Old 05-24-2018, 02:40 AM   #1
inarisound
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Default Loudness is confusing...

Hello guys!

I started exploring loudness and how levels works...

while using VU meter on monitor and Tone Generator I found something interesting that I don't understand...

If we have set Tone generator to produce constant sound with loudness lvl at 0db and then create identical tone generator (duplicate track)

we will get loudness lvl at 6 db..... but than duplicate it once again so we have 3 tone generators... we will get only 9,51 db...

So here is the catch.... the more sources with the same loudness lvl we add progressively we will receive less loudness change from the same source.



Here is a chart that I got:

1 tone generator with loudness = 0 db
(after we duplicate the same source)
2 = 6 db
3 = 9,51 db
4 = 12 db
5 = 13,93 db
6 = 15,51 db
7 = 16,84 db
8 = 18 db
.....
you see that loudness only get +6 db with pairs 2, 4, 8 , 16, 32

the higher we go the more tracks/sound sources we require to get this +6db


My question is.... why?!

What is the magic with duplicate, quadruple, quintuple....etc.
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Old 05-24-2018, 03:26 AM   #2
andyp24
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Decibels are a logarithmic scale....

What this means is that a 6dB increase means a doubling of the thing it's measuring.

Hence what you're seeing.
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Old 05-24-2018, 04:42 AM   #3
Philbo King
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Yes, 6 dB is a doubling of amplitude, equivalent to doubling the number of tone generators. So:
1 track: 0 dB
2 tracks: 6 dB
4 tracks: 12 dB
8 tracks: 18 dB
etc.

An interesting thing: This only works with doubling identical signals, which are called 'correlated'. If you do this with pink noise (uncorrelated waves), it totals up differently, giving less than 6 dB per doubling.
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Old 05-25-2018, 02:32 AM   #4
jrk
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Your Tone Generators aren't necessarily synchronized - so they'll often not be in phase. Depends on... (your guess here?). So the way they'll sum isn't predictable (or repeatable?)

Try it with just two instances - then turn one off (uncheck the box in the fx window) and back on again - do this a few times and you'll see the summed level change with the random phase relationship.

If you have an oscilloscope plugin you can look at the waveforms and see the difference.

The above only applies to periodic signals of course (sine waves and the like) if you use a noise (pink, white, whatever) they'll sum in a repeatable way - uncorrelated.
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Old 05-25-2018, 09:21 AM   #5
ashcat_lt
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Quote:
Originally Posted by Philbo King View Post
Yes, 6 dB is a doubling of amplitude...
Well, technically, db = 20 * log10 (output / input), which works out to 6.0206... db per doubling. 6 isn't the exact number. There are some JS plugs that use the approximation. It doesn't make enough difference most of the time to matter.
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Old 05-25-2018, 01:42 PM   #6
DVDdoug
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Quote:
So here is the catch.... the more sources with the same loudness lvl we add progressively we will receive less loudness change from the same source.
Your ears (and most perception) is also proportional or logarithmic. If you have a singer and you add another singer it becomes noticeably louder (about 3dB louder). But if you have 10 singers and you add one more you're probably not going to notice the change. You'd have to go from 10 to 20 singers to make it (about) 3dB louder.

There are different dB calculations for amplitude (voltage digital level) and for power (Watts).

Double the amplitude (or double the voltage) is +6dB and four times the power. Double the power is +3dB.

And doubling the number of singers is approximately double the power. On average the amplitude will be +3dB, but some peaks may be +6dB higher, and other peaks will be lower where the "waves" are out-of-phase.

For amplitude dB = 20Log(A/Aref) Aref can be the 0dB reference level, or an arbitrary "starting point" if you just want to know the dB change.

For power dB = 10Log(P/Pref).

Even though the references are different, a dB change in your digital level corresponds to the same dB change in your acoustic level. For example if 0dB in your DAW is 90 dB SPL out of your speakers. Reducing the digital level to -3dB will give you 87dB out of your speakers. (Most of us don't have calibrated systems so we don't know the SPL.)
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