Repro-1 (out now)

[Urs]

Witchcraft confirmed. Repeat; confirmed witchcraft.

Smells like Newton-Raphson but I don't understand where the delay went, as my current understanding was that there had to be one *somewhere*, even, in a very real sense, with ZDF filters.

http://urs.silvrback.com/zero-delay-feedback

2 things always mixed up: Computation of implicit non-linear equations vs. numerical integration. ZDF aka "delayless feedback loop" refers to former while latter indeed requires the presence of a unit delay (which is why I started a blog about it, and which is also why we're having this thread)

[Vesius]

Because the filter is reliant on it's own output as one of it's inputs. The incurs a 1 sample delay in software which would not be present in hardware as this would be to all intents and purposes instant. You have to do the maths to get the output, but you cannot do the maths accurately without the input. If the sampling rate was the same as the speed electricity moved across a circuit, this would no longer be a problem.

Now, you can juggle the outputs around a bit, and eliminate this delay on the input side (ZDF), but overall it's still delayed.

[FLWrd]

But one resistor's output is depending on the state of the other, and still it doesn't require a unit delay. That's because the behavior of the resistor can be expressed as a simple linear formula and we know how to solve a combination of those.

The behavior of an RC network can also be described in closed form, e.g. for the stepping function: 1 - exp(-t/RC), if I remember correctly, even though the function of the capacitor depends on its own output. You can also solve it for a sine wave, and a sum of sine and cosine waves, etc.

But you can't derive a closed form for an arbitrary input for an RC network, and that's also true for more complex networks. However, the description of the network is does give an "immediate" description of the variables involved, so it then becomes a matter of solving it efficiently and sufficiently accurately.

[Vesius]

You're out of my depth, I'm afraid, I'm a software engineer with extremely limited understanding of circuits - but quite good knowledge of C++ ... so I think we are coming at things from the opposite perspective.

Urs, thanks for the link, I'll check that out - if you say a ZDF doesn't delay overall, that's good enough for me, I'll go and smash my head against a wall until I understand it better As you say in the blog, I suspect I have become confused over the resonance path implying a delayed feedback, even if it is implicit that it doesn't.

[FLWrd]

Try this. Suppose you have a simple equation: df / dx - f = 2x. This one can be solved analytically (http://www.wolframalpha.com/input/?i=df ... -+f+%3D+2x). But you could also try to solve it numerically if you new that f(1) = -1.2817 and f'(1) = 0.71828 and now you have to solve it for x = 1.00001, and then for x = 1.00002, etc.

[hakey]

but you cannot do the maths accurately without the input

The initial input comes from a best guess. One iteration of calculation is performed using that guess, which allows a more accurate guess. Further iterations are performed with progressively better guesses until a solution (input=output?) is arrived at. This all happens within one sample.

[Urs]

As you say in the blog, I suspect I have become confused over the resonance path implying a delayed feedback, even if it is implicit that it doesn't.

Indeed, a 1-sample delay in the feedback path has been state-of-the-art for a long time, possibly mostly because people did not want to smash their heads against any wall.

However, nowadays it's state-of-the-art to *not* have a delay in the feedback path. Because some people have smashed their heads against a wall and figured it out

[Urs]

but you cannot do the maths accurately without the input

The initial input comes from a best guess. One iteration of calculation is performed using that guess, which allows a more accurate guess. Further iterations are performed with progressively better guesses until a solution (input=output?) is arrived at. This all happens within one sample.

[louderr]

Lastly, one algorithm computes the actual equations of the form y = tanh( y ) as they are, but it involves computing the whole filter not once or twice, it involves computing it several times, usually between 2x and 6x until the correct solution is found. This algorithm provides for a mathematically accurate method without any form of unit delay.

Witchcraft confirmed. Repeat; confirmed witchcraft.

Smells like Newton-Raphson but I don't understand where the delay went, as my current understanding was that there had to be one *somewhere*, even, in a very real sense, with ZDF filters.

Unless, the previous state of the system is modelled as part of modelling the current state all within one sample ... but that previous state would require the previous previous state and so on ... urgh.

Anyhow, your secrets are your secrets obviously , I just like getting my brain spinning

Yeah this one hurt my feelings too Witchcraft +1 double-confirmed

[louderr]

Witchcraft confirmed. Repeat; confirmed witchcraft.

Smells like Newton-Raphson but I don't understand where the delay went, as my current understanding was that there had to be one *somewhere*, even, in a very real sense, with ZDF filters.

http://urs.silvrback.com/zero-delay-feedback

2 things always mixed up: Computation of implicit non-linear equations vs. numerical integration. ZDF aka "delayless feedback loop" refers to former while latter indeed requires the presence of a unit delay (which is why I started a blog about it, and which is also why we're having this thread)

I read Urs' blog and, despite very limited algebra ability, got the concept. WOW I wish I could do math, it's like magic when someone finds a way to trick the equations like that. So does that mean the high internal sample rate leaves enough room for the whole cycle to get solved before funnelling it into the (slower) DAW sample rate? Is that why this is possible? Witchcraft still suspected,but holding off on lighting the bonfire

[kybernaut]

Nice math head chit chat around here...
But... when can we expect the solution (which is which)?

[PAK]

What am I missing, exactly? I want to train my ears a little better. Is it possible that these filters gave wildly different results on various computers and speakers? Or is the variance more subjective, as it may very well be in my case? And what about the dropouts and artifacts across parts of the filter range in #3 and #4. Personally, I thought #5 worked okay and had good fidelity but it struck me as sort of "bland". Just reporting, interested in feedback on this

Preference is subjective, but there’s a few things to make it less so. The first is to know what changes when you switch between numbers 1-5 - IE the resonance and OSC B modulation patterns.

Next is trying to figure out what's unique to each. What you cannot adjust for, between model numbers using mod rate and cutoff/res controls, are the differences. There's no shortcut to trying things. The more settings you try, the more you may notice one doing something the rest don’t.

For example, you heard number 1 as “dirty”. You probably won't be able to get the others to sound quite like that, even if you adjust them. If you move OSC B to higher modulation rates, and play higher octave notes, what you call dirty sounds like traditional digital aliasing style noises to some of us.

But, because of the type of noises being made, all of them sound a bit like tuning a shortwave radio with OSC B modulation. So, in those cases, listen for the noises made as you sweep the mod rate control. You might notice 2 and 5 avoid the "digital type" noises most with sweeps. They'll sound more like cleaner laser blips that get faster or slower as you move the control, if that description makes sense. Try turning the mixer Osc volumes to zero to hear only the filter better.

So why didn’t 2 and 5 lead the poll? Why don’t many like 2? Well, if you take those noises away, you might notice you lose something else you like in the filters range. For example a more closed filter bass sound might lack something in the higher frequencies using resonance with number 5 versus number 1.

It’ll be interesting to see what Urs says about that. Maybe it's just that a bit of noise in the filter itself (not the mixer noise knob ) can help with impressions of higher frequencies..

How useful any of this is, beyond understanding your own tastes? Dunno.. especially in this case, since it mostly seemed to be about the noise differences. I doubt you'd be able to match the sweeping sound Urs made with his own Pro 1 with any in their present form. Emulating that sets himself a very high target.

[PAK]

I do not believe in comparing two synths based on different hardware schematics. It only makes sense to me to be comparing something like Monark to other Minimoog emulators, preferably at extreme settings where the shortcomings of virtual models become more apparent.

Why would you limit yourself like that? For example, if you switch to Diva's 12dB Cascade filter mode you'll hear feedback goes some way towards Monark territory. Likewise, for non-feedback sounds, the Uhbie filter is often much closer to Monark - especially for bass sounds.

Point being, if you follow that line of thinking, you wouldn’t notice that Diva covers more of what Monark does than you might otherwise think, because it needs to step outside of its Moog model to do it.

With regards to extremes exposing shortcomings, maybe not always. EG in NI's own Monark comparison I likely couldn't tell the difference between many examples using extreme settings. But I still heard a small difference between the oscillators in the opening sound

If anything, there may be an argument that the more you go towards extreme sounds the harder it is to express anything, whether preference or otherwise. Unless one is creating obvious unpleasant artifacts, does it really matter which one does the best wrrrr-burp clang noise? It might be better to think in terms of more complex harmonic musical interactions, and why we might want them, which sometimes goes hand in hand with extreme settings.

Settings, components, and calibration, along with recording chain, mean it’s never going to be that easy to compare things. Over the years that’s been used not only by people overstating how unique analogue hardware is but, on the other side, as the snowflake defence.. IE each hardware synth is its own unique snowflake, which is then used to explain why virtual versions sound different. That fails to address the elephant in the room, which is that often the differences are more about the consequences of circuit model simplifications, which all digital emulations must do. More extreme settings are just something which helps show those simplifications, but many other things can do that too

[louderr]

WOW @Pak thanks, that's so detailed and useful, I'm gonna do just that and see if it opens my perspective up somewhat. Appreciate it.

[zerocrossing]

What a load of BS..

No it's not. People can't really hear compression, or distortion artifacts, unless they know and understand what they are hearing. I've done this test with people many times - in general terms, people just don't know what "sounds good" means - often they hear a bunch of over-compressed, distorted awful mixes and assume it's goog sounding - until they are educated, and can hear the difference, and now *know* what sounds good and what doesn't.

I call B.S. My wife just got me a turntable for my birthday and I did an A/B test with an Apple AAC file and the analog copy and my self described "can't hear anything" wife and her cousin both instantly picked out the compressed file. What people can't always hear is when things are in isolation because so many factors can consipire to make something sound different.