Pitch & Volume

Image Description. A foghorn located adjacent to the Sumburgh Head lighthouse in the Shetland Islands of Scotland. Used to warn away ships from the shoreline in low visibility, these devices can produce sounds loud enough to cause permanent hearing damage to those nearby.
(Unukorno | CC BY-4.0)

In music, the highness or lowness of a sound is referred to as the sound's pitch, and the loudness of the sound is referred to as the sounds's volume.

Frequency & Amplitude

The pitch and volume of a sound are determined by the frequency and amplitude of its sound waves.

The frequency of a sound wave is a measurement of how quickly the individual waves are following one another. This measurement is usually expressed using the SI unit Hertz (Hz). 1 Hz is equivalent to one wave per second. Middle C on the piano keyboard has a frequency of about 262 Hz.

The amplitude of a sound wave is a measurement of how intense the wave is. As a result, scientists usually use units of length (like the meter) to express amplitude; acousticians prefer to use decibels (dB), which express volume in relation to standard limits of human hearing.

Waveforms

It is often helpful to visualize sound waves using a graph called a waveform. In this graph, the horizontal axis represents time, and the vertical axis can be understood as the position of a single particle in relation to its resting position. In a waveform, frequency is illustrated by the number of complete curves shown in a given horizontal distance, and amplitude is represented by the height of the curves.

A single waveform diagram showing a single cycle of a sine wave: a horizontal X axis with a curve that starts on the X axis, curve upward to a peak, curves down to cross the X axis and continues downward to a valley, then curves back up to the X axis. The distance from the X axis to the peak of the curve is labelled as 1 micrometer, and the width of the entire curve is labelled as .01 seconds.
Figure 1: A simple waveform with measurements included. A sound corresponding to this waveform — where air molecules are displaced by 1 micrometer at a frequency of 100 Hz — would have a pitch in a bass guitar's range and a volume like that of a passing truck.

Combining Sounds

When two or more sounds happen simultaneously, their sounds waves combine, so what reaches our ears is a single, complex sound wave. This combined wave is created by simply adding together the frequencies of the component waves at each point along the X axis.

Reinforcement

When two identical sound waves are played together, the frequencies are added together, resulting in a sound wave with a doubled amplitude — a sound twice as loud.

Figure 2: Two waveforms which reinforce one another. Combining two identical waveforms produces a waveform with twice the amplitude, since all values are doubled.

Cancellation

If two sound waves are identical but offset by half a cycle — so one waveform peaks when the other bottoms out — the frequencies will cancel each other out, resulting in silence. Noise-cancelling headphones use this technique by listening to ambient sounds and producing inverted sound waves that deaden their frequencies.

Figure 3: When two waveforms are exactly out of phase, they cancel each other out.

Beats

If the frequencies of two sound waves are slightly different, the combined sound wave will alternate between periods of reinforcement and periods of cancellation, producing pulsing beats of sound which slow as the frequencies get closer. Musicians sometimes listen for this phenomenon, called acoustic beating while tuning their instrument in preparation for a performance.

Figure 4: When two simultaneous sounds have slightly different frequencies, the combined waveform cycles between reinforcement and cancellation, creating a pulsing volume.

Pitch in Practice

Humans can generally hear frequencies from around 20 Hz to around 20,000 Hz, and can hear differences in frequency of about 3.6 Hz, meaning that humans are capable of discerning over 5,000 discrete pitches. Most musical practices, however, are designed around systems of much fewer pitches, though the particular pitches used vary depending on time period and culture.

Octave

Pitches with frequencies that are multiples of one another — for example, 100 Hz, 200 Hz, 400 Hz, 800 Hz and so on — have a universally fundamental relationship. Musicians call the interval between each of these pitches an octave.

Figure 5: When a pitch's frequency is doubled, the resulting tone is an octave higher.

Tuning Systems

Musical pitch is a continuous scale: given any two frequencies, there are an infinite number of different frequencies between them. Because listeners are usually unable to hear infinitesimally small differences — humans are typically capable of hearing frequency changes as small as 1 Hz — most musical systems make use of a discrete set of pitches.

Pitch Class

Most musicians hear frequencies at octave apart as being so consonant with one another as having a shared identity. This identity is called a pitch class, and is often given a shared name.

For example, in the tuning system used in most popular music today, the pitch A refers to frequency at 440 Hz, as well as those at 220 Hz, and 110 Hz, as well as 880 Hz, 1760 Hz, 3520 Hz, and so on.

Absolute and Relative Pitch

Most musicians train themselves to recognize the intervals between two different pitches. With this capability, given a named reference pitch, one can identify any other pitch by hearing the interval between them. This capability is commonly referred to as relative pitch.

Some people are able to identify pitches independently, without a reference pitch, a capability called absolute pitch or perfect pitch. This ability is innate and very rare, and scientists have not yet discovered what causes only some people to have it.

Though data suggests that absolute pitch is more common among musicians, this may be a result of people with absolute pitch being more inclined to pursue careers in music; possession of absolute pitch does not presuppose musical talent.

A photograph of Whitney Houston singing into a microphone in an outdoor venue while pointing to an unseen audience member.
Figure 1: American singer Whitney Houston performing in New York City in 2009. Houston, who had absolute pitch, was one of the best-selling musical artists in history.
(Asterio Tecson | CC BY-SA-2.0)

Pitch & Volume: Summary

  • As the frequency of a sound wave increases, the resulting sound's pitch increases.
    • Frequency is commonly measured in Hertz; 1 Hz corresponds to one complete wave per second.
  • As the amplitude of a sound wave increases, the resulting sound's volume increases.
    • Amplitude can be measured in units of length like nanometers or micrometers, but acousticians commonly use decibels, which measures loudness relative to environmental sound.
  • Waveforms illustrate sound waves as graphs of frequency versus amplitude.
  • When sounds occur simultaneously, they combine to create a single, complex sound wave.
    • When two identical sound waves occur simultaneously, their amplitudes combine to form a soundwave with higher amplitude, resulting in a sound that is twice as loud.
    • When two identical sound waves are offset by half a cycle, their amplitudes cancel each other out, resulting in silence.
    • When two simultaneous sound waves have slightly different frequencies, the interference pattern of the sound waves results in a pulsing sound, called acoustic beating.
  • An octave is the interval between a pitch and another pitch that has twice the frequency.
  • Pitches which are an octave apart are usually heard to share a sonic identity, called pitch class.
  • Most musicians train themselves to fluently identify the interval between two notes, a capability called relative pitch. Some people can identify a sound's pitch without relying upon a reference tone; this capability is called absolute pitch or perfect pitch.

Exercises