Ableton's Stock Compressor Makeup Gain Algorithm

[GDMcArthur]

Hi All,

I noticed a lot of people asking about how Ableton's makeup gain works. I am a mathematician/data scientist and I became a bit obsessed trying to understand how it works myself. The problem (as I and others see it) is that the stock compressor's makeup gain adds gain even when compression isn't being applied (i.e. there is no actual gain reduction happening). Audio engineers compensate for this by adjusting the general levels of the output gain by ear. As someone rooted in formulas, I hated this fact. Ableton seems to have an algorithm for "estimated" makeup gain until the actual compression is applied. Hence people typically notice way too much makeup gain being applied and adjust output levels accordingly, as mentioned. That is,

Makeup Gain = Estimated Makeup Gain + Gain Reduction

Gain Reduction is based on the typical formula:

Gain Reduction = (Input Level−Threshold) x (1− Ratio/1)

The "estimated" makeup gain is a bit trickier though and I had to backsolve for the alogrithm with various data points. I am not sure if I found the EXACT formula that Ableton uses, but did solve for a constant that seems to hold for various tests.

The formula is:

Estimated Makeup Gain = Constant x (1− Ratio/1) x ΔThreshold, where ΔT is the change in the threshold.

What I had to solve for is the constant the holds given any ratio and threshold and what I calibrated was the value .7

Thus, for example, assuming that no actual gain reduction is happening, if I have a ratio of 2:1 and a threshold of -10db (relative to 0db), then based on the formula provided the amount of makeup gain that I need adjust for is +3.5db.

That is, if I ONLY want to apply makeup gain to the actual gain reduction, I would reduce by compressors output by -3.5db to compensate for Ableton's strange algorithm.

I hope this formula helps people fine tune their sound a little easier than just by ear!

PS - .7?? WTF?!?!

[Synthbuilder]

PS - .7?? WTF?!?!

Whenever I see 0.7 I think one over root two. It pops up in a lot of audio calculations. Why that should be the magic number in this case I have no idea.

I never use the make up gain and prefer to do it all by ear.

[GDMcArthur]

PS - .7?? WTF?!?!

Whenever I see 0.7 I think one over root two. It pops up in a lot of audio calculations. Why that should be the magic number in this case I have no idea.

I never use the make up gain and prefer to do it all by ear.

Yeh, you're actually right it is 1/sqrt(2). I don't run into that number often enough in my world to recognize that easily. But I assume if you are in audio engineering it probably does pop up a lot. Minor nuance, but its worth noting that that in Ableton's algorithm they clearly just rounded to .7 after doing some testing with the number