MIXING & EFFECTS

# The dB Metering Scale

So it's come to this eh? You have no friends, no social life to speak of and so had nothing better to do than start reading about dB scales. Welcome to the lonely world of music production technology.

If you have been wondering why dB is used or why the maximum level is marked as 0 dB and values below it in negative dB then read on. Unfortunately the dB scale can't be explained in a single sentence. It's worth noting that going over 0 dB on a peak meter is only a problem if this happens on the Master mixer track (see 'Levels & Mixing', for an explanation), or on a Insert track routed directly to a audio device output.

### What is dB?

The peak meters in FL Studio are displayed in and against a dB scale. dB stands for deci (or tenth) of a Bel (unit of sound or electrical pressure named after Mr A.G. Bell). If you start reading around about dB it will become apparent that the dB scale has been used for many different physical measures - dB (SPL), dB(u), dB(v), dB(V), dB(m), dB(VU), dB(FS) and more! Probably not a great idea as this has lead to a lot of confusion and a number of different formulae for calculating dB.

The dB scale used on audio equipment is a relative scale. That is, the values displayed are relative to the 100% volume limit imposed by the audio output device or audio file (wav, mp3 etc). It is impossible to have more than 100% since that, by definition, is as loud as the equipment or digital audio file can go. One exception to this rule is inside FL Studio where the audio exists as numbers in 32 Bit float format. The Hint bar shows this percentage (%) as faders/knobs are moved or when the mouse cursor is placed over the scale. If we assume 100% = 1 then all levels then are relative to this reference value of 1. For example, if the level is at 50% of the maximum volume, the level is 0.5. The value is transformed into dB according to the following formula:

### Calculating dB

20 * log(X/Y) where:

• Y (reference level) - Assuming you haven't been fiddling with the Main volume fader, the 0 dB (almost top) scale represents 100%, or a level of 1. At this level we have used up all the bits of the D/A converter on our audio device or in the case of rendering audio to a file, all the bits of the save format. Go over this level (on the Master track) and we start to clip the signal, as described above. If Y = 1 (100%) then all level values are a ratio relative to this 100% level. The digital numbers representing level are a measure of power (remember that as we need it for later).
• X (signal level) - The signal level carried by the mixer track. This can vary between 0 (no signal) to more than 1. In this case the value represents the fraction (percentage) of the maximum signal level that your digital output format can carry. For example 0 (no signal), 0.5 (50% maximum level), 1.1 (110%, over the maximum level).
• Log (X/Y) - The purpose of taking the log (base 10 in this case), is to compact the number range. For example, X/Y may = 0.0123456789, however log(0.0123456789) = -1.9, much simpler to work with. Type 'log 10' into www.google.com, or any of the values you see here, and the Google calculator will spring into action. Compacting the range is useful as the X value can be very small. A nice property of log fractions is they come out negative, while logs of numbers greater than 1 positive. The dB's sign therefore shows whether the value is lower or higher than the reference. This is why the scale dB's are mostly negative. Given that 0 dB (log 1) is used to represent the maximum volume that can be rendered, all dB values on the scale are relative to this max level (most being fractions less than 1) and so calculate as negative dB values.
• 20 * (20 times) - Since the result of the log(X/Y) calculation gives 'tenths of Bels', for example, log(0.5) = 0.3. That would be 3 tenths of a Bell, the conversion into 1/10th units is achieved when 0.3 is multiplied by 10. But that's 10, not 20? Remember that our original measures are in power units, we are really concerned with air pressure (volume) or electrical pressure (voltage), to get this we square the result since (and you will just have to trust me on this, pressure happens over an area and areas are measured in square units) Pressure = Power squared. It turns out that to square a log value you simply need to multiply it by 2. i.e. 2 log(X) = (X)squared. But wait, that makes 10 times the log(X/Y) to convert into 1/10th units AND 2 times the log(X/Y) to convert to power units, or together 10*2 = 20 times the log(X/Y). So...
• 20 * log(X/Y), the difference (in dB) between any two sound pressures (loudness) or voltage measurements (signals) X and Y. For example, in the case of a 50% signal:
• dB =
• 2(squared to convert to sound pressure) * 10(to convert into 1/10th Bel units) * log(signal level/reference level) =
• 2 * 10 * log(0.5/1)
• 20 * log(0.5/1) =
• 20 * log(0.5) =
• 20 * -0.3 =
• -6 dB. So -6 dB is a drop in amplitude by 50% (or half).

In this case the reference level was 1, however it could be any other level that you are comparing the signal to (say 0.1/0.25). Try entering some of the following into Google, 20*log(0.5), 20*log(1) and 20*log(2).

...time to go outside, find someone, anyone and have a conversation about squirrels. Squirrels are cute, have tiny brains that weigh about 6 grams and so can't comprehend the dB scale. Squirrels are your friends!