# 9 The ranges of human hearing

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## 9.1 Frequency range

The lowest frequency humans can hear is approximately 20 Hz. The upper limit for humans is nominally 20 000 Hz (20 kHz), but this limit tends to decline with age, and for most of us it is well below this figure.

## Activity 27 (Self-Assessment)

Taking the upper limit of frequency as 20 kHz, how many octaves span the range of human hearing?

### Answer

Ten octaves. A simple approach is to divide 20 000 Hz repeatedly by two until we reach the lower limit of the human frequency range. The number of times the division can be carried out is the number of octaves. Thus, starting at the upper end of the range:

Hence the span is ten octaves.

## Activity 28 (Self-Assessment)

With age, your upper limit might drop from 20 kHz to 10 kHz. How many octaves have you lost?

### Answer

One octave, corresponding to a halving of the upper frequency limit.

Although human hearing covers a range of, say, ten octaves at best, seven of these octaves cover the bottom eighth of the range, from 20 Hz up to 2500 Hz, which corresponds roughly to the pitch range from E♭0 to E♭7 (Figure 26). As far as music is concerned, this is where the action is concentrated. Of the standard acoustic instruments, only the piano, harp and piccolo go higher than E♭7, and those not by very much.

At the lower end of the musical pitch range, the bottom note on a double bass or bass guitar, E1, has a frequency of just over 40 Hz. Not many instruments can go below this – the main ones are the harp, piano, double bassoon and organ. (The keyboard in Figure 26 is extended below the limit of a normal piano keyboard.)

Figure 26 Range of musical pitch

To say that musical instruments rarely produce pitches above E♭7 is not the same as saying that they rarely produce frequencies above 2500 Hz. The sounds produced by virtually all instruments are not pure sine waves. Instead, they are more or less complex mixtures of sine waves, covering a range of frequencies above the one that corresponds to the pitch being played. The important point to bear in mind is that the mixture of frequencies associated with a single musical pitch can extend well above the frequency corresponding to the pitch that is heard. The presence of these additional frequencies (sometimes called overtones, partials or harmonics) is partly what gives individual instruments their particular timbre.

## Activity 29 (Self-Assessment)

The ear is at its most sensitive around 4 kHz. Is this within the range occupied by the pitches mainly used in music?

### Answer

It is above the frequency of the pitches produced by virtually all instruments. However, it is within the range of the harmonics of some instruments.

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