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Volume and Expression
Last post Mon, Aug 30 2021 by Helmholtz, 67 replies.
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Posted on Sat, Aug 28 2021 17:25
by PaoloT
Joined on Tue, Dec 27 2016, Posts 1124

Originally Posted by: Dewdman42 Go to Quoted Post
right in line with the calculations I gave you earlier

Not that I pretend any merit, but it's the formula I proposed in the fifth post of this thread. I only needed confirmation with the most accurate measurement I could do.

I don't really get this idea of "it's resolved, so what's that you still want?". The process is more interesting than the pure result.


Posted on Sat, Aug 28 2021 17:47
by Dewdman42
Joined on Tue, Feb 27 2018, Posts 783
Sorry I am not meaning to stop any further discussion just checking to see whether you got past your original question which it seems like you did. I also did not mean to offend you by suggesting some math to use or to add my own thoughts about how to derive this number accurately. I hope that anything I have said has been helpful in some way, otherwise this thread has become toxic and I intend to leave it. Just wanted to make sure your question has been answered and i think it has been answered at least four different possible solutions.

Posted on Sat, Aug 28 2021 19:51
by PaoloT
Joined on Tue, Dec 27 2016, Posts 1124

Originally Posted by: Dewdman42 Go to Quoted Post
I hope that anything I have said has been helpful in some way

Absolutely yes, and thank you very much for this! You brought several interesting things to this articulate discussion!


Posted on Sun, Aug 29 2021 13:55
by Macker
Joined on Tue, Aug 21 2018, London, Posts 341

Paolo, the error exposed in the spreadsheet has some far-reaching consequences. You may or may not understand the theory behind this, but at the very least you do need to be aware that the erroneous thinking behind that error in the spreadsheet put the discussion on the wrong footing right from the start.

If you'll forgive the techie tedium, I'll go through it one more time.

The formula 20*log(CC ratio) originally (and wrongly) used for the spreadsheet is applicable ONLY IF the CC ratio (perhaps expressed as a percentage) determines audio level changes produced by a device according to what's called a linear law (also known as a straight-line law). That is to say, where a linear law applies to a specific CC-controllable device, any given % change in CC value on the device's input, will cause the same % change in audio level at the device's output. But in the case of volume controls, such as Sy Player's Master Volume and Expression faders, we know from my measurements that they don't work according to a linear law. And that's no surprise at all, because in fact volume controls are always physically manufactured (and now digitally modelled in software) to have what's called a logarithmic law. That's been the general rule as far back as the earliest days of electronics, and it's to match the fact that our ears (and certain other senses also) respond to stimuli in a physiological way that happens to be pretty close to mathematical logarithmic functions, as first described by Ernst Weber and Gustav Fechner in 1860.

The 20*log(ratio) formula is used to express voltage ratios as decibels. The standard definition of the decibel  specifies power ratio, not voltage ratio, and dB are defined as 10*log(power ratio). However, as long as impedance remains a constant, it can be shown that power is directly proportional to voltage squared. And in the magical world of logarithms, multiplying the log of a number by 2 is the same as squaring that number before converting the result to a logarithm. So we multiply the power-decibel formula by 2, and arrive at 20*log(voltage ratio). And in practice the result of the 20*log(voltage ratio) formula is sometimes expressed as dBV. Why voltage? Because voltage (in a well designed audio system) is directly proportional to the resulting sound pressure (units of which are called pascals, defined as Newtons per square metre), which is what our ears respond to. And because of this direct proportionality between voltage levels inside the sound system and the resulting sound pressures eventually produced in the acoustic domain, dB SPL (Sound Pressure Level) are used in the same way as dBV are used in the electronic domain, i.e. using 20*log(sound pressure ratio) to express audio level changes. In practice, dB SPL is always referenced to the threshold of human hearing, conventionally defined as 20 micropascals. And today, inside digital sound systems, instead of audio voltages we have numbers that are directly proportional to the voltage eventually produced by the digital-to-analogue convertor in the system's output stage. So the 20*log(ratio) formula still applies in digital sound systems, just as it did in the days of analogue mixing boards. Moreover, dBFS ("FS" = full scale) is merely the most convenient way to express an absolute level inside the sound system; in fact a ratio is still involved, but in this case the level of interest is referenced to the Full Scale level inherent in the system - regardless of whether the system is analogue or digital. It is customary to express attenuation or gain amounts as simply dB, not as dBFS, because for attenuation and gain, usually it is the ratio which is of interest, not the absolute level.


Now let's consider further the ratio part of 20*log(ratio). If we move the Master Volume slider from full scale (127) down to half scale (64), obviously we can call that a ratio of 0.5 or 50% in relation to the full scale setting on the device's input. But does that result in a 50% change in sound level on the output of this volume control device? No, it most certainly does not, as is verifiable by watching SyPlayer's output level meter, and from my graph and table of input/output measurements. If the sound level dropped from 100% to 50% we would expect to see a fall of 6dB in the output meter reading. But in reality  the sound level falls by 12dB. My 40*log(ratio) formula is simply a reasonably valid mathematical model of these faders, according to my measurements. The factor of 2 above the usual 20*log(ratio) expression is due to the inherent scaling of the logarithmic law of the fader devices. Calling it a "fudge factor" is merely admitting inability to understand the underlying mathematics, as well as an attempt to deflect attention from the fact that the original formula incorrectly assumed a linear law.

From what I've read in the thread - some of which I see has been subsequently edited - you've been advised all along to treat the two volume faders as if they were linear-law devices. I have added my advice that it may be possible to get away with this incorrect assumption just so long as very small changes of ratio are involved. But more generally, I don't see that there's any quick, easy or convenient way of working around the mathematical ramifications of the logarithmic law of these two faders, regardless of whether we express the output audio level changes as dB or as simple ratios. That said, logarithms and decibels owe their existence to their mathematical convenience. For example in working with audio, we can just add or subtract decibels, pretty much in the same quick and easy way as when, say, we do cash transactions in the grocery shop. As far as I know, nobody's invented or discovered a way of making things even more convenient than using those simple additions and subtractions.

My conclusion is that the goal of ignoring the log-law of the fader devices and getting away from decibels, is, sorry to say, just pie in the sky.

Well this dreadfully long lecture probably hasn't served to simplify or clean up the awful mess this thread got into. But I had to put it out there in the hope that, with any luck, nobody else will be led up the garden path by those very wrong technical assumptions and principles posted in this thread.

Posted on Sun, Aug 29 2021 17:39
by Dewdman42
Joined on Tue, Feb 27 2018, Posts 783
Macker you are the one that has dragged this discussion into the gutter with your endless blathering and accusing about how stupid you think other people are.

Unless you are making your measurements outside of the box using sound pressure meters or actual voltage meters, the stuff you just outlined is irrelevant. Digital audio workstation use dBFS as a measurement and the calculation from amplitude percent to dBFS is as I have said: 20 * log10 ( amp percent )

There are are no actual electronical faders involved here nor passage of sound through the air as sound pressure in these measurements.

I still do not see a clear explanation for the 2x factor from there, but I don’t disagree with your measurements either as i have measured the same. I don’t claim, as you seem to, to be any kind of expert on these matters I am simply responding to the thread. I still can find no explanation for this 2x increase above the standard dBFS calculation. If you know the correct answer and can share it without turning it into an offensive personalized attack and drivel I would be interested to hear it and can then relabel the spreadsheet with a better label then “fudge factor” to avoid your scorn. but I don’t think you truly do know the answer you are just blowing around a lot of irrelevant material that is not really helpful.

As I said from the very beginning and you attacked with impunity, the fader in synchron is stated by VSL thus far to be applying a simple linear attenuation on a percentage scale. I understand that you would like to see them label the fader with the equivalent db attenuation on its logrithmic scale so perhaps you can make a simple feature request rather then dragging me and everyone else on this thread through the gutter pontificating your expertise about DB’s and offensive accusations.

I still do not find a reasonable explanation yet for why this linear fader produces 2x of calculated dBFS. And I would be interested to know but this is seriously my last post on this thread because primarily you have made it very unfriendly, very toxic and way more work then it needs to be.

I also don’t particularly think synchron is in “dire” need of db labels on the GUI, but it’s also not a terrible idea. In the meantime I hope the calculations in the spreadsheet can help you or others to quickly calculate the effective attenuation expressed as DB’s.
Posted on Sun, Aug 29 2021 20:36
by Macker
Joined on Tue, Aug 21 2018, London, Posts 341


I rest my case.

No further questions, Your Honour.

Posted on Mon, Aug 30 2021 03:07
by Helmholtz
Joined on Fri, Aug 27 2021, London UK, Posts 5

To @Dewdman42,

You answered me by claiming I'm wrong. And you tried to back up your claim with some apparently technical points that don't make technical sense. Oh please, I'm no noob. All I spoke about was some testing I'd done, the fact that your spreadsheet gave answers way different from my test results. and that my test results agreed with Macker's numbers. Eventually you changed your spreadsheet, saying that a "fudge factor" seemed to be needed, instead of admitting you got it very wrong. And not a word of apology from you to anyone.

What's up with that?

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