Loudness Wars Part 2 — RMS, and Home Mastering for Idiots

What’s all this about RMS

In my last post, I threw around the term RMS a lot, and not everyone may know what that means. You can read up on it on Wikipedia but I can break it down for you here quicker.

RMS sounds for “Root Mean Square”, and what it means in terms of audio is that it is an average over time. You square every sample value in the input, add them together, divide by the number of samples, and take the square root. To steal a fancy formula from Wikipedia:

The reason you square the values is that audio signals are bipolar, meaning they’re greater than zero half the time and less than zero the other half. Squaring the samples gives you a string of numbers that is all positive. Taking the square root after you average them gets the average down into a value range as the original audio signal. There’s nothing magic about RMS calculations, or audio-specific; the octane rating of gasoline also involves an RMS computation.

Why is RMS measurement of audio levels important? Simple: because instantaneous levels (how loud a signal is right fucking now) and peak levels (the loudest instantaneous level) don’t mean shit to your ears. Only the average over time matters, because the auditory perceptual system of your brain makes sense of sound over a fairly coarse time frame — hundredths of seconds up to seconds.

And what does RMS dB mean in terms of digital audio? Well the dB part stands for deciBels, the standard unit of digital audio. deciBels is always a relative value — there’s some reference level that you’re comparing with to come up with a positive or negative number of deciBels. In digital audio the most useful reference point is 0 dBFS (deciBels Full Scale, which means the loudest signal that can be represented at the current word width. As Scotty used to say on Star Trek, ya kinn git na mare pawr than 0dBFS. So if I say that a signal’s volume is -12dB RMS, I’m saying that it’s average level is 12 deciBels quieter than the loudest it can possibly be.

The other wrinkle with deciBels is that it is a logarithmic scale. Without going into a bunch of math, what that means that if 0dBFS represents a numeric value of 32767, half that value (16384) is represented as -6dBFS, 8192 is -12dBFS, etc. Why is it a logarithmic scale? Simple: Your perception of sound works that way. A doubling of sound pressure doesn’t sound twice as loud, it just sounds louder, up to the point where your eardrums rupture.

You with me so far? Good.

Home Mastering for Idiots

If you master your own music, you’re an idiot. You’re better off paying some other geezer like me to do it. Why? Because I’ve done it often enough to know what to do, and I don’t have any personal stake in your music, and can make objective decisions about how to make it sound as good as possible

But, of course, I master my own stuff, so I’m an idiot, too. As soon as someone wants to pay money for my music, I’ll have someone else give it a go, but at this point, I’m enough a non-idiot to avoid completely fucking it up, and that will do for now. Which is part of the point — once you’ve finished some music, you may want to send out demos, give your mum a CD for the boombox in the kitchen etc. So you have to master it. Here’s what to do.

1. Measure the RMS level for the loudest passage of your track. In Sound Forge, this is under Tools->Specifics. Even free software like Audacity has a similar command.
2. Find a brick-wall limiter plugin. If you’re a dirty software pirate something like Wave L2 or L3 Ultramaximizer will do. Sound Forge has a thing called “WaveHammer” that does the same basic thing.
3. The RMS level from step one is a rough guide to where to set the threshold for limiting. Your goal is to get the loudest passage to about -10dB RMS. So if the measured RMS level is -15, you set the threshold at -5dB. This isn’t an exact thing, because the threshold is instantaneous and you’re trying to change the continuous average.
4. Run the limiter over your track, and re-measure the RMS level of your loudest passage. If you overshot the -10dB goal, undo the limiter, adjust the threshold up a dB or two. If you undershot, lower the threshold a bit.
5. When you hit your goal, save your file TO A NEW FILE., never overwriting the original. Why? Because you don’t want to go back and redo your mixdown in order to get back to the unmastered version. You may want to pay me to do a better job than this, right?

I’ve left out a lot of things I also do when mastering — EQ tweaks, multiband compression, exciters, even — gasp — adding reverb. But remember, you’re an idiot. Just make your mixes sound as good as you can, then get them loud enough to sound right.

6 Replies to “Loudness Wars Part 2 — RMS, and Home Mastering for Idiots”

  1. Yea lets all use numbers instead of our ears. Commercial tracks tend to average -8 RMS and they don’t use brickwall limiting to achieve that.

  2. “The reason you square the values is that audio signals are bipolar,”

    NO – if that were the reason then one might as well do abs instead of square and forget the root….

    1. RMS == root mean square. Squaring makes all values positive, mean == averaging, taking the root restores the magnitude.

      1. It doesn’t quite “restore” the magnitude, as the result will be different than an average of the absolute value would be. You can try it on paper.

    1. I don’t know what window is customary for computing RMS. Sound Forge will calculate it for the current selection, or the whole file.

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