The goal is to send the exact, unmolested digital samples from the file out to the DAC, which then sends its analog signal to the amp where you worry about how much to amplify that signal for listening.
When you set everything to 100% volume in software, you can assume that there is no software doing anything to alter the digital signal before sending it to the DAC (scales each sample by 1.0). But when you’re under 100% volume in software, it assumes you don’t have any analog control over the volume, so it needs to step in and alter the digital signal so that it shows up quieter to the DAC (ex. scaling each sample by 0.25). Depending on how that’s implemented, it can result in losing resolution and thus quality of the signal.
I think this mattered more on older software that’s more likely to use a smaller bit depth, but bugs happen, so why risk it and spend those extra cycles on a process that can only result in a worse signal, right?
There’s some confusing stuff in this response so before I get into the weeds, for all the people reading out there: you don’t lose quality by using your operating systems volume control.
Okay, with that out of the way, let’s say you wanted to adjust the volume of a digital stream that’s composed of samples. Each sample represents the original analog signals voltage at that slice of time when it was encoded. The number of slices per second is the sample rate, expressed in kilohertz and the voltage of the original signal is converted to a number, which is stored as a binary value whose length is expressed in bits, each of which can be either a one or zero and is referred to as the streams bit depth.
So you could have a stream whose sample rate is 44.1khz for example and that would mean that it was sampled 44,100 times per second. That same stream might have a bit depth of 16, and that would mean that the original signals voltage level was divided into 65,536 possible values. Depending on some other factors, that stream might just be cdda (a compact discs digitally encoded song information).
Now let’s say you had a computer that was handling that stream and was asked to reduce the volume of the stream by half by a user who can only stand to listen to it at that volume.
One way to do that job would be to decode the stream back into an analog voltage, attenuate it, recode it and then send it on its merry way. That would incur a decoding operation, require routing of that signal to either dedicated hardware to perform the attenuation and send the signal back and an encoding operation to make that now half as loud signal back into a digital stream that can then be sent wherever it’s destined.
Another way of handling that operation is simply dividing every slice of the streams 16 bit component by two, something that computers are very good at doing quickly.
It should come as no surprise then that the latter process is generally how it’s done.
But does that reduce quality or result in worse signal? That’s the question, right?
Well, any variation of one bit or less could be essentially deleted. A person could say “ah hah! The signal has been degraded!” And they’d be technically correct, but it wouldn’t matter.
In our example, the computer whose hands are all over our precious data stream is sending that adulterated information to a dac, which true to its moniker will convert the signal from a digital stream into an analog signal. That analog signal will then be sent to an amplifier with an analog volume control and from there to a set of speakers.
The amplifiers analog volume control is a resistor in the shape of a 3/4 arc with a wiper that can move back and forth across it, allowing anything put in one side to be resisted (or in the case of our ac signal, impeded) a varying amount depending on the users selected position of the knob attached to the wiper.
Okay but what is resisting a signal though? Well, a resistor will reduce the voltage between its two ends proportional to its resistance, measured in ohms. More ohms means more resistance.
For the purposes of our example, let’s assume the user has chosen an amplifier and dac combination such that the amplifiers volume control at minimum setting applies the minimum resistance necessary to completely attenuate the dacs maximum output and is not applying any resistance at its maximum setting. In other words, that it all works as expected and is perfect.
In this case, what’s the difference between sending a stream with data corresponding to a .5V signal that gets amplified as opposed to a stream with data corresponding to a 1V signal that goes through a resistor to bring it down to .5V before being amplified?
nothing
In fact, the digitally attenuated stream will probably sound better (closer to the original) because it’s not subject to the bourns/alpha ppm lottery!
Now.
Don’t let this stop you from listening to music however you like. My ass is itt admitting to using 40 year old record players to make sounds to cook to. But don’t worry about the computers volume control.
Yes, if everything aligns perfectly, there is no impact. The bit shift would be when you set the volume to exactly half, but that’s probably not going to be the case. The app volume control alters the signal slightly, multiplied by the OS altering it slightly, which has a virtual certainty of introducing a floating point rounding error on every single sample, so now the ratios between your samples is ever so slightly different. And for what reason? What did that operation gain you?
And no you’re not going to hear a difference, but the point of being an audiophile is less about hearing a difference, and more about good quality preservation practices.
okay, lets consider the worst possible rounding error in a 16 bit division operation:
i’ll divide the level of one sample by some number that will not divide evenly, lets say three, and consider the impact of the rounding error. for the purposes of making it so I know there will be a rounding error i’ll choose a number that three has a really bad time dividing into, say 65536.
65536/3=21845.3 with the .3 component repeating. perfect, that’s exactly horrible!
so if we were to just do the simplest rounding possible to fit that into a 16 bit integer, the decimal component is dropped, rounding down to 21845.
but what is the significance of that error? a samples volume level that’s one integer value off introduces a .003% error in level, but this isn’t supposed to be 21846, it’s supposed to be 21845.3. so the error that’s introduced is .001%!
that’s a pretty tiny error, but what if it was periodic and consistent enough to produce a harmonic component? that’d create harmonic distortion!
lets say there’s a periodic and consistent rounding error that has a frequency of 1000Hz. so every thousandth of a second, the rounding caused by the volume being set at 1/3 causes a rounding error and makes a sample off by .001%. such a repeating error would introduce a harmonic component into the signal that the dac produces and be measurable as harmonic distortion at 1000Hz!
but how measurable? well if, for example, the harmonic component of the signal introduced was at it’s absolute worst, and oscillated between a positive going error and a negative going error, it could introduce a peak at 1000hz of…
.002% of your dacs DBFS. so far below the noise floor it’s immeasurable.
even if you had two software volume controls set at 1/3 daisy chained together doubling that error it would be immeasurable. although if we picked a computer software package to use instead of a bunch of hypothetical worst cases the total volume of a signal would be summed and then applied once in order to minimize just this problem. the people writing that software are pretty smart and doing that saves their program a step!
but measurability or audibility isn’t the point, as you said. the point is to reproduce the sound as accurately as possible! so it really doesn’t matter how tiny the effect of rounding errors due to prime denominator volume settings is if it’s larger than the effect of the analog volume control that whatever signal the dac manages to reconstruct from our mangled stream is put through. we’re trying to adjust the volume down to a comfortable listening level, after all.
so how bad is the volume control? well, if i were to go to mouser and look at the potentiometers section, i could choose one with a tolerance as low as… .5%! and that’s a three-gang model that costs $50!
but what if i used a precision potentiometer? why, there’s a .15% tolerance part that’s available for the very reasonable price of $825!
okay the precisions are out of my price range, but those $50 ones could work. tolerance is just a number anyway, right? we want linearity! what does the datasheet say about linearity… 2%!
that’s not even considering the amplifier design’s distortion. lets assume it’s perfect.
so just passing the signal from the dac through the amps volume control causes possibly 200 times more error and distortion than adjusting the volume control in the computer.
i get the pursuit of the best possible reproduction, but the computer volumes got those cermet pots beat hands down.
Interesting point. What about the case where you have your digital volume set to 1%? Would this not squeeze the samples into 1/100 the dynamic range? If I set my volume to 1% it seems to me like those samples now have to all exist within the bottom 1% of the 16b range. Do you not lose at least 5-6 bits of precision on your signal doing this?
You don’t lose precision when you lower the volume (in either an analog or digital realm). You lose actual information!
Let’s say you have a recording you can only listen to with your volume at the 1% setting. Analog or digital, it doesn’t matter.
Your whole system has an acoustic noise floor at something like idk, 10 acoustic decibels. That is a really charitable number because I’ve never measured one that low and it directly corresponds to the loudness of another healthy persons breathing at rest. To give you an idea of how quiet that is, the acoustic decibel scale generally puts a ticking mechanical watch at twice as loud (20 decibels).
I don’t want to talk about decibels because I don’t want to explain the math in the detail I’ve been giving these posts, but we gotta at least cover a little:
Decibels are the measure of sound energy, their scale is logarithmic, so the base of the log function determines how many of decibels make for twice as much.
There are different decibels for measuring in different mediums with different references and they even use different logarithm bases.
Acoustic decibels are log10, so that 20 decibel ticking wristwatch is twice as loud as a person breathing and half as loud as whatever the workplace safety scale says 30 decibels is equivalent to.
Okay so now that we have a floor, we need to establish a ceiling. Let’s say that you did everything right and hooked all your stuff up, turned the volume on the amplifier all the way down, put your headphones, played a maximum volume test tone, maxed out the volume on the software, then turned the amplifiers volume control up until it caused you immediate physical pain. If you have really good hearing, that’s 115 acoustic decibels. Let’s say you got to 120 with the amplifiers volume control up all the way.
Okay, so the noise floor of your headphones on your head is 2^11 as quiet as the loudest sound you can tolerate hearing.
Now you set the volume control to 1%. Doesn’t matter which one. Everything gets 99% quieter. The parts of the signal that were 120 decibels before are now 1.2 decibels. They have been divided by 100, and it’s possible that rounding errors have added .006% error to their harmonic content. .006% of 1.2 is .0072 decibels. Not only is the loudest sound you can stand to hear now quieter than a person breathing, it’s below the noise floor of your system. Far, far below the noise floor. And any rounding error from dividing by 100 is as well!
Okay but what happens when you’re listening to music though? Let’s put aside all that hypothetical stuff and get rockin! Instead of talking about test signals and boring crap, let’s talk about a song!
So same established setup from before, but now you’re listening to a recording of someone playing the banjo while rocking in a chair. There’s a lot of different harmonic content in this signal, the birds chirping, the persons breathing, the wind, the chair creaking the boards of the porch and of course, the instrument itself!
All these different things are at different volumes and they represent components of the harmonic content of the signal you’re listening to. When you turn the recording down, you’re attenuating the signal. All of the signal. If you apply enough attenuation through your chosen volume control to lower the level of the banjo by 40 acoustic decibels then all the other components of the signal are lowered by 40 decibels too. If they were previously 50 acoustic decibels through your headset, they’re part of the noise floor.
The quietest information is simply lost.
Edit: there are massive amounts of information that have been simplified so much as to make this post incredibly inaccurate. Please do not use this as a reference for understanding how we measure or interact with sound. I’m sorry for not going into greater detail but it’s too early to explain the relationship and history of acoustic decibels and decibels per volt.
I’m sorry you have to type so much, I am familiar with most of it, but I appreciate your effort to make sure we’re on the same page without being a douche about it lol. It sounds like we’re saying similar things, but I don’t understand why lower precision is different from losing information. To me, that’s the same thing, it’s a lossy operation.
So the thing is, I have a pair of desktop speakers without any physical volume control that I primarily use for convenience. And for whatever reason, a comfortable listening volume with them is between 1-8% in the OS volume control. I guess the internal amp is just hardwired to be way too loud?
Anyway, I assume that this setup is resulting in objectively lower quality output than if I were to have a 100% signal going to a decent quality DAC/amp with analog volume outputting to the same speakers. And not in a “technically” kind of way, but in a very real “we just crushed the signal into 1/25th of its original scale” way. Would you agree? Am I mistaken?
no worries. i’ve been enjoying going back through this. you’re basically me 25 years ago emailing the winamp ppl to find out what volume control i should use to turn down (for what!).
so there’s a misconception here between compressing a signal and attenuating it. imagine you are looking at a frequency spectrum chart of some song instead of listening to it. it’s got some loud sounds, which show up as big peaks on the chart, and some quiet sounds which show up as small peaks on the chart and there’s a noise floor which is the stuff in the chart that’s not a peak at all.
if you plug a potentiometer in between your signal and the spectrum analyzer and turn down the volume, youll see all the peaks, loud and small, be reduced in amplitude by the same amount. this is called attenuation. the quieter sounds could be reduced until they are part of the noise floor and become imperceptible while the louder sounds would still show up.
it doesnt matter if you achieve attenuation by dividing the 16 bit level component of a stream of samples or by using a resistor as a voltage divider. the quiet and loud sounds are affected equally. those two ways of achieving attenuation function the same because they are performing the same operation.
now lets say you plug a rack mount compressor effects module in between your signal and your spectrum analyzer instead. you could apply more compression to the signal and achieve exactly what you describe, a smaller distance between the quiet and loud sounds, reduction of the original scale, removal of dynamic range, effective bit depth reduction! it would be actual factual “we just crushed the signal into 1/25th of its original scale”.
and if you used a module (or software package) with the capacity for it, you could tie the compression ratio to a gain control so that the compressors output got quieter when you turn the compression ratio up, resulting in more heavily compressed sounds at a quieter volume. that’s a neat little mastering trick to make recordings sound “lively” and “intimate”. makes all those pick scrapes and finger swishes stand out alongside the plucked strings.
you could also do the inverse, make all the quiet sounds louder, so that the guitar is as loud as the kick drums’ transient and it would make your whole song sound much louder and stand out better against background noise in a difficult listening environment like a car radio or cell phone inside a solo cup.
there are even modules that do the opposite, called… expanders! they do what you might expect, increase the dynamic range between loud and quiet sounds. a company called DBX made models for use in home stereos in between tape decks and the amplifier in order to reduce the noise floor of tapes.
but it’s none of that is attenuation, the operation that your volume control provides.
and you’re correct, both compression and attenuation are lossy operations no matter if they’re done with analog electronics or by a microprocessor operating on a buffer somewhere in memory. the difference is that attenuation is literally required to prevent permanent hearing loss and possible equipment damage, while compression is not.
Not an audiophile, so bexcuse the ignorance, but what is the logic of max volume in app?
The goal is to send the exact, unmolested digital samples from the file out to the DAC, which then sends its analog signal to the amp where you worry about how much to amplify that signal for listening.
When you set everything to 100% volume in software, you can assume that there is no software doing anything to alter the digital signal before sending it to the DAC (scales each sample by 1.0). But when you’re under 100% volume in software, it assumes you don’t have any analog control over the volume, so it needs to step in and alter the digital signal so that it shows up quieter to the DAC (ex. scaling each sample by 0.25). Depending on how that’s implemented, it can result in losing resolution and thus quality of the signal.
I think this mattered more on older software that’s more likely to use a smaller bit depth, but bugs happen, so why risk it and spend those extra cycles on a process that can only result in a worse signal, right?
There’s some confusing stuff in this response so before I get into the weeds, for all the people reading out there: you don’t lose quality by using your operating systems volume control.
Okay, with that out of the way, let’s say you wanted to adjust the volume of a digital stream that’s composed of samples. Each sample represents the original analog signals voltage at that slice of time when it was encoded. The number of slices per second is the sample rate, expressed in kilohertz and the voltage of the original signal is converted to a number, which is stored as a binary value whose length is expressed in bits, each of which can be either a one or zero and is referred to as the streams bit depth.
So you could have a stream whose sample rate is 44.1khz for example and that would mean that it was sampled 44,100 times per second. That same stream might have a bit depth of 16, and that would mean that the original signals voltage level was divided into 65,536 possible values. Depending on some other factors, that stream might just be cdda (a compact discs digitally encoded song information).
Now let’s say you had a computer that was handling that stream and was asked to reduce the volume of the stream by half by a user who can only stand to listen to it at that volume.
One way to do that job would be to decode the stream back into an analog voltage, attenuate it, recode it and then send it on its merry way. That would incur a decoding operation, require routing of that signal to either dedicated hardware to perform the attenuation and send the signal back and an encoding operation to make that now half as loud signal back into a digital stream that can then be sent wherever it’s destined.
Another way of handling that operation is simply dividing every slice of the streams 16 bit component by two, something that computers are very good at doing quickly.
It should come as no surprise then that the latter process is generally how it’s done.
But does that reduce quality or result in worse signal? That’s the question, right?
Well, any variation of one bit or less could be essentially deleted. A person could say “ah hah! The signal has been degraded!” And they’d be technically correct, but it wouldn’t matter.
In our example, the computer whose hands are all over our precious data stream is sending that adulterated information to a dac, which true to its moniker will convert the signal from a digital stream into an analog signal. That analog signal will then be sent to an amplifier with an analog volume control and from there to a set of speakers.
The amplifiers analog volume control is a resistor in the shape of a 3/4 arc with a wiper that can move back and forth across it, allowing anything put in one side to be resisted (or in the case of our ac signal, impeded) a varying amount depending on the users selected position of the knob attached to the wiper.
Okay but what is resisting a signal though? Well, a resistor will reduce the voltage between its two ends proportional to its resistance, measured in ohms. More ohms means more resistance.
For the purposes of our example, let’s assume the user has chosen an amplifier and dac combination such that the amplifiers volume control at minimum setting applies the minimum resistance necessary to completely attenuate the dacs maximum output and is not applying any resistance at its maximum setting. In other words, that it all works as expected and is perfect.
In this case, what’s the difference between sending a stream with data corresponding to a .5V signal that gets amplified as opposed to a stream with data corresponding to a 1V signal that goes through a resistor to bring it down to .5V before being amplified?
nothing
In fact, the digitally attenuated stream will probably sound better (closer to the original) because it’s not subject to the bourns/alpha ppm lottery!
Now.
Don’t let this stop you from listening to music however you like. My ass is itt admitting to using 40 year old record players to make sounds to cook to. But don’t worry about the computers volume control.
Yes, if everything aligns perfectly, there is no impact. The bit shift would be when you set the volume to exactly half, but that’s probably not going to be the case. The app volume control alters the signal slightly, multiplied by the OS altering it slightly, which has a virtual certainty of introducing a floating point rounding error on every single sample, so now the ratios between your samples is ever so slightly different. And for what reason? What did that operation gain you?
And no you’re not going to hear a difference, but the point of being an audiophile is less about hearing a difference, and more about good quality preservation practices.
okay, lets consider the worst possible rounding error in a 16 bit division operation:
i’ll divide the level of one sample by some number that will not divide evenly, lets say three, and consider the impact of the rounding error. for the purposes of making it so I know there will be a rounding error i’ll choose a number that three has a really bad time dividing into, say 65536.
65536/3=21845.3 with the .3 component repeating. perfect, that’s exactly horrible!
so if we were to just do the simplest rounding possible to fit that into a 16 bit integer, the decimal component is dropped, rounding down to 21845.
but what is the significance of that error? a samples volume level that’s one integer value off introduces a .003% error in level, but this isn’t supposed to be 21846, it’s supposed to be 21845.3. so the error that’s introduced is .001%!
that’s a pretty tiny error, but what if it was periodic and consistent enough to produce a harmonic component? that’d create harmonic distortion!
lets say there’s a periodic and consistent rounding error that has a frequency of 1000Hz. so every thousandth of a second, the rounding caused by the volume being set at 1/3 causes a rounding error and makes a sample off by .001%. such a repeating error would introduce a harmonic component into the signal that the dac produces and be measurable as harmonic distortion at 1000Hz!
but how measurable? well if, for example, the harmonic component of the signal introduced was at it’s absolute worst, and oscillated between a positive going error and a negative going error, it could introduce a peak at 1000hz of…
.002% of your dacs DBFS. so far below the noise floor it’s immeasurable.
even if you had two software volume controls set at 1/3 daisy chained together doubling that error it would be immeasurable. although if we picked a computer software package to use instead of a bunch of hypothetical worst cases the total volume of a signal would be summed and then applied once in order to minimize just this problem. the people writing that software are pretty smart and doing that saves their program a step!
but measurability or audibility isn’t the point, as you said. the point is to reproduce the sound as accurately as possible! so it really doesn’t matter how tiny the effect of rounding errors due to prime denominator volume settings is if it’s larger than the effect of the analog volume control that whatever signal the dac manages to reconstruct from our mangled stream is put through. we’re trying to adjust the volume down to a comfortable listening level, after all.
so how bad is the volume control? well, if i were to go to mouser and look at the potentiometers section, i could choose one with a tolerance as low as… .5%! and that’s a three-gang model that costs $50!
but what if i used a precision potentiometer? why, there’s a .15% tolerance part that’s available for the very reasonable price of $825!
okay the precisions are out of my price range, but those $50 ones could work. tolerance is just a number anyway, right? we want linearity! what does the datasheet say about linearity… 2%!
that’s not even considering the amplifier design’s distortion. lets assume it’s perfect.
so just passing the signal from the dac through the amps volume control causes possibly 200 times more error and distortion than adjusting the volume control in the computer.
i get the pursuit of the best possible reproduction, but the computer volumes got those cermet pots beat hands down.
Interesting point. What about the case where you have your digital volume set to 1%? Would this not squeeze the samples into 1/100 the dynamic range? If I set my volume to 1% it seems to me like those samples now have to all exist within the bottom 1% of the 16b range. Do you not lose at least 5-6 bits of precision on your signal doing this?
You don’t lose precision when you lower the volume (in either an analog or digital realm). You lose actual information!
Let’s say you have a recording you can only listen to with your volume at the 1% setting. Analog or digital, it doesn’t matter.
Your whole system has an acoustic noise floor at something like idk, 10 acoustic decibels. That is a really charitable number because I’ve never measured one that low and it directly corresponds to the loudness of another healthy persons breathing at rest. To give you an idea of how quiet that is, the acoustic decibel scale generally puts a ticking mechanical watch at twice as loud (20 decibels).
I don’t want to talk about decibels because I don’t want to explain the math in the detail I’ve been giving these posts, but we gotta at least cover a little:
Decibels are the measure of sound energy, their scale is logarithmic, so the base of the log function determines how many of decibels make for twice as much.
There are different decibels for measuring in different mediums with different references and they even use different logarithm bases.
Acoustic decibels are log10, so that 20 decibel ticking wristwatch is twice as loud as a person breathing and half as loud as whatever the workplace safety scale says 30 decibels is equivalent to.
Okay so now that we have a floor, we need to establish a ceiling. Let’s say that you did everything right and hooked all your stuff up, turned the volume on the amplifier all the way down, put your headphones, played a maximum volume test tone, maxed out the volume on the software, then turned the amplifiers volume control up until it caused you immediate physical pain. If you have really good hearing, that’s 115 acoustic decibels. Let’s say you got to 120 with the amplifiers volume control up all the way.
Okay, so the noise floor of your headphones on your head is 2^11 as quiet as the loudest sound you can tolerate hearing.
Now you set the volume control to 1%. Doesn’t matter which one. Everything gets 99% quieter. The parts of the signal that were 120 decibels before are now 1.2 decibels. They have been divided by 100, and it’s possible that rounding errors have added .006% error to their harmonic content. .006% of 1.2 is .0072 decibels. Not only is the loudest sound you can stand to hear now quieter than a person breathing, it’s below the noise floor of your system. Far, far below the noise floor. And any rounding error from dividing by 100 is as well!
Okay but what happens when you’re listening to music though? Let’s put aside all that hypothetical stuff and get rockin! Instead of talking about test signals and boring crap, let’s talk about a song!
So same established setup from before, but now you’re listening to a recording of someone playing the banjo while rocking in a chair. There’s a lot of different harmonic content in this signal, the birds chirping, the persons breathing, the wind, the chair creaking the boards of the porch and of course, the instrument itself!
All these different things are at different volumes and they represent components of the harmonic content of the signal you’re listening to. When you turn the recording down, you’re attenuating the signal. All of the signal. If you apply enough attenuation through your chosen volume control to lower the level of the banjo by 40 acoustic decibels then all the other components of the signal are lowered by 40 decibels too. If they were previously 50 acoustic decibels through your headset, they’re part of the noise floor.
The quietest information is simply lost.
Edit: there are massive amounts of information that have been simplified so much as to make this post incredibly inaccurate. Please do not use this as a reference for understanding how we measure or interact with sound. I’m sorry for not going into greater detail but it’s too early to explain the relationship and history of acoustic decibels and decibels per volt.
I’m sorry you have to type so much, I am familiar with most of it, but I appreciate your effort to make sure we’re on the same page without being a douche about it lol. It sounds like we’re saying similar things, but I don’t understand why lower precision is different from losing information. To me, that’s the same thing, it’s a lossy operation.
So the thing is, I have a pair of desktop speakers without any physical volume control that I primarily use for convenience. And for whatever reason, a comfortable listening volume with them is between 1-8% in the OS volume control. I guess the internal amp is just hardwired to be way too loud?
Anyway, I assume that this setup is resulting in objectively lower quality output than if I were to have a 100% signal going to a decent quality DAC/amp with analog volume outputting to the same speakers. And not in a “technically” kind of way, but in a very real “we just crushed the signal into 1/25th of its original scale” way. Would you agree? Am I mistaken?
no worries. i’ve been enjoying going back through this. you’re basically me 25 years ago emailing the winamp ppl to find out what volume control i should use to turn down (for what!).
so there’s a misconception here between compressing a signal and attenuating it. imagine you are looking at a frequency spectrum chart of some song instead of listening to it. it’s got some loud sounds, which show up as big peaks on the chart, and some quiet sounds which show up as small peaks on the chart and there’s a noise floor which is the stuff in the chart that’s not a peak at all.
if you plug a potentiometer in between your signal and the spectrum analyzer and turn down the volume, youll see all the peaks, loud and small, be reduced in amplitude by the same amount. this is called attenuation. the quieter sounds could be reduced until they are part of the noise floor and become imperceptible while the louder sounds would still show up.
it doesnt matter if you achieve attenuation by dividing the 16 bit level component of a stream of samples or by using a resistor as a voltage divider. the quiet and loud sounds are affected equally. those two ways of achieving attenuation function the same because they are performing the same operation.
now lets say you plug a rack mount compressor effects module in between your signal and your spectrum analyzer instead. you could apply more compression to the signal and achieve exactly what you describe, a smaller distance between the quiet and loud sounds, reduction of the original scale, removal of dynamic range, effective bit depth reduction! it would be actual factual “we just crushed the signal into 1/25th of its original scale”.
and if you used a module (or software package) with the capacity for it, you could tie the compression ratio to a gain control so that the compressors output got quieter when you turn the compression ratio up, resulting in more heavily compressed sounds at a quieter volume. that’s a neat little mastering trick to make recordings sound “lively” and “intimate”. makes all those pick scrapes and finger swishes stand out alongside the plucked strings.
you could also do the inverse, make all the quiet sounds louder, so that the guitar is as loud as the kick drums’ transient and it would make your whole song sound much louder and stand out better against background noise in a difficult listening environment like a car radio or cell phone inside a solo cup.
there are even modules that do the opposite, called… expanders! they do what you might expect, increase the dynamic range between loud and quiet sounds. a company called DBX made models for use in home stereos in between tape decks and the amplifier in order to reduce the noise floor of tapes.
but it’s none of that is attenuation, the operation that your volume control provides.
and you’re correct, both compression and attenuation are lossy operations no matter if they’re done with analog electronics or by a microprocessor operating on a buffer somewhere in memory. the difference is that attenuation is literally required to prevent permanent hearing loss and possible equipment damage, while compression is not.