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Does analog gear really sound "better", or is it just a learned response?
Old 21st June 2018
  #1651
Gear Nut
 

I need to clarify one thing: by 100% replication do you mean actually perfect replication, or perhaps you allow for small inaudible errors (e.g. different background noise)?

If you mean the latter, skip to the second part of the post.
Otherwise, if you mean the former, then I need to agree with Bakelite here:
Quote:
Originally Posted by Bakelite View Post
I don't believe 100% replication of anything exists outside of pure math. If you're dealing in terms of applied mathematics then there is no way anything can be replicated or measured with 100% accuracy.
You say that
Quote:
Originally Posted by psykostx View Post
What I am saying is that both modeling methods will always fall short of 100% behavior replication [...]
and then
Quote:
Originally Posted by psykostx;
A digitized signal when reconstructed is exactly the same as the original analog input.
but the two thing contradict each other. The digitized signal is only mostly reconstructed, e.g., the background noise might be different. So that is not 100% pure exact reconstruction, but that difference is irrelevant (to me at least).

If you mean 100% as "no audible errors" (even with some reasonable further processing), then that should be possible to achieve.

First, let me say that I never did any analog circuit modelling, but standard ways of bounding errors should work for any time-dependent signals, and so I guess it should also work for audio.

Quote:
Originally Posted by psykostx View Post
To explain what I'm trying to get across, first it must be a given that individual components don't behave individually, and also can't be usefully measured individually within a circuit without deconstructing the circuit piece by piece and compensating input/output for the missing runs. Because of this, there are two ways to measure circuit behavior with any sort of cost efficiency. One is to account for each component individually, which when all measurable specs are taken into account, will already prove a heavy tax on processing power. The other method is to run test signals through the entire circuit and model functions that account for the differences in output signal against input. The first technique provides incredibly believable models of analog synthesizers and complex analog time domain based effects. The second provides analog models that are indistinguishable from hardware when dealing with digitally generated ITB signals but begin to show as less than ideal when factors such as room ambience and other complex acoustic "artifacts" inherent in, reasonably speaking, all transducer generated signals.
If you model your components as equations, then the process of solving these equations takes into account all the dependencies. The outcome might be not exactly the same as the dependencies of the original system, but there are methods of bounding the total error. For example, if you can prove that under your assumptions, the energy contained in the >1MHz band constitutes some negligible amount of the total energy of the signal, then you can bound how much other components can be affected and hopefully prove that the total error of the whole system is small enough.

In particular, this kind of analysis can allow you to trim dependencies to save computational cost, and still arrive at good results (i.e., with a bounded total error).

Now, this kind of a model can be very complex (to expensive to run as a plugin), but you can use it to get a better idea of what particular box does. For example, you could learn that as long that as the input is only in the audible range, it is enough to use models of order 42 (whatever that means in the context) to get the error into inaudible range. This knowledge allows you to try simpler input-output identification and still arrive at good results.

Furthermore, if you have a reasonable claim that model X can express well what gear Y is doing, then the only thing you need to do is to find the parameters of the model X. It does not matter how will you find them, whether it is by passing all kinds of audible and inaudible signals, or by passing specially crafted audible audio signals (of course, only if these actually can reveal the parameters of the model).

And finally, I am not in the domain of electrical circuits, but I would expect that most standard components have already been modeled with enough accuracy for audio and that work can be reused (i.e., you don't need to model each component or block of components from scratch).

Quote:
Originally Posted by psykostx View Post
What I am saying is that both modeling methods will always fall short of 100% behavior replication, because both methods are missing scores of behavior, even if combined, not because it can't be measured, but because the measurement methods when applied to digital signals, do not contain enough data to reconstruct all relevant behavior, as sampling theorem predicts.
But that is fine if the more complex model predicts which signals (and what measurement techniques) are enough for accurate identification.

Quote:
Originally Posted by psykostx View Post
Circuit behavior [... long cut...] of their behavior.
Yes, but when you attempt to model some gear, have an idea what kinds of happens in it, and what kind of techniques you need to apply. If testing with inaudible signals are necessary for proper modelling, then let it be so. At least I hope that people do that.

The final line is that, if you can prove that your identification method should give you inaudible error (say, even after some reasonable additional processing), then either the modelling assumptions are incorrect, or it actually sounds as good as hardware.
Old 21st June 2018
  #1652
Gear Maniac
 

it's funny that it's only in the minds of sound engineers and musicians . the audience doesn't care. it doesn't matter at all.
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Old 21st June 2018
  #1653
Gear Nut
 

Quote:
Originally Posted by UnderTow View Post
That is why I wrote "If it occurs far outside the audible range, it won't be audible unless it affects stuff in the audible range and that can be measured and modelled." This is pretty obvious and undeniable if you ask me.
There are two things to address here. First, if we are talking about individual components or sub-blocks of them, then we need to take into account how that additional inaudible signal affects processors further down the chain.

Second, even if we are talking about modeling the whole gear box, how do you know if your model is expressive enough? You cannot make it too expressive, because then there might be a problem with what kind of test signals you need to use for proper identification of all parameters (it may even be infeasible).

I agree with you that you can model analog gear with digital tools with accuracy far beyond what humans can notice. But I agree with psykostx that it is really easy to miss something and that special care needs to be taken to account for all kinds of signals (which costs lots of time and effort).

Also, this is a general forum, not a conference for experts in the area. Your obvious might be not somebody else's obvious.

Quote:
Originally Posted by UnderTow View Post
You can look at the whole contraption as a black box. It doesn't matter what happens inside. You just look at what output is caused by any given input within the appropriate bandwidth for human hearing and you have everything you need to know to create a model.
Black box approach is ok only if you have any reasonable guess at what kind of model is expressive enough to handle the type of processing the black box does (and then that box is not so black anymore). To play the devil's advocate, in that black box you could have a component that recognizes if the input signal is a cover of the "Stairway to Heaven" song and then, if it is, completely changes the processing path. Unless you test that black box with a very particular signal, you wouldn't even know that there is some additional complexity that you need to model. While that is a ridiculous example (I am sorry I could not find a better one), I hope you understand how it applies to our discussion.
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Old 21st June 2018
  #1654
Gear Nut
 

Quote:
Originally Posted by Arksun View Post
Of course being an electrical signal it can be measured, at any frequency. Who says analog modelling has only ever been done by looking at the data within the audible frequency range? I'm sure plenty measure far greater range. They can look at as much data as they want to figure out whats happening to the signal, so not really an issue in that respect.
Yes.

Quote:
Originally Posted by Arksun View Post
What Psykostx seems to be arguing is that analog components have an almost magical voodoo element which cannot be understood by analysing all the data from the input to output (even when its per individual component). Like they were created in the heavens and sent down to us humans to use, except they weren't, they were created by human engineers according to specs. Before we even begin to analyse the input output data we already have the original design specs and understanding that the original engineers put into creating those analog components in the first place.
We have the specs, but 1) the specs do not tell you everything (behavior that is negligible in individual elements can be magnified when everything is connected together), and 2) that only shows what the engineers wanted to have. For example, it could have happened that by accident they created a component or a whole box that has some quirks that are the beloved feature of some customer X. If you model by the specs then it is possible that the quirks will not be there, and that's why treating components as having magical voodoo element is sometimes helpful (although I doubt such an approach in general is sustainable as a business).

Quote:
Originally Posted by Arksun View Post
IMHO there is no inherent limitation, its more simply a matter of time and effort by the software designers as to how accurate it should be, that is if the goal is even to make something a 100% clone, it could just be to learn from the best elements of its behaviour to create something totally new, or more dynamic, more controllable, which would actually be far more preferable in my book. Let the best of the past influence, but not dictate limitations for new tools
Yes!
Old 21st June 2018
  #1655
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Quote:
Originally Posted by random musican View Post
Black box approach is ok only if you have any reasonable guess at what kind of model is expressive enough to handle the type of processing the black box does (and then that box is not so black anymore).
Being a non-expert, I just have to ask, if you carefully model an LA-2A, measuring inputs and outputs, using a multitude of examples, and then create software that perfectly mimics that, what the heck difference does it make what goes on inside the black box? You put a signal in, it comes out sounding like an LA-2A.

Unless you somehow think you have to model every possible input (infinite). So the software can get to 99.999%. Who on earth needs more? You can prove your point in abstract mathematical terms, but like you said, this is a general forum.
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Old 21st June 2018
  #1656
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norfolk martin's Avatar
 

Quote:
Originally Posted by random musican View Post
That is simply not true. The interdependencies of components are sometimes very complex and thus create create signals with energy in the band beyond hearing that still might have an effect on the audible range. I am unsure, but I think an example of this is tape bias signal – it is outside of the audible range, yet the tape machines work better with it. Thus, if you model a tape machine and do not model the bias, you might actually have an incomplete model (i.e., one that poorly matches reality).
Tape bias is present to overcome the essentially non-linear transfer characteristics of oxide as a storage medium. Tape is not linear at the low and high ends of the magnetic scale. If you think of a flattened 'S' shape, that is the transfer curve of magnetic tape. The middle of the curve is linear, i.e., 1 unit of magnetism in = 1 unit stored on the tape , 2 units in = 2 units stored , etc.

At the top and bottom of the curve however, things are non linear. if you simply apply a musical signal onto the record head, the resulting recording would be highly distorted at low levels because, the tape storage isn't linear in that range of magnetic inputs

Bias essentially shifts the recorded signal into the linear range of the tape. This was initially done by adding a DC current to the signal, not AC, but this had a couple, of problems because it left the tape with a permanent magnetic polarity, and this caused noise on playback. Ac bias solved the noise problem because it left the tape with no average polarity .

The Ac bias frequency is set well above the range of hearing, usually between about 80 and 150 KHZ. It is certainly not intended to add inter-modulation products to the recorded sound.
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Old 21st June 2018
  #1657
Gear Nut
 

Let me quote you backwards.
Quote:
Originally Posted by robert82 View Post
Unless you somehow think you have to model every possible input (infinite). So the software can get to 99.999%.
This is exactly the issue. 99.999% is fine for me, but that number has to happen for (almost) every possible input.

Quote:
Originally Posted by robert82 View Post
Being a non-expert, I just have to ask, if you carefully model an LA-2A, measuring inputs and outputs, using a multitude of examples, and then create software that perfectly mimics that, what the heck difference does it make what goes on inside the black box? You put a signal in, it comes out sounding like an LA-2A.
Here is an example which I hope will not sound rude to you, I'm just trying to emphasize the issue. It might seems stupid, but something similar happens frequently when doing machine learning wrong.

Suppose we use our multitude of examples to train a model, which gives us almost ideal accuracy on these examples. However, if you run your model on any other signal, instead of processing that signal with the known LA-2A sonic footprint, you get back a part of our training example set. Well, it does sound like LA-2A, but it's a different song (a mashed part of)! This is not what we intended, and the problem is that our model needs to generalize from the training examples to other possible signals (maybe not all of them, but enough to be useful).
Old 21st June 2018
  #1658
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Quote:
Originally Posted by random musican View Post
I need to clarify one thing: by 100% replication do you mean actually perfect replication, or perhaps you allow for small inaudible errors (e.g. different background noise)?

If you mean the latter, skip to the second part of the post.
Otherwise, if you mean the former, then I need to agree with Bakelite here:


You say that

and then

but the two thing contradict each other. The digitized signal is only mostly reconstructed, e.g., the background noise might be different. So that is not 100% pure exact reconstruction, but that difference is irrelevant (to me at least).

If you mean 100% as "no audible errors" (even with some reasonable further processing), then that should be possible to achieve.

First, let me say that I never did any analog circuit modelling, but standard ways of bounding errors should work for any time-dependent signals, and so I guess it should also work for audio.



If you model your components as equations, then the process of solving these equations takes into account all the dependencies. The outcome might be not exactly the same as the dependencies of the original system, but there are methods of bounding the total error. For example, if you can prove that under your assumptions, the energy contained in the >1MHz band constitutes some negligible amount of the total energy of the signal, then you can bound how much other components can be affected and hopefully prove that the total error of the whole system is small enough.

In particular, this kind of analysis can allow you to trim dependencies to save computational cost, and still arrive at good results (i.e., with a bounded total error).

Now, this kind of a model can be very complex (to expensive to run as a plugin), but you can use it to get a better idea of what particular box does. For example, you could learn that as long that as the input is only in the audible range, it is enough to use models of order 42 (whatever that means in the context) to get the error into inaudible range. This knowledge allows you to try simpler input-output identification and still arrive at good results.

Furthermore, if you have a reasonable claim that model X can express well what gear Y is doing, then the only thing you need to do is to find the parameters of the model X. It does not matter how will you find them, whether it is by passing all kinds of audible and inaudible signals, or by passing specially crafted audible audio signals (of course, only if these actually can reveal the parameters of the model).

And finally, I am not in the domain of electrical circuits, but I would expect that most standard components have already been modeled with enough accuracy for audio and that work can be reused (i.e., you don't need to model each component or block of components from scratch).



But that is fine if the more complex model predicts which signals (and what measurement techniques) are enough for accurate identification.



Yes, but when you attempt to model some gear, have an idea what kinds of happens in it, and what kind of techniques you need to apply. If testing with inaudible signals are necessary for proper modelling, then let it be so. At least I hope that people do that.

The final line is that, if you can prove that your identification method should give you inaudible error (say, even after some reasonable additional processing), then either the modelling assumptions are incorrect, or it actually sounds as good as hardware.
The signal passing through a component does not model the behavior of the component in general, only the behavior with that signal. There may be factors of this behavior independent of the input signal, which means that the same signal may be processed entirely differently dependent on variables outside the immediate scope of said component. I think once you understand that, your other questions about my post will be answered. Also my previous posts answer your other questions. I did go to school for physics, which included two semesters of circuit analysis in algebra and calculus. Funny though I didn't learn how to put pen to paper for sampling theorem problems until I made a point of it a few years ago. It's really a bit of basic calculus renamed with fancy audio words.

As you can see by reading replies to my posts, most people have only approached both calculus and sampling theorem algebraically (pre-calculus level) and so don't understand the very specific and literal specific meanings of words used in my posts. They make assumptions based on keywords in examples for the layperson/hobbyist, usually, although sometimes they're simply making assumptions and are too lazy/uninterested to interpret jargon from a different branch of science/math and formulate an understanding of what is being attempted to communicate.
Old 21st June 2018
  #1659
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ponzi's Avatar
Quote:
Originally Posted by KingsX View Post
I can deal with autotune. But that melismatic singing...maybe I'm too old, but I absolutely can't STAND it...
Agreed, but I can't deal with autotune either.

(Philosophical discussion deleted--even I found it boring)
Old 21st June 2018
  #1660
Gear Nut
 

I think I might be missing something here.

Quote:
Originally Posted by psykostx View Post
The signal passing through a component does not model the behavior of the component in general, only the behavior with that signal.
But, if you have a good model, then you can estimate, based on that signal, what would be the response to other signals.

Quote:
Originally Posted by psykostx View Post
There may be factors of this behavior independent of the input signal, which means that the same signal may be processed entirely differently dependent on variables outside the immediate scope of said component.
What stops us from modelling these outside variables as well? I know that gear can sound different depending on the power supply, temperature of the components, presence of other processors (in particular measurement equipment too), etc., but we can estimate the amount of influence these have on the output signal and model them too if necessary (and I guess that original hardware designers tried to minimize the outside influences as much as possible).
Old 21st June 2018
  #1661
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bogosort's Avatar
Quote:
Originally Posted by psykostx View Post
You're thinking in terms of only frequency bandwidth. A digital signal/waveform only has two components, time and intensity. An electronic signal has those components for each of its other components, ie magnetic component, voltage, current, resistance. More than one waveform involved, even if only one is pertinent to the output signal of an analog device, the others can still change circuit performance with regards to the relevant waveform. (again a poor example however it's an obvious one).
A system's frequency response is dependent on those aspects, and so the mathematical model of the system accounts for them. For example, when a circuit element is described as having an impedance Z at some frequency, the value of Z is a complex number R + jX (with R purely resistive and X purely reactive) that accounts for the phase difference between voltage and current at that frequency. When X is positive, the element is inductive (current lags voltage); when X is negative, the element is capacitive (voltage lags current). The transfer function of the element encodes its total impedance as a function of frequency, characterizing the element for all frequencies. The relationship between voltage and current is implicit in the impedance model, which is used to build a complete mathematical description of the system.

Nonideal behavior can be handled in different ways, depending on its effect on the application. An ideal resistor is purely resistive (Z = R), but real resistors exhibit parasitic inductance and capacitance. Yet this doesn't mean that we have to model every resistor as a complex impedance. For typical through-hole resistors, the parasitics are on the order of nanohenries and picofarads, which is very significant for high-speed circuits (signal frequencies in the hundreds of MHz), but totally insignificant for audio circuits.

So, in the context of audio circuits, a resistor justifiably can be modeled as a purely resistive element. If we want to model its temperature coefficient, no problem, the purely resistive element R becomes a function of temperature R(T). Maybe we want to add Johnson noise to the model, no problem, add some Gaussian noise: R(T) + e(t). Does the noise term need to be a quantum-correct model of electron movement? Of course not, because our ears cannot tell the difference.

Likewise, we do not need to solve Maxwell's equations in real time to model all the magnetic fields induced by signal currents. In the vast majority of audio circuits, magnetic fields are either shielded or entirely insignificant. To give an idea of typical magnitudes involved, the magnetic field strength 3 cm from a wire carrying a 1 mA current is about 10 nanoTesla, which is 2,500 times weaker than the Earth's magnetic field. Analog designers are well aware of how noise can be coupled onto signal, and spend considerable effort thwarting those paths, e.g., by routing higher current wires/traces away from signal-carrying traces.

The point is that for audio applications we do not need to model the entire physics of a circuit.
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Old 21st June 2018
  #1662
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Quote:
Originally Posted by random musican View Post
I think I might be missing something here.


But, if you have a good model, then you can estimate, based on that signal, what would be the response to other signals.



What stops us from modelling these outside variables as well? I know that gear can sound different depending on the power supply, temperature of the components, presence of other processors (in particular measurement equipment too), etc., but we can estimate the amount of influence these have on the output signal and model them too if necessary (and I guess that original hardware designers tried to minimize the outside influences as much as possible).
That's exactly what I'm saying, those variables can't be accounted for 100%, the model is always an estimate. It's not mathematically possible to perfectly model analog circuitry using contemporary processing technology, there are too many permutations of cause and effect feedback that are outside the influence of the signal itself yet still affect it. Even plugging a piece of gear into a different signal chain can totally change its behavior. Analog gear being part of a chain is simply another aspect of audible behavior modification, which can be modeled, but now your factors are increasing by logarithmic proportions, on a logarithmic order of magnitude. Simple sampling changes in test signals is an approximation, unlike sampling theory, which works on functions, because true functions have predictable factors, not other functions as factors (that may or may not be true functions).

Most people assume that measuring the signal is measuring the behavior, because sampling theorem guarantees 100% duplication for the signal and changes to the signal by functions that use the signal as a variable. But not all behavior are functions of the signal. There are non-sinusoidal behaviors as well as complex functions an non-functions with complex factors.
Old 21st June 2018
  #1663
Gear Addict
 

Right on... well said. Oftentimes, in design engineering, "close enough" really IS close enough.

Quote:
Originally Posted by bogosort View Post
A system's frequency response is dependent on those aspects, and so the mathematical model of the system accounts for them. For example, when a circuit element is described as having an impedance Z at some frequency, the value of Z is a complex number R + jX (with R purely resistive and X purely reactive) that accounts for the phase difference between voltage and current at that frequency. When X is positive, the element is inductive (current lags voltage); when X is negative, the element is capacitive (voltage lags current). The transfer function of the element encodes its total impedance as a function of frequency, characterizing the element for all frequencies. The relationship between voltage and current is implicit in the impedance model, which is used to build a complete mathematical description of the system.

Nonideal behavior can be handled in different ways, depending on its effect on the application. An ideal resistor is purely resistive (Z = R), but real resistors exhibit parasitic inductance and capacitance. Yet this doesn't mean that we have to model every resistor as a complex impedance. For typical through-hole resistors, the parasitics are on the order of nanohenries and picofarads, which is very significant for high-speed circuits (signal frequencies in the hundreds of MHz), but totally insignificant for audio circuits.

So, in the context of audio circuits, a resistor justifiably can be modeled as a purely resistive element. If we want to model its temperature coefficient, no problem, the purely resistive element R becomes a function of temperature R(T). Maybe we want to add Johnson noise to the model, no problem, add some Gaussian noise: R(T) + e(t). Does the noise term need to be a quantum-correct model of electron movement? Of course not, because our ears cannot tell the difference.

Likewise, we do not need to solve Maxwell's equations in real time to model all the magnetic fields induced by signal currents. In the vast majority of audio circuits, magnetic fields are either shielded or entirely insignificant. To give an idea of typical magnitudes involved, the magnetic field strength 3 cm from a wire carrying a 1 mA current is about 10 nanoTesla, which is 2,500 times weaker than the Earth's magnetic field. Analog designers are well aware of how noise can be coupled onto signal, and spend considerable effort thwarting those paths, e.g., by routing higher current wires/traces away from signal-carrying traces.

The point is that for audio applications we do not need to model the entire physics of a circuit.
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Old 21st June 2018
  #1664
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bogosort's Avatar
Quote:
Originally Posted by psykostx View Post
It's not mathematically possible to perfectly model analog circuitry using current processing technology, there are too many permutations of cause and effect feedback that are outside the influence of the signal itself yet still affect it.
Forget DSP for a moment. Do you believe that we can model analog circuitry mathematically?
Old 21st June 2018
  #1665
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Quote:
Originally Posted by bogosort View Post
Forget DSP for a moment. Do you believe that we can model analog circuitry mathematically?
possibly yes.

but not by any "consumer" computer

throw real time characteristics into the equation... possibly not.

as far as vst's go, its only recently they've included aftertouch algorhythms.

and tbh... they dont sound too good when playing them.
Old 21st June 2018
  #1666
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bogosort's Avatar
Quote:
Originally Posted by Preston135 View Post
possibly yes.

but not by any "consumer" computer

throw real time characteristics into the equation... possibly not.

as far as vst's go, its only recently they've included aftertouch algorhythms.

and tbh... they dont sound too good when playing them.
I meant mathematical model, as in a set of equations that can be written on a piece of paper.
Old 21st June 2018
  #1667
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Quote:
Originally Posted by bogosort View Post
I meant mathematical model, as in a set of equations that can be written on a piece of paper.
it can be quite simple math if you use letters as numbers.

but you need to factor in the time to calculate it.
Old 21st June 2018
  #1668
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Quote:
Originally Posted by Preston135 View Post
as far as vst's go, its only recently they've included aftertouch algorhythms.
What am I missing? Many VSTs have aftertouch or channel pressure or whatever the brand chooses to call it, that can be routed to any parameter any other controller can be routed to.
Old 21st June 2018
  #1669
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Quote:
Originally Posted by newguy1 View Post
What am I missing? Many VSTs have aftertouch or channel pressure or whatever the brand chooses to call it, that can be routed to any parameter any other controller can be routed to.

when i say recently i mean in the last 8-10 years...

however i still don't feel a very good interaction with vsts. something seems to be lagging somewhat.

i've not heard a vst yet that has made me think "right.... now i need to dedicate a computer with a vst host to play this from my sequencer"
they ALL have that horrendous sizzleing sort of sound to them.

not that that is anything to do with analouge. the digital and fm synths don't have it.

Last edited by Preston135; 21st June 2018 at 08:05 PM..
Old 21st June 2018
  #1670
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soundebler's Avatar
Quote:
Originally Posted by Preston135 View Post
possibly yes.

but not by any "consumer" computer

throw real time characteristics into the equation... possibly not.

as far as vst's go, its only recently they've included aftertouch algorhythms.

and tbh... they dont sound too good when playing them.
Only recent discovered the true meaning of putting vibrato in after touch on a synth that i have few decades . Got to vibrate the finger to get the vibrato going always thought simply pushing harder is the way . That make even harder emulating , but would not be impossible in the future .

Having nothing against digital and it have it advantage , but for experience it is a bit different . Do remember listing to first generation cd together with vinyl and cd sounded just as good . Put my vinyl by the garbage and till today no regrets , but using compact cassette for recording . The top end limitation help to get Arp Pro Soloist nice cut in top end , the synth go way 24 KHz . Using DBX noise suppressor help to bring Eminent 310 noise down and it do kind of filtering, do use noise gates but when they open noise come also.

More like spiritual thing and the people are in able to mysterious things that can not be explained by normal logic . The people make the gear and the music we listen to and every evolutionary step it do seem different . Also the rise of Ai could mean a fully automated production process , that scares me
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Old 21st June 2018
  #1671
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Quote:
Originally Posted by bogosort View Post

So, in the context of audio circuits, a resistor justifiably can be modeled as a purely resistive element. If we want to model its temperature coefficient, no problem, the purely resistive element R becomes a function of temperature R(T). Maybe we want to add Johnson noise to the model, no problem, add some Gaussian noise: R(T) + e(t). Does the noise term need to be a quantum-correct model of electron movement? Of course not, because our ears cannot tell the difference.
We have to be very careful here. The same rationalizations could be made for capacitors, that a capacitor in an audio circuit could justifiably be modeled as a purely capacitive element, since the parasitic inductance and resistance are too small to matter in a high impedance audio circuit. But then different caps with the same value and seemingly negligible parasitics can sound different.

And then what about non-linearities in passive components? Modeling everything with linear elements, it would be impossible to have any passive circuit generate distortions. But they do. How to model second order effects like capacitor plate and transformer winding vibrations, skin effect causing resistance modulation, voltage coefficients of resistors? How to model dielectric absorption, non-linear polarization of dielectrics, magnetization curves of transformer cores, etc? All these things can potentially contribute to the sound of analog circuits made with real components. Not saying they all do. Depends on a lot of things. But they also can't all be swept under the carpet as negligible.
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Old 21st June 2018
  #1672
Gear Addict
If the question is purely for audiophiles ..engineers...ill put it this way...running a 16 channel mix from my laptop to my prism lyra sounds great!! Now running the same stems through my ssl analog x-rack with 16 inputs with analog pans and volume controls puts an even bigger smile on my face....i hv my answer no need to ever wonder for me again
Old 21st June 2018
  #1673
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norfolk martin's Avatar
 

Quote:
Originally Posted by bogosort View Post
Forget DSP for a moment. Do you believe that we can model analog circuitry mathematically?
Ohhoo ..can of worms. Yes and no, IMO.

Or yes, but the degree of complexity may become too great to be practical at some point.

All design rests, to a large degree on modeling circuits mathematically. At the lowest level, a designer who wants to know what the output of, say:

a certain transistor with stated characteristics, in a circuit with a +10v supply rail, a 1 uF coupling capacitor on the input, a 10K bias resistor, A 1K emitter resistor and a 10 K load resistor

When

a 1v p-p sine wave at 1Khz is placed on the input;

doesn't need to build the circuit to know what the output will be. If all specs are accurate, it can be mathematically determined by a simple equation.

It is when a circuit is pushed into non-linear operation that the mathematical description of its operation become more complex. if the non-linearity itself has strongly random features, the equation becomes increasingly complex..

Eventually, I assume it will become too complex to be used.

By example, although it is possible to describe white noise over a substantial time period by an equation , is there an equation to predict the exact combination of frequencies that noisy transistor produces in a a near to instantaneous time period?
Old 21st June 2018
  #1674
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Originally Posted by u87allen View Post
We have to be very careful here. The same rationalizations could be made for capacitors, that a capacitor in an audio circuit could justifiably be modeled as a purely capacitive element, since the parasitic inductance and resistance are too small to matter in a high impedance audio circuit. But then different caps with the same value and seemingly negligible parasitics can sound different.
I would not say that capacitors have a sound. Rather, circuits have a sound, and a capacitor's contribution depends on its role in the circuit. For example, a circuit that uses a large electrolytic (the worst type in terms of non-ideal behavior) as a coupling cap won't sound any different if we replace it with an equally large film type. The cap is there to block dc, and simply won't carry enough signal voltage to affect the sound of the circuit. Likewise, for a well-designed power supply, the precise characteristics of the bypass caps won't matter at all.

In the cases where the choice of cap does matter, such as filter stages, a more detailed capacitor model can be used. Even here, though, good designers tend to use caps that have negligible audio effects, such as polypropylene types.

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And then what about non-linearities in passive components? Modeling everything with linear elements, it would be impossible to have any passive circuit generate distortions. But they do. How to model second order effects like capacitor plate and transformer winding vibrations, skin effect causing resistance modulation, voltage coefficients of resistors? How to model dielectric absorption, non-linear polarization of dielectrics, magnetization curves of transformer cores, etc? All these things can potentially contribute to the sound of analog circuits made with real components. Not saying they all do. Depends on a lot of things. But they also can't all be swept under the carpet as negligible.
This is what measurement is for. If a circuit uses carbon comp resistors with large voltage coefficients, then the modeler needs to test the resistance as a function of voltage; this becomes the resistor model. If the dielectric absorption of a cap is significant (easily testable), model the cap as a capacitor in parallel with several smaller capacitors, each with a series resistance.

Note that most of these nth-order effects are highly variable between components of the same type, so we should expect two compressors of the same brand to have variable amounts of per-component nonlinearity. Yet we also expect the two compressors to sound the same, and they usually do, because a big part of the circuit designer's job is to minimize the effects of non-ideal components. The modeler's job is to find the right amount of detail that characterizes the sound. Both jobs are hard! But neither is impossible.
Old 21st June 2018
  #1675
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Originally Posted by norfolk martin View Post
Ohhoo ..can of worms.
I asked because if he doesn't believe that even mathematical modeling is possible, then there's no point in trying to convince him that digital modeling is possible.

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It is when a circuit is pushed into non-linear operation that the mathematical description of its operation become more complex. if the non-linearity itself has strongly random features, the equation becomes increasingly complex..

Eventually, I assume it will become too complex to be used.
Right, so the weather is a good example of a nonlinear system that is (currently) too complex for us to model accurately. Fortunately, analog sound processors are not nearly so complicated or nonlinear.

But you're right, even the small nonlinearities of analog circuits can be challenging to model mathematically. The problem is that most of the friendly, comfortable mathematical tools that we've developed to handle these sorts of things only work with linear systems. In order to use them, the nonlinear systems have to be "linearized" over small ranges, and then combined piecewise. Alternatively, there are mathematical tools (like Volterra series) specifically designed for nonlinear systems, though I've never formally studied them.

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By example, although it is possible to describe white noise over a substantial time period by an equation , is there an equation to predict the exact combination of frequencies that noisy transistor produces in a a near to instantaneous time period?
Quantum mechanics tells us that there can never be such an equation. Or, if your prefer, we can think of it in terms of Fourier duals: the more precisely we zoom in on a specific time, the less precisely we know what specific frequency we are seeing (and vice versa).

But while there isn't an equation that can predict exactly what the noise output of a transistor will look like, there is a simple equation that describes band-limited white noise, and our ears would not be able to tell the two apart.
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Old 22nd June 2018
  #1676
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Originally Posted by bogosort View Post
The cap is there to block dc, and simply won't carry enough signal voltage to affect the sound of the circuit.
This is what I thought at one point: "It's only a coupling cap. There's simply not enough voltage and current(line level signal, input Z of the headphone amp is 10KΩ, driver is a Lynx-2 soundcard) through the cap to be of any consequence here." And then I swapped out an EPCOS 4.7uF poly-cap for a Clarity 4.7uF poly-cap. Very noticeable difference in the coherency of the sound from the upper-mids through the high frequencies.
Old 22nd June 2018
  #1677
Gear Head
It seems there are two different discussions going on here. One emphasizes that 'you can't clone infinity' and with an infinite number of non-linear permutations there is no (and never will be) a model of cloning that can account for every possible outcome of a signal. Then there is the discussion around the premise to find solutions within a limited, but acceptable, range of conditions.
I often go back to this video as a good example of digital modelling. Guitar players love tubes and transformers. Here's a studio musician who makes a career out of playing them and is modelling his amps. The meat of it starts around 2:00. the A/B is very interesting. And this technology is already a few years old.

we can discuss theoretical impossibilities all day long but in the end, what is the practical application of that?

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Old 22nd June 2018
  #1678
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Originally Posted by u87allen View Post
This is what I thought at one point: "It's only a coupling cap. There's simply not enough voltage and current(line level signal, input Z of the headphone amp is 10KΩ, driver is a Lynx-2 soundcard) through the cap to be of any consequence here." And then I swapped out an EPCOS 4.7uF poly-cap for a Clarity 4.7uF poly-cap. Very noticeable difference in the coherency of the sound from the upper-mids through the high frequencies.
4.7 uF is way too small for a coupling cap. At 20 Hz, the cap will present an impedance of 1.69 k! No wonder changing the cap changed the sound; it's a terrible design choice. Try replacing it with a large-value electrolytic, it should open up even more. Anything over 470 uF should be fine. At that size, the signal voltage that develops across the cap will be tiny, making the electrolytic's performance irrelevant.
Old 22nd June 2018
  #1679
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Originally Posted by bogosort View Post
I would not say that capacitors have a sound. Rather, circuits have a sound, and a capacitor's contribution depends on its role in the circuit. For example, a circuit that uses a large electrolytic (the worst type in terms of non-ideal behavior) as a coupling cap won't sound any different if we replace it with an equally large film type. The cap is there to block dc, and simply won't carry enough signal voltage to affect the sound of the circuit. Likewise, for a well-designed power supply, the precise characteristics of the bypass caps won't matter at all.
That hasn't been my experience. Many will argue the best coupling cap is a piece of wire, and there is some truth in that.

The old SSL 4k sound is in part due to all the coupling caps. The newer SSL has eliminated them for DC coupling where possible. So they intentionally chose a more difficult design path, no reason to if caps didn't matter.

Fred Forssell makes wonderful gear. In his writings he talks about spending lots of time designing a low impedance power supply. Again no reason to if a few electrolytics would do the job.
Old 22nd June 2018
  #1680
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Originally Posted by johnnyc View Post
That hasn't been my experience. Many will argue the best coupling cap is a piece of wire, and there is some truth in that.

The old SSL 4k sound is in part due to all the coupling caps. The newer SSL has eliminated them for DC coupling where possible. So they intentionally chose a more difficult design path, no reason to if caps didn't matter.

Fred Forssell makes wonderful gear. In his writings he talks about spending lots of time designing a low impedance power supply. Again no reason to if a few electrolytics would do the job.
There's no shortage of hearsay about coupling capacitors, but Doug Self writes authoritatively about the subject. His data doesn't lie.

I get that the idea of placing an electrolytic in the signal path seems truly terrible, but the reticence goes away once you realize that a big enough cap acts like a piece of wire at audio frequencies. If there's no signal voltage across the cap, then it literally can't affect the sound, no matter how nonlinear the cap itself may be.
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