How Sound Becomes Pitch
Sound is heard because of fluctuations in air pressure, tiny variations from normal atmospheric pressure caused by a vibrating object. These pressure changes reach our ears and cause our eardrums (tympanic membranes) to vibrate as well. When the energy behind these fluctuations is strong enough, it creates waves in the air, waves of sound. 5 2
Red represents high pressure and Blue represents low pressure.
This rise and fall in pressure follows a repeating, back-and-forth motion that we call simple harmonic motion, a motion also seen in the swing of a pendulum or a mechanical metronome. While the object slows at the turning points and speeds up at the center, each full swing (or cycle) takes the same amount of time. This regularity makes the motion periodic.
The number of cycles that occur each second is the frequency, measured in Hertz (Hz). One Hertz equals one cycle per second. For example, if a vibration repeats 440 times per second, it has a frequency of 440 Hz and a period of 1/440 second per cycle. Heinrich Hertz (1857–1894), a German physicist, gave his name to this unit after pioneering work in electromagnetism.
Simple harmonic motion is the fundamental mechanism behind most musical sounds in the orchestra. We can illustrate it on a graph where P stands for air pressure and t stands for time, producing a sine wave.
Sinusoidal change in air pressure caused
by a simple vibration back and forth where
P = air pressure and t = time
Any object that vibrates in simple harmonic motion is said to have a resonant mode of vibration, a frequency at which it will naturally tend to vibrate when set in motion. However, most real-world objects have several resonant modes of vibration, and thus vibrate at many frequencies at once. Any sound that contains more than a single frequency (that is, any sound that is not a simple sine wave) is called a complex tone. Each individual frequency that goes into the makeup of a complex tone is called a partial. It is one part of the whole complex tone.
From Pure Tones to Complex Sound
An object vibrating in simple harmonic motion resonates at a natural frequency, its resonant mode. Most real-world objects, however, don’t vibrate in just one way. They have multiple resonant modes, producing many frequencies at once. These combinations create complex tones. 5 10
Each frequency in a complex tone is called a partial. When all the partials are integer multiples of a fundamental frequency, the sound has a harmonic spectrum, and each partial is called a harmonic.
Even though these harmonics are separate frequencies, they combine into a single periodic waveform and are heard by the human ear as one tone with a clear pitch. This is the essence of harmonic sound: coherence and blend.
Helmholtz and the Sensation of Tone
In the mid-1800s, German scientist Hermann von Helmholtz (1821–1894) explored why certain tones sound musical. In his classic work On the Sensations of Tone, he observed that tones with a clear, moderate series of harmonics (especially up to the sixth partial) are perceived as rich, resonant, and musical.7
Not All Sounds Are Harmonic
Every instrument in a modern orchestra generates complex tones, but not all produce harmonic partials. For example, cymbals and gongs create richly complex sounds, but their partials are inharmonic, not neat multiples of a fundamental. These sounds are vibrant but lack a clear pitch.
Timpani are a unique case. They also do not produce a fully harmonic spectrum, yet they are considered pitched percussion. Their perceived pitch arises from a small group of quasi-harmonic partials, enough to create a sense of tonal identity, though not a perfect harmonic series.
Strings and Air: The Harmonic Instruments
Among the instruments that do produce harmonic spectra, strings, winds, and brass, pitch is determined by how the vibrating medium behaves. These instruments generate tones through:
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Strings or columns of air vibrating along their full length (the fundamental), or
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In fractions of that length (producing upper partials or harmonics).
Points where the medium doesn’t move, called nodes, divide these fractions. The shorter the segment, the higher the frequency of vibration.
Mathematically, the frequency of each harmonic is inversely proportional to the size of the vibrating segment:
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Halving the length doubles the frequency (an octave above),
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Dividing into thirds triples the frequency (an octave and a fifth above),
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And so on.
The resulting harmonic series forms the basis of musical tone and tuning.
Looking Ahead
In the next section, you’ll see how the harmonic series appears in traditional staff notation and hear what each partial sounds like. Each tone in the series will be demonstrated as a simple sine wave, one pure frequency. As you follow along, listen carefully to how the pitch changes and how the intonation of each partial behaves, especially as they rise higher on the staff.