I've been studying up on audio recording on the web, so that I can make decent recordings for my research. Making good recordings is a lot more involved than you might think. One of the perhaps needlessly overinvolved aspects is understanding gain.

A microphone detects sound and produces a faint electrical signal, usually too faint for practical use. So, the signal is amplified. But if you amplify the signal too much, you get distortion. Once the signal passes from the analog to the digital domain, you have forever lost some information, so the natural thing is to get as much gain as you can before the A/D conversion.

So how do you know how much gain is enough but not too much? A good indicator is a peak meter. Here's a picture of an analog peak meter (called a PPM):

In the digital world, the practical equivalent looks something like this:

We'll ignore the wacky scale on that analog meter for now. Notice the scale on the DPM—it goes from 0dB at the top to about -70dB at the bottom. Now, decibel (dB) is a ratio, meaning it has no meaning without some reference point. In this case it's actually dBFS (dB full scale), calculated as dBFS = 20log₁₀(|x|/1.0) when representing samples as floating point numbers between -1.0 and 1.0. Whatever you divide by inside the logarithm is your reference. You would divide by the maximum sample value if you were using fixed point or some other representation. So our reference is 1.0, aka full scale. Since we can't go over full scale, all dBFS numbers will be less than or equal to zero.

So, if you record such that you are just below 0dBFS, you are using every bit of quantization to its fullest. The trick is that you often don't know just how high the maximum peak will be (unless perhaps you're recording something repeatable, like playing back a tape). So, you need to leave a little headroom in case you have some peaks that are larger than average. How much headroom to use is hotly debated, but really it is just a function of the kind of thing you're recording (and the environment in which it is being recorded). There is no substitute for experience here. Here's a hint: record stuff with plenty of headroom, find out what the maximum peak, and calculate how much extra headroom you have. Do that a bunch, and you will begin to get an idea of how much headroom you need.

Or, don't record that stuff, just watch a meter. Good digital meters will have a resettable maximum peak indicator.

But there's more. The peak isn't a good indicator of how loud it is. Loudness is perceived more closely to the average signal amplitude. The most common way to calculate this is Root Mean Square (RMS): sqrt(sum(x)/length(x)). A common meter which measures loudness (although it doesn't measure RMS, exactly) is the VU meter. You may have seen it:

The VU meter does not measure peaks, but it does measure loudness. But there's a trick. 0 dB is not 0 dBFS, but rather 0 dBu, which in turn is usually 4dBV. Those are electrical voltage references for the analog world. In this world, you aim for 0dB to be "forte", and it's ok if the meter occasionally goes higher than 0dB. Remember the wacky scale on the analog PPM meter? It reads dBV, i.e. 4 on the PPM is 0 dBu (but the marks are usually 4 dB increments, so 5 on a PPM would be +4 dBu).

So how do we relate these to the digital world? Well that depends on your ADC. In practice there will be some variation in how the same strength (dBu) signal is converted to digital, although the variation is probably not too great. The important thing is to use the proper meter. When you're doing a digital recording, the proper scale is dBFS and it's irrelevant what analog signal you need to get the dBFS you need. Not entirely irrelevant—you want to make your signal hotter earlier because that reduces the noise introduced by each component in the system, but ultimately how much gain you apply (early in the system) is governed by your digital meter.

But wait, aren't most digital meters peak meters? Yes, but there are loudness meters if you look for them. On Linux and OS X with JACK, look at jmeters (a derivative of the neglected meterbridge). At the time of this writing they it has VU and PPM meters, though you will have to play with them to get the hang of their reference points. Or I could walk you through it.

Go grab some calibration tones. Included in the zip available there are 1kHz sine wave at -20 dBFS RMS and various pink noise tones (different bandwidths) at -20 dbFS RMS. But wait, what's this?

octave:1> [x,sr] = wavread('1khz sine wave -20 dBFS.wav');
octave:2> 20*log10(sqrt(sum(x.^2)/length(x)))
ans = -23.322
octave:3> [x,sr] = wavread('PINK NOISE FULL bw -20 dBFS.wav');
octave:4> 20*log10(sqrt(sum(x.^2)/length(x)))
ans = -22.908

Gee, looks like those are -23 dBFS RMS doesn't it? Well, technically they are. But here's the rub: the smart people at the Audio Engineering Society declared that in the analog world we should measure a sine wave with -20dB peak as -20dB RMS, i.e. a sine wave has the same measurement on a peak and AES-17 RMS meter. Whether they originated this or it came from history I don't know, but probably the latter. So, since a sine wave has about 3dB crest factor, these test tones have -23 dBFS true RMS, but -20 dBFS AES-17 RMS. Confused yet?

So we fire up jmeters -t vu x and jmeters -t ppm x, then hook up the JACK connections and play the sine wave. The VU meter settles nicely on -10 VU and the PPM reads 2. So it would seem that Fons has decided that 0 VU should be -10 dBFS, which gives 10 dB headroom. The gain is adjustable if you don't like that choice, by the way.

Ok, so now you know enough about meters to be a little dangerous. Now let me throw another wrench in things. Let's talk about mastering. After you record all the tracks, you need to mix them together into songs and then finally master the album. Mastering is (to oversimplify) all about loudness. You want the songs to all fit together when you play the whole album. You don't want some songs to sound too loud relative to others. Ideally, you'd want all albums to have similar loudness. But you and I know that isn't usually the case. This is the result of the "loudness war". Over the past 20+ years, albums have been getting louder and louder and louder. Everyone wants the loudest-sounding album. Everyone wants to be the baddest.

And bad they are. audio engineers have always mastered to take full advantage of the medium. You can count on the highest peak usually being right up to the clipping/distortion threshold. It's only right. But then how do things get louder? Dynamic range compression. I won't go into the technical details of how it works, and I exhort you to read up on it. Just Google loudness war. Suffice it to say compression brings the peaks (and valleys) closer to the RMS. The loudness war is a crying shame. So much music that could sound so good sounds so terrible because the life has been compressed out of it.

So what does this have to do with metering? Well, the whole point of this post is to inform you of the K-System meters. A smart audio engineer by the name of Bob Katz (author of the newest book on my wishlist, Mastering Audio) proposes this system which borrows from history and other industries that have standards which have protected them from the loudness wars. He proposes 3 meters, the K-20, K-14, and K-12 meters. The number is the amount of headroom above 0 dB, so a K-20 meter will set 0dB equal to -20 dBFS, and 0 dB again means "forte". Then, you calibrate your studio monitors such that pink noise that reads 0 dB RMS gives 83 dB SPL (sound pressure level) to your ears. You need fancy equipment to do that, but unless you're mastering in a studio (in which case you have the fancy equipment) it doesn't really matter. The CD has dB FS, not dB SPL. If everyone did this, even if everone calibrated "forte" to -20 dBFS, all the CDs would sound about the same loudness, there would be plenty of dynamic range to make the music come alive, and the world would be a happy place.

I have talked to Fons and he has been working on a K-20 meter for jmeters. I've also been writing one with a simple printf display, which I will make available once I get it working properly. The take-home lesson is to record such that your highest peak is as close to 0 dBFS as you can get without clipping, and master to forte (83 dB SPL) at -20 dBFS RMS.

But there's still that question of headroom. Why not just adjust the gain so that forte is -20 dBFS RMS and be done with it? I'm not implying you wouldn't have to master to get a professional-sounding recording (mastering is more than just adjusting gain), but that it should give you a nice volume with enough headroom. I think it's a great idea. I'm glad I thought of it (though I'm sure I'm not the first). But make sure you're using as many bits as possible for quantization, preferably 24 bits, since you are potentially sacrificing bits for extra headroom.

I hope this little treatise was interesting and/or useful. To learn much more, I recommend starting at Bob Katz' articles on level practices.