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.