Linear and Logarithmic Scaling

One issue that you run into repeatedly in acoustical analysis is that human perception is logarithmic in nature and covers a relatively huge range of values. Everyone’s hearing is a little different but in general, the difference between the threshold of hearing and the threshold of pain – the quietest sounds we can hear and the loudest sounds we can stand – is somewhere around 120 decibels (dB). That works out to six orders of decimal magnitude (the difference between one and one million, e.g.). 

In terms of frequency, the audible spectrum for humans is typically defined as 20 Hz to 20 kHz, a range of four logarithmic “decades”. Admittedly, many or perhaps most of us are unable to hear across that entire range but it might be safe to say that most people can hear across a range of at least three decades, e.g., from 80 Hz to 8 kHz, which is still a pretty wide range of numbers.

The thing is, we do not hear differences between all those numbers equally in either case. To our senses, the difference between one and two is not the same as the difference between two and three, as it would be if we perceived the world linearly. To us, the difference between one and two sounds (or looks, or feels) more like the difference between two and four, or four and eight, or eight and sixteen… (you get the idea).

Charting audio and acoustic data on logarithmic amplitude (magnitude) or frequency scales does two useful things for us then; it helps to make the wide ranges of values that our hearing encompasses more manageable and it results in a presentation of the data that is often more meaningful in terms of human perception. None of this is to say that linear scales don’t have their uses, but for most of the things we do in Smaart, logarithmic scales and units (decades, octaves and decibels), tend to do a better job of showing us what we want to see in a way that makes intuitive sense.