As discussed, lowering the volume in software (which is what you likely mean by "controlling the DAC") is accomplished by reducing bit depth. By definition you're reducing the amount of signal present which makes your S/N worse. If by "controlling the DAC" you mean reducing the signal at the DAC's analog stage then there's nothing theoretically wrong with that (except that it's rarely if ever the case in computer sound cards or hi-fi DACs) as it is the equivalent to adjusting the volume on your (integrated) amp.

Probably the most common exception to the above is people using a digital EQ to attempt to improve the sound of a mediocre computer audio setup. Most digital EQs allow for both "boost" and "cut" -- increasing or decreasing the amplitude of individual frequency bands. If you EQ the music the proper way you should only cut frequency bands in order to emphasize the other bands to suit your listening tastes. For example if you want to try to increase the amount of bass you should cut the mids and the highs and turn up the volume (on your amp) to compensate. EQing this way ensures that you're not forcing the signal into clipping by boosting too much.

You still won't get great results because if you're lacking bass or highs then it's most likely because you're not running full range speakers. If the sound does change when you EQ it's most likely due to increased distortion, not because you're appreciably increasing the amount of bass present. That's not true for full range speakers but if you have full range speakers you probably wouldn't need to EQ in the first place. (Full range speaker are usually 20 - 50hz to 20khz.)

If it's still not clear than think of it this way: Standalone CD players don't have volume controls. Their output will be "max volume" of what's on the CD. You can think of your computer and sound card like a (crappy) CD player. Make sure it's at max volume and adjust the level on your external amp or amplified speakers.

No, reducing the amplitude of a digital signal does not change its bit depth. If the amplitude of the digital signal is reduced, then a couple of bits on the MSB side will be constant. However, reducing the bit depth would make bits on the LSB side constant.

To state it differently, a lower bit depth increases the quantization levels and results in lower quality audio. Reducing the amplitude retains the same quantization level, and therefore has no reduction in audio quality (At least, not due to bit depth, it does change the SNR as you suggested)

To further muddy the waters, in most cases using software volume control won't noticeably reduce audio quality. The main point I was trying to make is that on most computer setups 100% volume should be the least noisy, most accurate signal that it's capable of.

Is this a safe assumption though? As much as I consider myself knowledgeable in this area, this is way off my radar.

Even if this assumption does hold, the answer does make a good point when it comes to per-application volume controls, which are certainly performed digitally.

Your point on SNR is a very good one, particularly on the low-end, but I would question whether any computer at max volume would produce a signal strong enough to cause distortion. I generally run my computer at around 90% volume but that's merely a habit carried over from having an analog hifi stack.

Take the example of a guitarist. He turns his guitar up as high as he can, then the amp gain as high without distorting it. Then at the sound console. etc

The reason for this the later in the chain you are, the more electronics and cable is involved which adds noise to your signal. Highest signal-to-noise is achieved by ensuring you have as much signal as you can running thru from the get-go.

In the case of a computer, again it doesn't matter how volume changes are done- crank up your software as high as you need (but not beyond the point of distortion), then adjust it further at the speakers.

In practice that will often be right. In theory it is not.

With an analog signal what you actually want to do is avoid gain, whenever possible. You don't want to add as much gain at every step and then attenuate later. Gain adds noise and removes dynamic headroom.

So, assuming a guitar with passive electronics, you want to turn it all the way up (which adds no gain, passive electronics only attenuate a signal) and put everything else at unity gain (i.e. no attenuation and no additional gain). That will be labeled "0" on mixer faders and is about 80% of the way up on the fader.

We'll ignore guitar amplifiers for the moment, where the distortion that happens when you run out of headroom (clipping, i.e. "fuzz") and the sonic properties of vacuum tubes when they're near the top of their dynamic range (i.e. "tube warmth") are desired effects.

Now, so assuming you have a signal that you want clean all the way to the output, you've got things at unity all the way across the board, and it's not loud enough, then you start looking at where to add gain.

This is where we get to the part about you being in practice correct for many cases.

What we're looking to avoid is adding noise. Cabling exposes signals to RF interference and attenuate the signal since they're not perfect carriers. The more cables and interconnects down the road from the source we are, the more noise will have been introduced. Since we don't want to amplify the noise, it's usually best to amplify the signal at the point closest to the source since less noise will have leaked in. If you amplify a signal 4 connects down your signal path, there will be a lot of noise that you're amplifying along with your source's signal.

However, not all (pre-)amplifiers are created equal. Some, in fact, are pretty noisy themselves. There are certainly points where with a noisy pre-amp, you'll degrade the signal more by amplifying it in an earlier-in-your-signal-path pre-amp than you would boosting it at a very clean pre-amplifier one step down the chain. One of the big differences between cheapo mixers and high-end mixers is the quality of their first-in-the-signal-path pre-amps. A gain-adding stomp box is almost certainly going to be noisier than a Mackie pre-amp.

Now, since this started off talking about the sound coming out of consumer grade computer components (rather than a nice break-out box), it's worth noting that their analog amplifiers are pretty universally terrible. If you have a reasonably short and well-shielded cable, you'll generally be better off leaving it at "unity" (i.e. not boosting the pure signal that's coming out of the digital-to-analog converter), but adding it at the next step in your chain -- the mixer, receiver or powered monitors.

Now, to finish up, I'll circle back around to my first point -- since boosting the signal itself adds noise, if you're having to attenuate it later on, you're adding unnecessary noise. Your strategy of turning things up all the way until they clip is not a good one if you're having to then attenuate the signal later on for it to be at the correct levels for the mix. Ideally what you want is to have all of your faders at unity (again, labeled 0) and then to add gain at the quietest pre-amp (usually early in the chain) available until you hit the loudest volume that the channel will need to be in the mix. Fortunately, the folks designing mixers know that sometimes the situation on the ground is different in a live sound context and you'll actually need to go beyond unity, which is why mixers don't peak-out at there, but allow you to boost the signal there on an as-needed basis.

Edit: Minor addendum -- this assumes that you're not sending weak signals down long, unbalanced cables. If you are, that changes the calculus a little since they'll pick up a lot of RF on the way and you hack that around that by boosting before the cable and attenuating afterwards. But don't do that. That's what DI units are for.

The sound console is different. You want everything in the console to be trimmed to around 0 dB on the console's meters, and NOT as loud as possible without distorting. Trimming it to 0 dB gives you consistency between channels making it easier to work with the faders, and gives you however much headroom the console is designed to work with. "Loud as possible" will mean somewhere like +24 dB on some consoles, which is too hot to work with. Yes, they have that much headroom -- nominal line level is +4 dBu, around 1.2 V, and consoles have internal voltages in the 15-24V range.

The same goes for recording, you typically want things to peak at something like -18 dBFS. Making things peak "loud as you can without distorting" is the job of the mastering engineer, and it happens right before you stamp out CDs or MP3s or whatever.

Without distorting it? Are you sure you have some sound knowledge? That doesn't sound like you know many guitarists... ;)

qv. https://www.youtube.com/watch?v=4gDsbOraiqg

No it's not -- I was just pointing out that he's going on about various stuff without hitting the critical meat of the issue at all.

It would be nice to have some statistics about the number of lines of a reply on SO or HN and the amount of 'upvotes'. I think a lot of people would be surprised...

What would be the difference? I've never seen a DAC with an analog volume control. Any DAC I've ever seen with volume control does so digitally, usually with toggable steps (+6DB, +12DB, etc) or rarely with a programmable gain. Either way the DAC is adjusting the incoming digital signal prior to conversion. It would be really strange to try to make an analog adjustment to the output before the reconstruction filter.

http://www.xilinx.com/products/boards/ml505/datasheets/87560...

Digital audio levels are fixed -- i.e. 0 dBFS (dB relative to digital "full scale"), thus you want the audio as close to full scale (0dBFS) as possible. This is the reasoning behind what you've probably heard described as the "loudness war". 0dBFS is the reference point beyond which no signal can exceed.

Contrast that with analog audio, be it the DAC (digital-to-analog converter) on your soundcard that splits to a "line out" (likely 3.5mm a/k/a/ 1/8" TRS connector outputting audio at -10 dBV, the "consumer" level) and "headphone jack" (i.e. line level signal -> headphone amplifier). Once the audio signal becomes analog, you must then be concerned about gain staging. If you have a crappy sound card, you shouldn't reduce the analog output, because, in order to achieve the same loudness, you will have to increase the gain on your 'speakers' (a/k/a/ "pre-amplifier"; often integrated into cheap 'all in one' computer audio playback systems). Remember that the noise floor remains the same regardless of gain settings, so by reducing the "line out" level, you are only increasing the noise floor (i.e. level of noise).

For all of you geeks out there... If you are looking to cut through the bullst and get a quality playback system, look into a setup that has a quality DAC and/with monitor controller, a separate preamp, and quality monitors. Benchmark has a great USB DAC, and or Lavry Engineering is what the professional mastering studios use (their DAC costs well over $20k, and not because of crap like 'voodoo diamond dust covered gold-plated platinum wires', but, in part, because it has an internal oven and temperature monitoring circuitry to keep the internals at precise temperatures). You can get a great monitor controller from Dangerous Audio or Coleman. Bryston preamp's are very popular in the professional setting, as are PMC and Bowers & Wilkins monitors.

This happens both on my desktop Linux system and my Linux laptop.

You can verify it easily by playing either a 0dB sine-wave mp3 (first google hit: http://www.dr-lex.be/software/testsounds.html) or trying to get a sine-wave test-tone generator. You'll hear the point where distortion kicks in pretty drastic as soon as you reach the clipping level. With a spectrum-analyzer (e.g. FrequenSee on Android) even slight clipping will be very visible (peaks at 3x, 5x, 7x, ... the base frequency will suddenly appear).