Not a big deal, but just wondering why the max send level is 6.02 and not just 6.00

Also my default send level on preferences is checked for -6dB but that actually gives me a -6.02dB on mixer.

What’s the deal with the .02 cents, I mean it messes up my brain and my OCDs

Hi,

As you can see the Volume fader maximum is also 6.02. I believe, there is some math (and probably rounding) behind it.

I think I figured out the math behind it…

For 16bit audio the dynamic range is 96dB.

## dynamic range

Dynamic range is the ratio of the smallest expressible value to the largest. 96dB is the ratio of 65535 to 1.

Actually 96.32dB

## math

20log(65535)=96.329466075304994155687087375572

So in order to have the maximum dynamic range we then should have 16(bit) x 6.02 = 96.32

I still don’t get though why the prefixed -6dB send value is -6.02. I mean it’s halfway so there should be no reason to be like that.

I guess the programmer rounded the command to -12dB (counting from the top of the dynamic range) instead of -12.02dB.

Anyway, as you can tell I am killing time here…

cheers

I think it comes from the following:

When the power of a signal is doubled you can say the power gain is 2 (you doubled the power). In dB this is calculated as 10log(2) and the result is 3,01 dB. The double of the double is 6,02 dB. So, when you put your fader at +6,02 dB, you have four times more power in the output signal.

When you talk about amplitude, you consider that doubling the power means that the amplitude gain is now sqrt(2) (that is the output signal’s amplitude is 1,4142 times greater than the input, and that causes that the power is doubled). When you calculate dB in terms of amplitude gain you do 20log(1,4142) and the result is of course 3,01 dB again. Another amplification by sqrt(2) in amplitude will be 6,02 dB above the original signal.

The same is valid in down direction: if the amplitude reduces in sqrt(2), in dB that is 20log(1/sqrt(2)) and the result is -3,01 dB. Another reduction in sqrt(2) will be -6,02 dB from the original.

If you don’t know the world of deciBells, maybe this can help:

Cubase does not work with decibels internally, those are just calculated for the display.

The Cubase mixer uses 32 or 64 bit floating point internally.

The only explanation at the moment I can think of that can explain the discrepancy between the -6 and -12 preference settings for default send level is the following:

The default send levels get saved in the UserDefaults.xml as int values:

```
<int name="Default Send Level" value="0"/> (= 0dB)
<int name="Default Send Level" value="1"/> (= -6dB)
<int name="Default Send Level" value="2"/> (= -12dB)
```

That must mean that those preset int values are mapped internally to float values to be used in the mixer. I cannot imagine why, but it could be that the value for -6dB is stored a “0,5” (which would result in -6.02dBFS when converted), and the value for -12dB is stored as “0.2511…”, which gets converted to -12.0dBFS (rounded).

Don’t ask me why that should be, no idea. Doesn’t really make sense to me, tbh, but would somehow explain this inconsistent behaviour.