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The analogue-summing '3D' effect: what actually is it?

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Re: The analogue-summing '3D' effect: what actually is it?

Postby blinddrew » Tue May 26, 2020 1:03 pm

That was my initial thinking.
I've got a completed project that i might get time to play with again. But it's 60-odd tracks so not a quick option.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Hugh Robjohns » Tue May 26, 2020 1:35 pm

Martin Walker wrote:The Airwindows Console plug-ins add slight 'pre-distortion' to each channel via its Channel plug-in instances, and then the combined mixed signal is passed through a single Console Buss plug-in, which provides the reciprocal 'undistort' curve:
Image

I'm slightly confused as to what that diagram is showing, Martin. Rather than showing pre-distortion levels, it appears to be a transfer plot indicating very mild but complementary downwards compression and upwards expansion with very high thresholds.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Folderol » Tue May 26, 2020 1:40 pm

Well I just checked though all of the examples and for the life of me I can't detect any difference. The way the examples are presented doesn't help. There is no fast silent A/B switching. On the few occasions the original author does any A/B stuff, there is a very pronounced 'clunk' which is a distraction.The only thing I hear is what seems to be a slight overall volume change.

Clearly I'm missing something but I have no idea what.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Martin Walker » Tue May 26, 2020 3:04 pm

Hugh Robjohns wrote:I'm slightly confused as to what that diagram is showing, Martin. Rather than showing pre-distortion levels, it appears to be a transfer plot indicating very mild but complementary downwards compression and upwards expansion with very high thresholds.

Spot on Hugh, as always! ;)

The lower (purple trace) displays the Airwindows Console Channel plug-in, which hypes treble (increases slew rate) and cuts amplitude above the high threshold (soft limiting).

The upper (cyan) trace displays the Console Buss plug-in, which in turn cuts treble by reducing slew rate, and then hypes the amplitude above the same high levels (soft expansion).


I've pasted below a few words about Console's mechanics and ideology from Chris Johnson of Airwindows - there's some waffle in there (I believe he's on the autistic spectrum), but I get the essence of his thought process as follows:

1. Digital summing is mathematically perfect.

2. If Analogue summing can sound euphonically 'better' then this must be due to real-world imperfections.

3. These must therefore be imperfections in a non-perfect virtual earth mixer.

To my ears the results of his algorithm intended to model these interactions between the mixed channels speak for themselves, but here's how he describes it:


"Imagine if you had two channels in an analog mixing board. They're both electrical circuits, have tubes or transistors. Those can distort, and we all know about adding distortion: lots of 'emulations' just only do that. Imagine they have to mix. You take an output off the resistive network they feed, and then you've got your mixdown. So far so good… If they are in phase, they're both putting out positive (or negative) voltage. It matches, sums up, so the channels are working together. If they're OUT of phase, depending on what the resistive network is like, that means they are trying to do a thing that'll cancel out. The output will be zero or near zero… BUT, it's also changing the input impedance of the resistive network. That means the channels will try to distort more easily. It's like their energy is wasted, fed through the resistive network uselessly. The one channel's pushing, the other's pulling, they both kinda fall over: to make a given output, they're both less effective. They're burning some of their energy feeding each other and not the output, and they will distort more easily because the impedance of the resistive network's dropped, but not in a way that gives you more energy to the output.

THAT is what Console has always modeled. If the combination of tracks cancels out and takes you closer to zero, the distortion on the channels is still very much present but the output doesn't go as close to the max output and therefore the UNdistort can't restore what was there.

So, you can get null-tested perfect output if there's only one channel/source, but as soon as you start modulating what's happening (especially as channels cancel each other) the distortion in the channels shows through. It makes the signal not come across, in those instants the signal is more distorted and lower in output. Turns out, reproducing those instants with perfect digital math sounds unnatural. It doesn't sound like analog hardware gear, and it doesn't even sound like sounds mixing in air. It's flat when it's too perfect, like all the sounds are mixing on the surface of your eardrum. Some of us have hated that sound for a loooooong time."



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Re: The analogue-summing '3D' effect: what actually is it?

Postby Martin Walker » Tue May 26, 2020 4:09 pm

By the way, thanks to both Drew and Dr. Huge for confirming that they can hear the changes on my audio snippets.

And to Folderol, one of the trickiest parts of achieving those demos was to get the differences big enough to hear despite the 128kbps streaming restrictions of Soundcloud. I'm happy to forward uncompressed WAV files if you think it would help, but I suspect it's a perceptual thing - once you've honed in on what changes you can hear it easily again, and I've since heard very similar differences between ITB and Hardware analogue summing box demos, with similar restrictions (at least a dozen channels being mixed together).


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Re: The analogue-summing '3D' effect: what actually is it?

Postby Folderol » Tue May 26, 2020 4:46 pm

Thanks for the offer Martin. However, although I'm somewhat miffed at not detecting the difference, I don't think it has any bearing on my own compositions which are entirely inside the box.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby blinddrew » Tue May 26, 2020 5:02 pm

Martin Walker wrote:And to Folderol, one of the trickiest parts of achieving those demos was to get the differences big enough to hear despite the 128kbps streaming restrictions of Soundcloud. I'm happy to forward uncompressed WAV files if you think it would help,
If you upload uncompressed WAVs and set the files to be downloadable then people can download the original format and load them into their DAWs...
Just sayin' ;)
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Martin Walker » Tue May 26, 2020 5:12 pm

blinddrew wrote:
Martin Walker wrote:And to Folderol, one of the trickiest parts of achieving those demos was to get the differences big enough to hear despite the 128kbps streaming restrictions of Soundcloud. I'm happy to forward uncompressed WAV files if you think it would help,
If you upload uncompressed WAVs and set the files to be downloadable then people can download the original format and load them into their DAWs...
Just sayin' ;)

The reason I didn't before is that the track in question hadn't been released, but it now has ('Truning 495' from the album 'All Steamed Up' - https://yewtreemagic.bandcamp.com/album/all-steamed-up )

So I've just amended the permissions so you can all download all three file snippets in uncompressed 16-bit/44.1kHz WAV format.


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Re: The analogue-summing '3D' effect: what actually is it?

Postby blinddrew » Tue May 26, 2020 5:35 pm

:thumbup:
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Re: The analogue-summing '3D' effect: what actually is it?

Postby DC-Choppah » Tue May 26, 2020 5:46 pm

In analog, the summing of signals is a non-linear, time-dependent process. A digital summer is a linear, time-independent process.

For a linear, time independent mixer you just add up signals into a constant impedance Z

Itotal(t) = I1(t) + I2(t) + I3(t) ...
Z = constant (impedance of network)
Vtotal(t) = Itotal(t) * Z;

where I1,I2,I3 etc is the current for each signal to be mixed.


The digital math in the summer can become a non-linear time dependent process.
To model the nonlinear time-dependent process, the current in the summer at an instant of time is:

I(t) = I1(t) + I2(t) + I(3) ...

The impedance is made to be a function of the signal, theoretically due to heating
Z(t) = a + b*I + c*I^2 + d*I^3 ...

where you choose the constants a,b,c,d ... to model the nonlinear network.

Vtotal(t) = I(t) * Z(t)


If you set b=c=d=0, the nonlinear model becomes linear and time independent. But as soon as you wake up these terms, you get nonlinear, time-dependent mixing.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Dr Huge Longjohns » Wed May 27, 2020 2:29 pm

I'm sure lots of you understood that, but alas my brain is too small! But the concept of time related and not time related I grasp, thanks DC.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Hugh Robjohns » Wed May 27, 2020 3:48 pm

I fear DC's maths is oversimplified to the point of not actually illustrating the point he wanted to make.

The argument is that a linear summation (as in a standard DAW) assumes the signal currents are feeding a purely resistive load in the signal-summing element (whatever that might be*), so the source voltages are added in an entirely linear fashion, moment by moment, to generate the output mix signal voltage.

Analogue mixers are designed to work that way too, of course, but the physics of real electronics gets in the way and messes things up a bit.

So, instead of the source signal currents feeding a purely resistive load, that load also has inductive and capacitive elements, otherwise known as 'reactive elements'.

The thing about reactive element is that if you feed in a signal with a step-change in amplitude, you don't get a step out, you get a rising or falling 'shark's fin' shape of signal depending on whether it's inductive or capacitive, respectively. In other words, an instananeous change in amplitude gets smeared out over time.

So, feed a load of rapidly changing signal currents into a reactive load and what comes out the far end isn't a simple linear addition of the source elements. It's a much more complex combination of smeared source elements! And that smearing changes the phase relationships of signal components, and, when considering a stereo signal, that affects the stereo imaging. It's all very subtle of course, but that's part of what's going on.

HTH

*Different analogue mixing systems have employed very different mixing topologies. For example, the earliest mixers simply used large resistors to combine signals, losing a lot of signal level in the process (and this kind of purely passive summer is still available today, requiring a mic preamp to rebuild the signal level post-mix). In contrast, the early Neve consoles used transformers to sum the channel outputs, while later (and most modern) consoles -- specifically like the SSLs, for example -- used active 'virtual earth summing'.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby DC-Choppah » Thu May 28, 2020 10:56 pm

To add more complexity to the circuit model and account for reactance - which means that the impedance is a function of the rate of change of the signal, rather than just the signal itself, then you have to add terms in the polynomial that are proportional to the rate of change of the current - how much it is changing at an instant (time derivatives). That looks like this:


I(t) = I1(t) + I2(t) + I(3) ...

The impedance is made to be a function of the signal, theoretically due to heating, and also the time derivatives (rate of change) of the signal due to parasitic capacitance and inductance:

Z(t) = a + b*I + c*I^2 + d*I^3 ... + B*dI/dt + C*d2I/dt^2 + D*d3I/dt^3 ... + Q*1/(dI/dt) + R*1/(d2I/dt^2) + S*1/(d3I/dt^3) ...

where you choose the constants a,b,c,d ... and B, C, D ... Q, R, S... to model the nonlinear network

Vtotal(t) = I(t) * Z(t)

You have to have terms for the time derivatives, and the inverse of the time derivatives to model both inductance and capacitance respectively.

You can actually put test signals into a network and measure these terms a,b,c,d,B,C,D,Q,R,S ... to try and model the network.

You guys are actually hearing this stuff. It is real.

This is where folks talk about even or odd harmonics. Strong even harmonics mean that the 'even' terms are more dominant (a,c,C,R).

It is really cool that you guys can hear this stuff.
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Dr Huge Longjohns » Fri May 29, 2020 1:38 pm

Well I was seriously bewildered by the last post but this one is seriously above my pay grade! :D
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Re: The analogue-summing '3D' effect: what actually is it?

Postby Logarhythm » Fri May 29, 2020 2:16 pm

Dr Huge Longjohns wrote:Well I was seriously bewildered by the last post but this one is seriously above my pay grade! :D

Roughly it's saying that the impedance changes dependent on:

The current, "I";
The rate that the current changes with respect to time (the "time dependent" bit referred to in DC Choppah's previous post), "dI/dt";
The rate that the rate at which the current changes with respect to time, changes with respect to time, "d²I/dt²";
(Etc)

The exact contribution that each of these elements of the calculation make is dependent on the specific properties of a given circuit.
The notation "dI/dt" is shorthand for saying "how much variable I (in this case, the current) changes as a result of a change in t (in this case, time)". It's a bit more subtle than that in some ways, but IMO this is an entirely valid way to view a differential without getting into actual calculus. Which is fun, but I know that is an opinion that isn't shared by everyone :D

Another way to look at it in terms of what is "happening" inside whatever equipment is being considered is something like (grossly over-simplified but sort of conveys the gist) :

Digital: 1+1=2
Analogue: 1+1 = about 2 ish, dependent on many variables to do with how the specific circuit works and how it's being used/driven. The answer to the sum is therefore generally going to be slightly "wrong" (or perhaps better to say not perfectly "right"), but that wrongness can sound very right if the flavour of wrong is good, and some analogue circuits can give a very pleasing flavour of wrong.

In summary, Walkers should probably launch SSL-flavoured fried potato things. Or something like that.
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