Sound is considerably more difficult to measure than temperature or pressure. Since it occurs over a range of distinct frequencies, or ƒ, its level must be measured (or predicted in the case of an analysis) at each frequency to understand how it will be perceived in a particular environment.

Our ears can sense sounds at frequencies ranging from 20 to 16,000 Hertz (Hz), but designers generally focus on sounds ranging from 44 to 11,300 Hz for room acoustics. Despite this limit, measuring a sound at each frequency would result in 11,256 data points per reading!

To make the amount of data more manageable, this 44-to-11,300-Hz spectrum is divided into octave bands. Each octave band is identified by its center frequency and is delimited such that the band's highest frequency is twice its lowest frequency. The "octave band center frequency" is 2 0.5 x flowest, so the 44-to-11,300-Hz spectrum contains eight octave bands with center frequencies of 63, 125, 250, 500, 1000, 2000, 4000 and 8000 Hz. Sound not only encompasses a wide spectrum of frequencies, but an extensive range of volumes as well. The loudest sound the human ear can hear (without damage) is 10 million times greater than the quietest perceptible sound. Numbers of this magnitude make using an arithmetic scale cumbersome, so a logarithmic scale is applied instead. Converting the arithmetic range of 1 to 10 million using a "base 10" logarithmic (log10) scale yields a range of 0 to 7. The 0-to-7 scale must also be tied to a reference value, Nref , by which measured values, N, are subsequently divided. (The reference value for sound pressure is 20 micropascals; for sound power, it's 1 picowatt.) The unitless result is described as "bels" or, more commonly, "decibels" (dB). "Deci-" is simply a prefix meaning 10-1. The relevant equation is:

Measuring sound with a logarithmic scale means that logarithmic addition must be used to add and average sound levels. Sound measured in a particular octave band is the logarithmic sum of the sound at each of the band's frequencies. The good news is that, unlike averaging, logarithmic summing doesn't mask the magnitude of a tone. Unfortunately, it doesn't indicate that the ear hears a difference between an octave that contains a tone and one that doesn't, even when the overall magnitude of both octaves is identical. So the process of logarithmic summing, though practical, sacrifices valuable information about sound "quality."

Continue on to Single-Number Descriptors.