There are some instances when a limited amount of knowledge can do a great deal of harm. For instance, you might know that a bit of sun is good for you. If you are not fully versed in the effects of sun exposure to the skin, you might be wondering what those strange, asymmetrical spots are that keep popping up all over your body. Get those checked out; seriously I worry about you sometimes…
Other times, a basic understanding of something might be helpful the most of the time. Take Euclidean geometry for example. If you aren’t an astrophysicist or a nuclear scientist, pretty much everything you need to know falls into Euclidean space.
But there are also times when the common sense understanding of something gets you by enough so that you don’t realize all the other times that it is absolutely wrong and leads you astray. This is the case with our friend the decibel.
I was working on a record a while back with producer/engineer extraordinaire Paul Kolderie (Radiohead, Pixies, Mighty Mighty Bosstones) and he mentioned something in passing that really caught my attention. I can’t really recall what the situation was, but we were setting up a session and he said to me “I can’t stand it when people ask me to change something by half a dB. A dB is the lowest possible change you can perceive, so saying half a dB is meaningless.”
Many nights I woke abruptly from sleep in a cold sweat tormented by what he had said. Something sounded so right and yet so wrong about that. I mean, if I told you to change something by half a dB twice—both equally insignificant changes by his definition—I would get a change of full dB, and therefore a significant change. Using some simple extrapolation, you can’t keep considering fractional changes in decibels as insignificant, because surely enough they add up.
So what exactly is a dB and what change in dBs is significant to our ear and in our mix? Well, without getting overly scientific about it and also restricting the question to audio applications (sorry electrical engineers), a decibel is a convenient unit of measure that expresses very large changes in magnitude against a reference level in a concise manner. Concision was important back in the days of hand calculation.
When they were busy wiring up the world for telephone usage, Bell Laboratories thought it’d be really swell if they could measure the amount of degradation in audio level over a mile of telephone cable. They did the calculations but soon found that expressing the quantities in conventional terms meant using insanely large and unwieldy numbers. So they decided to use a logarithmic function to bring the numbers to more manageable figures for simple calculation. Logarithms of numbers are useful because they have some of the same arithmetic applications as regular integers (for example, you can add two logarithms with the same base just like adding to regular numbers). The unit they came up with became known as a Bell in honor of the company and Mr. Alexander Graham Bell. So a decibel is actually 1/10 of a Bell.
So why do we talk about tenths of something? After all we don’t regularly deal in decimeters or decigrams. Well in the mid 1800s, some very clever psychophysicists began studying something called Just Noticeable Differences (JND) in sensation. A JND is the smallest incremental change in a sensation that is perceptible to the average person. This could be the JND in touch as measured in PSI or the JND in sight as measured in lumens. Someone discovered that a tenth of a Bell roughly correlated to the smallest detectable change in a sound to the human ear. As such, the decibel became a very important measurement in audio because it was simple to express changes that actually meant something with regard to common perception.
It is important to note that JNDs relate to the AVERAGE person. As such, musicians and audio professionals are often able to detect much more minute changes in audio level.
When studying JNDs, another useful but perhaps counterintuitive aspect of the decibel arose—a doubling of volume roughly correlated in a change of +/- 10 dB. This is useful but strange in that the arithmetic is skewed—you ’d expect a doubling in the perceived volume of something that sounds at +2 dB to be +4 dB. But then again, what is a doubling of something that measures 0 dB? This exposes some of the fundamental limitations in the simple definition of the decibel—human perception complicates the simple calculations.
Such problems spurred further investigation into situational applications of JNDs and Signal Detection Theory was born. In basic terms, the object of Signal Detection Theory is to figure out what extra factors go in to our perception of a sound and how it compares against “noise” or unrelated signals. For instance, does a +1 dB change to a signal still sound like an increase of 1 JND if the sound is played over white noise? What about if the original signal is 100 Hz sine wave? What about 30 KHz? What if the original signal is a voice played over a country band? Or a metal band?
It was discovered that the JND of a signal changes based on frequency range and initial level. A JND is around 1 dB for soft sounds at frequencies in the low and mid range—the frequencies we perceive most readily. Really loud sounds can have a JND of 1/3 to 1/2 dB. Really soft sounds on the edge of audibility might have JNDs of a couple dB.
Furthermore, other things can color sounds in such a way that you can take the same sound, add something to it and suddenly the JND might be more or less than a dB. Perceptual Encoding Theorists look for factors outside the Critical Band of Frequency for a sound (the frequency or frequencies that define a sound) that would alter our perception of it. For instance, adding a slight reverb in some cases might cause the JND to rise (meaning you need to turn the signal up more to get a perceivable change) or adding a harmonic exciter in most cases would cause the JND to lower (meaning you wouldn’t need to turn the signal up as much to get a perceivable change). This is because new nerve endings are being excited and these cause our minds to perceive the sound in a different way than we had previously.
As you can see, the decibel is not quite as simple as its common sense understanding in the audio world. So when you need to make something appear twice as loud, you know what to do. When somebody tells you to make their vocals 20 dB louder, you know that that is laughably extreme (for the most part) and you should adjust your corrections appropriately. When someone asks you to turn something down by 1/3 of a dB, you know that it is really only going to be detectable if that sound is already pretty loud.