Academic Question about gain peaking

[Scythe]

I wonder what prevents the digital recording environment to have infinite gain levels?
As in why don't we have access to infinite volume without distortion?
As in why does a project eventually go into peaking at red and beyond if there are enough tracks with high volume levels?

Analog I can understand the limitations there but how does it work in the digital realm?

I'm struggling to articulate my question but I hope it's kind of clear lol!

[Topcheese]

I would just assume it's because of the limitations of your DAC. At some point you're going to have to bring it on home, unless this is an Android?

Do you mean something like this?
https://theproaudiofiles.com/analog-sum ... eferences/

[Scythe]

I mean in general regardless of Daw - why is there even a ceiling on the level of volume in a project?
For e.g;
If I have 30 tracks with excellent gain staging (during recording) in a project all set at 0db, the master track WILL go into total red and beyond at all times.
They all seem to have a mathematical adding effect to the overall project volume.

why is that? why don't we have infinite 'volume space' in the digital realm?

does any of this make sense?

[rrichard63]

I'm not sure what the terms "infinite loudness" and/or "infinite gain" even mean, but I'll assume that Scythe has an answer to that question.

What programming language has a data type that can represent infinity with any precision? If there is such a thing, then it might be possible to design and program a DAW that can represent "infinite gain" (however defined). Otherwise, DAWs will always have a finite maximum level at which (very severe) distortion sets in. The range of a 32 bit or 64 bit floating point number is very large but it is still finite.

And the range of these floating point numbers is far beyond what any DAC can process. Those internal representations are reduced to integers before any DAC ever sees them.

[Scythe]

ok infinite just being a way to represent an idea...so not literal.
but why does distortion set in?

why is it that if there are 30 tracks running at 0db, the master track will distort heavily - even assuming there is really good input gain staging done.

how are they all adding to the distortion to the master track?

[Topcheese]

Right off the bat you set a "reference" of 0 db, so when you keep adding tracks(energy in the form of waves), at some point you're going to exceed the capabilities of the the electronics to be able to deliver a clean signal back to you without eventually producing puffs of smoke. That's really what a reference is for. You can use it to create headroom, but the more tracks you add, the smaller the room gets ... that room is not infinite.

I'm sure if you were a super computer, then you might be able to reap the benefits of "infinite" power, but mere mortals have to rely on good ol DACs.

Now if you're Elon Musk asking can you blast a rocket into space with a subwoofer, then I could see you reaping the benefits of "infinite" power, but I don't even think he's there yet.

Perhaps, I'm still not understanding the question, so sorry if it's not the answer you were looking for.

Edit: Maybe this will help. http://www.acs.psu.edu/drussell/demos/s ... ition.html

[Scythe]

so the more powerful a computer gets, the more headroom it can handle is that it?
headroom - does it depend on computing power?

[Topcheese]

Ultimately power is going to be your friend here, so yes you could say that. I'm not really the academic type, so I'll defer a real answer to someone here that really knows their stuff.

The best I can do is point you to another video that will hopefully get a smile from you. https://www.youtube.com/watch?v=cYdpOjletnc

[Topcheese]

It's not that its impossible, it's just not a desirable thing. This might shed some light on why. https://spectrum.ieee.org/semiconductor ... sy-in-cuba

[Scythe]

lol @ ol' Max!

yeah not sure about the embassy business....it's a good attempt at the explanation though.
Thanks for the replies mate

[Topcheese]

Thanks for bearing with me. I may be in the same boat as you, as I'm struggling to make sure I understand the question. I was thinking of the damage that could be physically done by creating and using increased headroom like that.

One transient peak leads to another, next thing you know your stadium full of people are all laying there unconscious. I would think it's because of physical laws that you have to reduce the gain as you add more tracks(sound).

I think I'm explaining it the wrong way, but here's how I understand Headroom, it's not necessarily dependent on a powerful computer, but it's probably going to have better components, and that's where you'll get the extra headroom.

Please feel free to correct me, because if you haven't noticed, I tend to get off the beaten path. Have a great day!

https://upload.wikimedia.org/wikipedia/ ... ndos10.svg

[rrichard63]

so the more powerful a computer gets, the more headroom it can handle is that it?
headroom - does it depend on computing power?

If I understand your question correctly, then headroom doesn't depend on computing power but rather on the data type used to store sample values. 64-bit floating point numbers can provide more headroom than 32-bit floating point numbers, which provide more headroom than 16-bit floating point, etc. Unless I am mistaken, if you want "infinite" headroom then you need an infinity-bit floating point data type. I'm pretty sure that's not going to be invented any time soon.

As a purely practical matter -- when human ears are going to listen to the resulting mix -- the limitation is the data type inside the DAC. Most of the time these days that's a 24-bit fixed point (integer) data type.

Also as a purely practical matter, 64-bit floating point has a lot of headroom. I don't think we need more than that.

[Scythe]

I see - so Mixcraft 32 bit has less headroom than 64 bit? is that right?
Or is that a different thing altogether having to do with plug-ins etc..?
I'm not very good with the techie side of all this

[Acoustica Greg]

I see - so Mixcraft 32 bit has less headroom than 64 bit? is that right?
Or is that a different thing altogether having to do with plug-ins etc..?
I'm not very good with the techie side of all this

Hi,

No, the only difference between 32- and 64-bit Mixcraft is that the latter can access more than 4 GB of RAM. It doesn't affect your headroom. rrichard63 was talking about the format of the audio files themselves.

Greg

[shayneoneill]

Internally, uncompressed audio is just a series of numbers between 0 and 2^16 (or 24/32/64/whatever). Lets just for the sake of ease go old school for the sake of explanation, and imagine we're all 80s cats in mirror shades and akai samplers, and we're dealing with 2^8, thats a number between 0 and 256. So you divide that in two and the wave form is between -128 -> 0 -> 128 and that has to represent the amplitude of the wave at any point. The higher the number , the louder the wave. When a signal comes in LOUDER than that, the number cant be stored anymore, and it slices off the top of it and you get what looks a bit like a square wave, nasty nasty digitial distortion.

When thats upped to 2^16 thats 65536 (or +-32768) and gets exponentially higher each bit added to the number.

Now heres the thing. Because ultimately these numbers are representing physical waveforms, tat doesnt mean 2^16 is 256 times louder than 2^8, it means the signal is much more detailed.

Now modern DAC/ADC converters do have a lot more headroom, and some of that extra bit space can be used to let you go a bit further into "the red" without too much signal damage, but you cant just have infinite gain. because that means infinite amplitude, infinite volume, infinite speakers blowing out of cones, infinite computers catching on fire and ultimately infinite insurance premiums!

More bits = more detail, not more volume.