# Half And Double Of 0Db

Hi folks, I’ve a complicated question about the dB scale. I’m not good at mathematics so I need some help! I’ve been searching the net for an answer to this for ages and I can’t find any reliable info. So here goes:

I’m interested to know what the precise value of half and double from 0dB. Many moons ago Renoise had a lot more of its faders in percent. This meant that if you set a fader at 50% it would be precisely half of the relative 0dB point, which also meant that the bit depth resolution was effectively and neatly halved (instead of truncated to some other weirder decimal). Through this I found that 50% of 0dB is in fact -6.021dB, and NOT -6dB like a lot webpages tell you it is.

Since that time my ears have become more sensitive to mixing dynamics, and although it may be me convincing myself, -6.021dB does sound better than -6dB with the dynamics. It just feels more true and honest compared to the original signal. Call me mad, but in mastering applications this fraction of a feel is very important. Anyway,

You can prove this to yourself by opening up the Hydra device, which does its modulation parameter by percent. Tell one Output to map the TrackVolPan Volume control and set the Max value to 0dB. Slide the Hydra’s Input to 50% and you can see the pre-fader has now gone to -6.021dB.

Now, how to find double 0dB? Well, I tried this: On the same channel open up a Gainer. Tell Out2 to map to the Gainer’s Gain parameter, and set the maximum to -6.021dB. Now slide the Hydra Input to 75% and the result is +3.522dB. Is this anywhere remotely correct? Most explanations of the dB scale on the web tell me that +3dB is double of 0dB, but now I don’t know what to believe.

The reason why I ask all this is that I’ve become interested in Pan Law and I’m thinking of a way to make up for the fact that Renoise hasn’t yet got a Pan Law option. I need to know what the precise value of double 0dB is, so that my Pan Law boost will be bit-harmonic, rather than being at some odd truncated value. Some software has a Pan Law option of +3dB, but like I’ve said I’m wondering how precise that is. If I can get the correct value, I can boost the side data of any channel to correct for loss of power in panning, especially in moving pan sounds.

Thanks for any help!

Actually I think the -6.021 might be an issue with the floating point calculations. With all respect to the dev-team… I doubt the Renoise sliders are a suitable tool to do hyper-accurate scientific calculation or use them as scientific reference.

I found this site quiet interesting: dB:What is a decibel

Lots of useful infos there.

Cheers
-BA

Thanks for the link BA, but it doesn’t quite answer my questions. I think I might see what one of the Devs say.

There where actually quite a lot of questions in your post.

For the scaling with the Hydra I doubt this is correct or in any way meaningful. Assigning frequencies to keys did also not work because of floating point issues. The results you get are related to the overall numeric range that’s the Hydra/volume slide/gainer is capable of and imho falsified by cut floating point in addition.

I’d stay with scientific numbers & calculations.

-BA

And btw… I’m sure you know about the saying “Master by ear. Not by view and not by numbers.”

Maybe this is of some help. This should be the renoise db chart, put it in excel and create charts if you wish.

``````
Multiplier;dB
0;-200.00000000
0.05;-26.02059991
0.1;-20.00000000
0.15;-16.47817482
0.2;-13.97940009
0.25;-12.04119983
0.3;-10.45757491
0.35;-9.11863911
0.4;-7.95880017
0.45;-6.93574972
0.5;-6.02059991
0.55;-5.19274621
0.6;-4.43697499
0.65;-3.74173287
0.7;-3.09803920
0.75;-2.49877473
0.8;-1.93820026
0.85;-1.41162149
0.9;-0.91514981
0.95;-0.44552789
1;0.00000000
1.05;0.42378598
1.1;0.82785370
1.15;1.21395681
1.2;1.58362492
1.25;1.93820026
1.3;2.27886705
1.35;2.60667537
1.4;2.92256071
1.45;3.22736004
1.5;3.52182518
1.55;3.80663396
1.6;4.08239965
1.65;4.34967888
1.7;4.60897843
1.75;4.86076097
1.8;5.10545010
1.85;5.34343457
1.9;5.57507202
1.95;5.80069223
2;6.02059991
2.05;6.23507722
2.1;6.44438589
2.15;6.64876920
2.2;6.84845362
2.25;7.04365036
2.3;7.23455672
2.35;7.42135725
2.4;7.60422483
2.45;7.78332169
2.5;7.95880017
2.55;8.13080361
2.6;8.29946696
2.65;8.46491748
2.7;8.62727528
2.75;8.78665388
2.8;8.94316063
2.85;9.09689720
2.9;9.24795996
2.95;9.39644032
3;9.54242509

``````

200 is (relatively) arbitrary number denoting infinity, in practice there is no such thing as minimum dB value, but in digital domain there is a limit in which there is no point to go beyond cause the multiplier nears the zero.

50% volume is indeed -6.021
200% volume seems to be 6.021 too.

20 log (ratio)

Way logarythms work half and double are going to be EXACTLY THE SAME just one positive, one negative. Same for ten times or one tenth, etc etc etc.

20 log2 (doubling) = 6.02059991… (Punch it into the calculator on your computer if you want more precision. Hit 2, then Log, the Times, then 2. Equals.)

Ok ok. I see the picture. Thanks for the useful replies. Certainly boggles the mind a bit, and give a strong case to just mixing by ears (without picking numerical values).

So there is such thing as something that is bit-perfect. But perhaps not easy to get anything that is bit-harmonic? Does this mean that any possible implementation of Pan Law adjustment is complete arbitrary? (i.e. it sounds-about-right?)

I don’t know about that, renoise does it’s internal processing in floating point, this is already data conversion and works on totally different principles than integer based PCM. So I don’t think you get guaranteed bit perfect result even if you get your math correct, nor is there much difference when you don’t.

Goodness gracious!