+∞, Logic Pro and digital audio

N.B. This article is pure postulation based on previous experience and limited programming knowledge

There’s been various discussions on Logic Pro forums recently which usually take a similar form to this. Somebody will post a photograph of their master fader with the readout at the top stating some ridiculous decibel number - possibly even +∞ dB, with the caption “That hurt”, or something similar. A number of people who have never seen this sort of relatively common thing before will reply in shock, some will reply with “this solution worked for me!”, but never once have I seen anybody explain what it is that is going on here, and why it is nowhere near as scary as it looks.

My Computer-Sciencey postulation would be dodgy buffer logic, probably an overflow in one of Logic’s stock plugins, given that I’ve not seen this in other DAWs recently (though I did once experience it with an FL Studio stock plugin; I suspect a similar sort of thing was at fault). But what does any of that even mean?

An analogy

Warning: this is a pretty technical article. Imagine it like this: If you watch a video of the sun, do the billions of gigawatts of energy it produces get spewed out of your screen and engulf your house in flames? Of course not! Your screen can only produce a set level of brightness, and after that, it will simply clip (which is called “overexposure” in video/photo terms). We know that if you put the highest brightness value you can (#ffffff) into a screen, you get white. You are doing exactly the same with your audio interface!

A quick guide to digital audio

You’ve heard of audio being 16-bit or 24-bit, possibly even 32 or 64 bit floating point. When your DAW records or processes audio, it places a sample point at a fixed position in the time domain, equivilent to once every 1/samplerate seconds. These sample points represent the amplitude of the wave at that point. However, given that the analogue value coming in from your mic or guitar or what-have-you is an indiscrete value (a bit like height rather than a discrete value like shoe size), and your computer cannot store an indiscrete value, it must be quantised.

The accuracy of that quantisation defines how much data, and thus storage space and bandwidth, is needed. 16-bit, which is a perfectly acceptable resolution in most cases, has 2^16 individual “voltage levels” it can represent amplitude with, 65535 levels in real terms. At that point, the human ear cannot distinguish between level 65535 and 65536. These levels are so similar that our ears write them off as basically the same thing, meaning that you don’t hear any sort of distortion.¹

But, when you hit “voltage level” 65536, you can’t go to 65537. That simply won’t work, it’s a hard ceiling. In binary terms, you’ve set all of your 16 available bits to 1: 11111111 11111111². You can’t just add another bit, or you’d be in 17-bit, and things just don’t work like that! What really happens is one of two things. Most DAWs will “hard clip” - no matter how much more sound you give them, they will never go above the value of 65536, and will just flatten any waveform above that value (digital clipping). If you are using a “dumb” system, your programme will pretend there is a 17th bit, and thus set the value to 65537: 00000000 00000000 1³. But given that this 17th bit doesn’t exist in your hardware, it gets deleted:00000000 00000000, and the number you end up with is a big fat zero.

And as a result of that, you’ve just created a discontinuity. By jumping from the highest possible voltage value to the lowest possible, what you’ve created is the same thing as when you forget to crossfade between two audio clips: a click. This is called a buffer overflow - because you tried to put more data into the buffer than it is capable of holding.

Why is Logic trying to deafen me?

Sometimes in audio, it can be useful to treat the sample value as 1-x rather than x. This means working from Full Scale down, rather than -∞ up. In practical terms, this means inverting the buffer. If you invert the buffer after overflowing it, you will end up with all 1s. This is one possible way of a multitude that could result in the output value being all 1s.

However, the signal this would output would be DC (0Hz). People describe loud distorted sounds. I’d suggest that this could possibly be a bitrate mismatch in a plugin - if a plugin is storing 32-bit values in a 24 bit buffer, this will have the effect of amplifying and digitally clipping that sound quite significantly. On reflection, this is probably the most likely explaination for what is happening here, but I can’t be sure.

+∞ dB, really???

No, not at all. Such things do not exist. Logic uses 64-bit float internally, which has stupidly ridiculous headroom. But the metering is relative to the output format you use (because the format describes the headroom, and thus Full Scale), so when Logic tries to fit a 64 bit signal which is very loud because of a bitrate mismatch into, say a 16 or 24 bit output format, it just ends up clipping. Given this, Logic just gives the value +∞ dB to say there is a lot of stuff above this that’s getting clipped off.

Even the screenshots I’ve seen with +200dB aren’t really at +200dB. Fine, maybe that is true internally, but as soon as logic puts that value down the wire to your audio interface, it will only produce the loudest sound it can produce. It could not physically ever produce anything over about 110dB through the normal headphones these people seem to be using, and even if you are running your headphones through a 5000 watt PA amplifier, they’d have burned out long before you reach anywhere near +200dB.

+200dB means 200 decibels above the point at which the audio began clipping (Full Scale - hence dB relative to FS - dbfs). In order to demonstrate this, get any sound in Logic, and add a bunch of gain plugins, each adding 24dB of gain. Enable them one-by-one with your interface/amp volume set extremely low. Notice how at some point, even though the number gets progressively higher in Logic, the sound stops getting louder, and only harmonics are added. Don’t try turning up your monitor volume, you may burn out the voice coils in your speakers!

Effectively what we are doing here is causing a bitrate mismatch. We are putting too many bits into our 16/24 bit buffer, and they are getting clipped off, creating a loud waveform. But Logic, with its 64 bits, can still see all of the clipped off stuff, and thus measure where, if we had 64-bit headroom, the peak level would be.

But never will that reach your ears or your speakers.

Equally never will these high digital values damage the digital processors (this is a question I saw somebody ask). A digital processor knows no difference between 0 and its highest possible buffer value, there is no difference⁴ in voltage between these two.

Practical Tips

A lot of people suggest putting a limiter on the master. I don’t. For all I know, Limiter may be the plugin with the mismatch problem! But more fundamentally, a limiter is not going to react quick enough. It is not designed to operate on the individual buffers of audio, but in a more musical way, across macrodynamics within the audio. Limiters will almost always introduce latency and could cause mixing issues for people who are not experienced in mixing into a nonlinear mixbus. Having said that, I love mixing into a hard limiter and almost always do it; irreverence is fun!

REAPER has the solution, as is so often the case. In the settings is an option which will mute the mixbus instantly if any peak above a certain level is detected. I’ve got it set to the default of +18dbfs, which has always seemed sensible to me. Loud enough that I can do silly things with audio and overpower my limiter if I really want to, quiet enough that if a mismatch occurs, I won’t damage my speakers or ears.

This works instantly, and on the buffer, meaning that an errant buffer will never reach your speakers. Every DAW should have this, but I’m sure doing this as a plugin would be extremely easy. In the meantime, keep your volume low. The final limiter your audio goes through is the knob on your audio interface or amp - YOU control the maximum voltage level of the output, Logic merely requests it.

I hope this article has helped you understand what is going on with your audio, and why things like +200dB or +∞dB cannot exist, that your audio output level is limited by the maximum possible voltage value your amp can produce.

Tagged as: technology thoughts music debunk