting the relative levels of the M and S channels, we can control the overall correlation once converted back into L-R stereo and thus control the perceived width.

The limitation of this technique is that you need a side signal to start with, and this technique generally works better though when you have an actual stereo signal, rather than just panned mono. In terms of this interpretation of the stereo field, a constant power pan law applied to a mono signal essentially amounts to rotating the signal in the stereo field, yet it remains a straight line so won't be perceived as wide.
Seeking asylum in any country willing to acknowledge my right to exist.

losangeles
KVRist
Topic Starter
87 posts since 5 Nov, 2022

Post Sun Nov 27, 2022 1:14 pm

mystran wrote: Sun Nov 27, 2022 12:46 pm Usually you'd assume the listener is at least close to the sweet spot, but with stereo speaker setups one should typically expect listening conditions to vary, so things like ITD panning are going to be rather unpredictable.


The limitation of this technique is that you need a side signal to start with, and this technique generally works better though when you have an actual stereo signal, rather than just panned mono. In terms of this interpretation of the stereo field, a constant power pan law applied to a mono signal essentially amounts to rotating the signal in the stereo field, yet it remains a straight line so won't be perceived as wide.
I assume you meant *IID* in the first paragraph.

Also, regarding the second paragraph, I suppose more specifically I’m wondering why if, yes, you have a true stereo source signal and play it back it would be “ordinary” wide. But if I increase the sides signal LEVEL, how does this correspond to psychoacoustic width? All we’re doing according to the basis representation is re-expressing it in a new basis after adjusting some coefficients. Is there a psychoacoustic explanation as to why a louder sides signal makes it appear wider (rather than less deep)?

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mystran
KVRAF
7332 posts since 12 Feb, 2006 from Helsinki, Finland

Post Sun Nov 27, 2022 1:31 pm

losangeles wrote: Sun Nov 27, 2022 1:14 pm
mystran wrote: Sun Nov 27, 2022 12:46 pm Usually you'd assume the listener is at least close to the sweet spot, but with stereo speaker setups one should typically expect listening conditions to vary, so things like ITD panning are going to be rather unpredictable.


The limitation of this technique is that you need a side signal to start with, and this technique generally works better though when you have an actual stereo signal, rather than just panned mono. In terms of this interpretation of the stereo field, a constant power pan law applied to a mono signal essentially amounts to rotating the signal in the stereo field, yet it remains a straight line so won't be perceived as wide.
I assume you meant *IID* in the first paragraph.
No. I mean ITD. Because you can't really predict the exact placement of the speakers or the listener, you can't really predict the exact ITD as observed at the listener's position, hence it's unpredictable. On the other hand, if we assume the listener is at more or less even distance from each of the speakers, then IID is comparatively much more predictable.
Also, regarding the second paragraph, I suppose more specifically I’m wondering why if, yes, you have a true stereo source signal and play it back it would be “ordinary” wide. But if I increase the sides signal LEVEL, how does this correspond to psychoacoustic width? All we’re doing according to the basis representation is re-expressing it in a new basis after adjusting some coefficients. Is there a psychoacoustic explanation as to why a louder sides signal makes it appear wider (rather than less deep)?
It's not about the signals being louder. If you imagine the stereo signal is a composition of many signals all panned at various positions across the stereo field, then increasing the level of the side channel relative to the mid signal effectively stretches the stereo field such that all these panning positions cover a wider angle. This is the case even if you compensate the overall gain such that there is a net-zero change in loudness.
Seeking asylum in any country willing to acknowledge my right to exist.

camsr
KVRAF
7252 posts since 17 Feb, 2005

Post Sun Nov 27, 2022 1:41 pm

mystran wrote: Sun Nov 27, 2022 1:31 pm
It's not about the signals being louder. If you imagine the stereo signal is a composition of many signals all panned at various positions across the stereo field, then increasing the level of the side channel relative to the mid signal effectively stretches the stereo field such that all these panning positions cover a wider angle. This is the case even if you compensate the overall gain such that there is a net-zero change in loudness.
+1
Maybe the stated "example" is not informative enough, but in most general circumstances, a little boost to the side signal is typically perceived as wider.

Unaspected
KVRAF
3177 posts since 4 May, 2012

Post Mon Dec 12, 2022 1:25 pm

Found them!
Curves.gif
Curves2.gif
These might not be all that informative - though they are as pretty as I remember. The second shows various curves used for the pan: linear, sine, ^2 and the last was something that I don't remember.

Might be more helpful if I run two images side by side to show the mixing of a hard panned sine with a saw or something like that.
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