Science, Maths & Technology

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Sound for music technology: An introduction

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# 7 Pitch and loudness

## 7.1 The subjective experience

Two of the properties of sound that we have examined from an objective stance, frequency and amplitude, have a fundamental importance to our appreciation of sound and music. In this section I want to look more closely at the subjective interpretation of these two properties of sound. I should stress that I am talking about sine-wave sounds in this section. The complex, non-sinusoidal sounds encountered in music add extra layers of complexity to the relationships I am discussing here.

Keeping the frequency of a sine wave constant and varying the amplitude changes the loudness: the bigger the amplitude, the louder the sound.

The effect of changing the frequency of a sine wave is rather harder to pin down. Changing the frequency changes the pitch; you might say that the sound becomes higher or lower.

To summarise this message:

• Loudness is the subjective property of sound that is heard to change when the amplitude is changed while the frequency is held constant.

• Pitch is the subjective property of sound that is heard to change when the frequency is changed while the amplitude is held constant.

Generally, pitch is felt to exist on a continuum from low to high. Low pitches are associated with low frequencies, and high pitches are associated with high frequencies. However, although pitch is experienced as being on a continuum, for musical purposes a series of more-or-less fixed points on the continuum is usually defined. These are the pitches to which we give letter names, such as A, B, B, and so on.

These apparently simple correspondences between amplitude and loudness, and between frequency and pitch, are complicated by a number of factors. One of these is the uneven response of the hearing system. The human ear is not equally sensitive to all frequencies within the range of human hearing, being most sensitive at around 4 kHz. Changing the frequency of a sine wave, particularly over a wide range, while holding the amplitude constant can result in a change of loudness. It is also true that changing the amplitude of a sound while holding the frequency constant can result in a slight shift of pitch. Nevertheless, it is broadly true that we experience changes of amplitude as changes of loudness, and changes of frequency as changes of pitch.

Another factor that complicates the relationship between the objective and subjective properties of sound is the way the ear judges changes of amplitude. This is something I shall return to when I discuss decibels.

Does reducing the amplitude of a sound by half mean that the sound is half as loud? This question is concerned with the subjective interpretation of amplitude, so there is no hard-and-fast answer that everyone is sure to agree with. In fact, you may have find the concept of halving the loudness of a sound to be almost meaningless. Nevertheless, most people find that halving the amplitude does not halve the loudness. Usually a bigger reduction is required to give the impression of a halving of loudness. Another way to express this is to say that the amplitude must be more than doubled to give the impression of a doubling of loudness.

We shall return to the relationship between amplitude and loudness when we look at decibels later in this unit.

The correspondence between frequency and pitch, though not exact, is sufficiently close for us to use frequency to define the pitches used in music. For example, in the pitch standard known as concert pitch, the pitch of the note A above the note middle C (Figure 22) is set at 440 Hz (A4).

Figure 22 Frequency of A4 in concert pitch

Other pitch standards are in use, particularly for the performance of older music, and even concert pitch is not universally used by contemporary performers.

### Activity 23 (Self-Assessment).

Two of the following statements are true and one is false. Find the true and false statements.

• (a) If two equal-amplitude sine waves A and B are exactly in phase, the result of adding them will sound twice as loud as A or B by itself.

• (b) Reducing the amplitude of a sine wave always reduces its loudness if the frequency is held constant.

• (c) A sound of a particular amplitude may be audible at about 4 kHz, but inaudible at 1 kHz.