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An understanding of level is fundamental to sound engineering. And clearly, from the recordings I receive from aspiring engineers and musicians, not everyone has it, yet.
'Level' is a term with a precise meaning. For a real sound traveling in air (or any other medium), its level is measured in terms of sound pressure. Sound pressure is the difference from normal air pressure caused by the sound.
Difficult bit coming ---
Sound pressure is measured in newtons per square meter. The newton (named for Isaac Newton) is a measure of force.
For the technical, one newton is the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
For the non-technical, one newton is about the weight of a smallish apple.
Sound pressure can also be expressed as pascals where one pascal equals one newton per square meter.
--- end of difficult bit.
Although it is certainly possible to measure the level of a real acoustic sound, in most sound engineering practice we don't do that. The exceptions are live sound and film sound.
But when sound is converted into an electrical signal, level is vitally important to all of us. Electrical level is measured in volts and millivolts (a millivolt is one thousandth of a volt).
In coarse terms we often talk about 'mic level', which roughly equates to a few tens of millivolts. We talk about 'line level' also, which is around a volt.
We also have level inside digital audio systems. Sound here is represented as numbers rather than voltages. Rather than use the raw numbers, we almost always talk in terms of decibels.
One key concept of level here is 0 dBFS - 'FS' stands for 'full scale'. 0 dBFS is the highest level any particular system is capable of.
Let's suppose for a moment that you are looking at the waveform display in your favorite audio recording software.
You can see the waveform wiggling up and down within the track, and there is lots of clear space above and below it.
This means that the level is low. If the level gets too low then the noise of the system will start to become noticeable.
How low is too low? Well it depends what you are recording. If you are recording a sound that is unpredictable in acoustic level, then you will record it at a fairly low level just in case something really loud comes along.
If you are recording a sound that is consistent in level, then you can record it closer to 0 dBFS.
When you are recording, the amount of leeway you allow between the highest signal level you expect and 0 dBFS is called 'headroom'. The term headroom is used in different contexts with a similar meaning.
Suppose the level goes all the way up to 0 dBFS. That's OK, as long as it just touches that level.
If the signal attempts to go higher than 0 dBFS then it will be clipped - the tops and bottoms of the waveform will be squared off. Although very mild clipping can sometimes go unnoticed, you are definitely in the danger zone. Red lights spell danger and must be avoided.
When you are mixing, then there is a certain level to aim for - -2 dBFS (that's minus two in case it isn't clear - sometimes on computers the minus sign and the two are broken apart onto separate lines).
This figure comes from CD mastering. A CD factory may reject a master if the signal doesn't at some point rise above -2 dBFS.
When you are mixing you can go all the way to 0 dBFS because the signal levels contributing to the mix are totally predictable. But don't try to go above this or the signal will clip.
There is a whole encyclopedia that could be written about level, but let me move on to...
'Volume' is a word from the old days of sound. At some point in time, the manufacturer of a radio set wondered what he should call the knob that made the sound louder or quieter. Some bright spark came up with the word 'volume'.
Volume can mean the same as level. Turn the volume of your radio set all the way down, then start turning it up slowly. The level will rise in proportion.
But when you get to a certain point something different will happen. In the old days of vacuum tube radio sets, when the volume reached a certain point the signal would start to distort mildly.
You could continue turning the volume up. The sound would get louder, but the peak level of the electrical signal driving the loudspeaker wouldn't increase much.
This is the same with modern transistor radio sets, except that the output signal to the loudspeaker clips, rather than being gently rounded as in the older vacuum tube equipment.
When a signal clips, the peak level can't get any louder. But you can continue turning up the volume. The clipping will get harsher and eventually you will reach a point where the sound is too harsh and you will stop and back off.
We can see from this that volume and level are similar, but only up to a point.
There is another way to look at volume. It is purely subjective and difficult to put any measurements to.
Imagine this however - you have two loudspeakers connected to your hi-fi and can switch between them. Each has the same sensitivity but one is tiny, the other is large.
The tiny speaker will produce a sound that is loud and will poke you in the ear, if you turn the volume up sufficiently. The large loudspeaker will produce a fuller sound with more 'weight'. It is easy to interpret this as a greater 'volume of sound'.
Although volume is largely a subjective experience, it is often useful to think of sound in this way.
Another subjective term is...
Increasing the level increases the loudness. Increasing the volume can increase the loudness. Or it might just increased the 'poke you in the ear with a sharp stick' factor. It depends on the loudspeaker.
Look back at the waveform on your computer. Use the normalize function so that its peaks reach all the way up to 0 dBFS.
You have now increased the level of the signal, within your recording system, to its maximum. You cannot increase the level any more without clipping.
Look now at the areas between the curve of the signal and the zero line in the center (imagine a horizontal zero line in the center if your system doesn't display one).
These areas relate to the subjective loudness of the signal.
Now apply a compressor plug-in. This will bring down the peaks of the signal. Use the make-up gain function to bring the peaks back to 0 dBFS. Print this to disk so you can open it up on another track and view the original and the compressed version one above the other.
Listen to the two tracks separately. The compressed version will be louder than the original, but its peak level will be the same.
What is different however is that the area enclosed by the signal on the display is greater. The space above and below the signal is less.
It is clear therefore that making the area enclosed by the signal on the display greater will increase the subjective loudness of the signal.
If you apply more compression (don't forget make-up gain to restore the peak level), then this area will increase and so will the loudness.
To go into a flight of fancy you can increase the level and ignore clipping. Eventually you will reach a point where the signal is mostly at 0 dBFS in both positive and negative directions, and the transitions in between are almost instantaneous.
It will sound dreadful, but it will certainly be loud. And this can happen without the peak level increasing. It's worth trying as an experiment, but be careful with your speakers (and your ears!).
In conclusion, level is a precise term capable of unambiguous expression and interpretation. Volume and loudness are connected with level, but there are other aspects that make them subjective rather than objective quantities.