The basic dynamic scale

Detecting how big a sound is, is the most primitive ability of our detecting system. If the reader wonders why I have not used the term amplitude before, it is for the same reason that we cannot talk about the frequency of a pitched note. It has several frequencies and we now know that some of them contribute to the pitch sensation too. The term for the excursion through which a pure tone vibrates is its amplitude, but since all noises and musical sounds consist of several frequencies, each with a different amplitude, it is best for the time being to stick to words with ordinary meanings such as big and small. All the frequencies in a sound contribute to the sensation of loudness. And our ancestors probably detected roughly how big a noise was before they had any sense of loudness; some animals with no cortex can. Loudness itself is a sensation.

We have no absolute assessment of loudness; like almost every other modality we can sense, our judgement is comparative, whether a sound is louder or less loud than the previous one. The rough scale which our hearing system automatically provides is that the sound vibrations have to increase three times to double the loudness sensation, at all parts of the loudness range. Starting with low level sound, to be twice as loud the vibrations must increase about three times, ten times to be four times as loud, thirty times to be eight times as loud, and so on. Why our hearing behaves that way was very valuable. We needed to know whether a noise was getting louder, probably meaning getting nearer, and an increase in the vibrations of a tiny noise that we needed to detect, would be a negligible increase in a big one. It means that an instrument has to increase its sound output by about as much to go from f to ff as to cover the range from pp to f, something it is difficult to get young orchestral players to appreciate. But it does not mean, as even one or two otherwise respected acoustics books suggest, that ten violins in unison will be four times as loud as one. The rule applies to increasing a single sound, and several independent sound sources do not add loudness as steeply as that.