Frequency is the number of wave cycles that occur each second, while pitch is the perception of how high or low a sound seems. The two concepts are closely related, but they are not identical. Frequency is an objective, measurable physical property of a sound wave. Pitch is a subjective auditory sensation produced when the brain interprets sound.
In general, increasing the frequency of a sound raises its perceived pitch, while decreasing the frequency lowers its pitch. However, pitch perception is more complicated than simply detecting frequency. The harmonic content, intensity, duration, and context of a sound can all influence the pitch a listener perceives.
Understanding frequency and pitch connects the physics of waves with acoustics, hearing, and music theory.
Key Takeaways: Frequency and Pitch
- Frequency measures how many wave cycles occur per second and is measured in hertz (Hz).
- Pitch describes the perceived highness or lowness of a sound.
- Higher frequencies generally produce higher pitches, while lower frequencies produce lower pitches.
- Frequency is a physical quantity, while pitch is a perceptual attribute.
- Doubling a frequency raises a musical tone by approximately one octave.
- Musical pitch depends strongly on a sound’s fundamental frequency, but harmonics and other acoustic properties also affect perception.
- Loudness, timbre, and duration are separate attributes of musical tones.
What Is Frequency?
Frequency is the number of complete cycles of a periodic wave that pass a point per unit time. The symbol for frequency is usually f, and its SI unit is the hertz (Hz).
One hertz means one cycle per second:
1 Hz = 1 cycle/s
For example, a sound wave with a frequency of 440 Hz repeats its pressure pattern 440 times each second.
Frequency applies to all periodic phenomena, not just sound. Electromagnetic waves, water waves, alternating electrical currents, pendulums, and vibrating strings all have frequencies.
For sound, frequency describes how rapidly the source and surrounding medium oscillate. A tuning fork labeled 440 Hz, for example, vibrates approximately 440 times each second and produces pressure variations in the surrounding air at the same frequency.
Frequency, Period, and Wavelength
Frequency is the reciprocal of the period, which is the time required for one complete cycle:
f = 1/T
where:
- f = frequency in hertz (Hz)
- T = period in seconds (s)
Frequency is also related to wavelength and wave speed:
v = fλ
or:
f = v/λ
where:
- v = wave speed
- f = frequency
- λ = wavelength
For sound traveling at a particular speed, higher-frequency waves have shorter wavelengths, while lower-frequency waves have longer wavelengths.
For example, using a sound speed of approximately 343 m/s in air at 20 °C:
| Frequency | Approximate Wavelength |
|---|---|
| 20 Hz | 17.2 m |
| 100 Hz | 3.43 m |
| 440 Hz | 0.780 m |
| 1,000 Hz | 0.343 m |
| 10,000 Hz | 3.43 cm |
| 20,000 Hz | 1.72 cm |
The speed of sound changes with the properties and temperature of the medium, so these wavelengths are approximate.
What Is Pitch?
Pitch is the auditory sensation that allows a listener to arrange sounds from low to high.
A low-frequency sound generally has a low pitch, such as the lowest notes of a piano or the sound of a large bass drum. A high-frequency sound generally has a high pitch, such as a piccolo note or a high whistle.
Unlike frequency, pitch is not simply a physical measurement of a wave. It is a perception created by the auditory system.
This distinction is important:
Frequency describes the sound wave. Pitch describes how the sound is perceived.
For a simple pure tone, pitch corresponds closely to frequency. For complex sounds such as musical instrument notes and human voices, the relationship becomes more complicated.
Frequency vs Pitch
Frequency and pitch are closely related but describe different things.
| Property | Frequency | Pitch |
|---|---|---|
| Meaning | Number of cycles per second | Perceived highness or lowness of sound |
| Type | Physical quantity | Perceptual attribute |
| Unit | Hertz (Hz) | Usually described using musical notes or relative pitch |
| Measurement | Instruments measure it directly | Determined by auditory perception |
| Main determining factor | Oscillation rate | Primarily frequency or fundamental frequency |
| Higher value generally means | Faster oscillation | Higher perceived sound |
| Applies to | All periodic phenomena | Auditory perception |
A frequency exists whether or not anyone hears it. Pitch requires a listener or auditory system capable of perceiving the sound.
Relationship Between Frequency and Pitch
For simple tones, increasing frequency increases pitch.
A 200 Hz tone sounds higher than a 100 Hz tone, and a 1,000 Hz tone sounds higher than a 500 Hz tone.
However, the relationship between frequency and perceived pitch is not linear. A change from 100 Hz to 200 Hz is perceptually much more comparable to a change from 1,000 Hz to 2,000 Hz than to a change from 1,000 Hz to 1,100 Hz.
In each of the first two cases, the frequency doubles.
This ratio-based relationship is particularly important in music.
Frequency and Octaves
Two tones whose frequencies have a ratio of 2:1 are separated by an octave.
For example:
- 110 Hz → A2
- 220 Hz → A3
- 440 Hz → A4
- 880 Hz → A5
- 1760 Hz → A6
Each successive A has twice the frequency of the A one octave below it.
Similarly, moving downward by an octave halves the frequency.
This logarithmic relationship between frequency and musical interval is one reason frequency and pitch should not be treated as interchangeable quantities.
Musical Notes and Frequency
In modern Western music, 12-tone equal temperament divides an octave into 12 equal frequency ratios called semitones.
Because an octave represents a frequency ratio of 2:1, the frequency ratio between adjacent semitones is:
2^(1/12) ≈ 1.05946
So, moving upward one semitone multiplies the frequency by approximately 1.05946.
If A4 is assigned a frequency of 440 Hz, the frequency of a note n semitones away is:
f = 440 × 2^(n/12)
Positive values of n give notes above A4, while negative values give notes below it.
For example, A♯4/B♭4 is one semitone above A4:
f = 440 × 2^(1/12)
f ≈ 466.16 Hz
Different tuning systems use somewhat different frequency relationships, and even the reference frequency assigned to A4 has varied historically. A4 = 440 Hz is a widely used modern reference rather than a physical requirement of music.
Musical Note Frequencies
In 12-tone equal temperament with A4 = 440 Hz, each semitone has a frequency 2^(1/12), or about 1.05946, times the frequency of the note below it. The following table lists the frequencies of notes in the octave from C4 (middle C) through C5.
| Note | Frequency (Hz) |
|---|---|
| C4 | 261.63 |
| C♯4/D♭4 | 277.18 |
| D4 | 293.66 |
| D♯4/E♭4 | 311.13 |
| E4 | 329.63 |
| F4 | 349.23 |
| F♯4/G♭4 | 369.99 |
| G4 | 392.00 |
| G♯4/A♭4 | 415.30 |
| A4 | 440.00 |
| A♯4/B♭4 | 466.16 |
| B4 | 493.88 |
| C5 | 523.25 |
To find the corresponding notes in other octaves, double the frequency for each octave higher or halve it for each octave lower. For example, C4 is approximately 261.63 Hz, C5 is 523.25 Hz, and C3 is 130.81 Hz.
Worked Example: Finding Frequency From Wavelength
Problem: A sound wave travels through air at 343 m/s and has a wavelength of 0.686 m. What is its frequency? Approximately what musical pitch does this frequency correspond to?
Start with the wave equation:
v = fλ
Solve for frequency:
f = v/λ
Substitute the known values:
f = (343 m/s)/(0.686 m)
f = 500 Hz
The sound therefore has a frequency of 500 Hz.
For comparison, the equal-tempered musical note B4 has a frequency of approximately 493.9 Hz. So, a 500 Hz pure tone is slightly sharper than B4.
Answer: The frequency is 500 Hz, corresponding approximately to a slightly sharp B4.
Fundamental Frequency and Harmonics
Real musical sounds usually contain more than one frequency.
When a string, air column, or other resonating system vibrates, it can vibrate simultaneously in several modes. The lowest frequency associated with a periodic complex tone is called its fundamental frequency.
Additional frequency components are called harmonics when their frequencies are integer multiples of the fundamental.
For a 100 Hz fundamental, the harmonic series begins:
| Component | Frequency |
|---|---|
| Fundamental / 1st harmonic | 100 Hz |
| 2nd harmonic | 200 Hz |
| 3rd harmonic | 300 Hz |
| 4th harmonic | 400 Hz |
| 5th harmonic | 500 Hz |
The relative strengths of these components help determine the characteristic sound of an instrument.
A violin and a flute playing the same musical note can have approximately the same fundamental frequency but sound very different because they contain different mixtures and amplitudes of harmonics.
Pitch and Fundamental Frequency
For many musical sounds, perceived pitch corresponds closely to the fundamental frequency.
For example, a periodic tone with a fundamental frequency of 220 Hz is normally perceived as having a pitch near A3, even though the sound may also contain components at 440 Hz, 660 Hz, 880 Hz, and higher frequencies.
But the auditory system does not simply select the lowest frequency present.
One striking demonstration is the missing fundamental.
Suppose a sound contains frequencies of:
200 Hz, 300 Hz, 400 Hz, 500 Hz…
These frequencies fit a harmonic series whose fundamental would be 100 Hz, even though there is no actual 100 Hz component in the sound.
Listeners may nevertheless perceive a pitch corresponding to approximately 100 Hz.
This phenomenon shows that the auditory system uses the relationships among frequency components when determining pitch.
How Humans Perceive Pitch
Sound waves entering the ear cause the eardrum and middle-ear structures to vibrate. These vibrations ultimately produce motion within the fluid-filled cochlea of the inner ear.
Different regions of the cochlea respond preferentially to different frequencies. High frequencies produce their strongest response near the base of the cochlea, while lower frequencies produce their strongest response farther toward the apex.
This spatial organization is called tonotopy.
Hair cells convert mechanical motion into electrical signals, which travel through the auditory nerve to the brain. The nervous system then processes both the frequency content and timing of these signals.
Pitch perception therefore depends on a combination of mechanisms rather than a single frequency detector.
Place and Temporal Information
Two important sources of auditory information contribute to pitch perception.
Place information comes from where vibration produces its strongest response along the cochlea. Different positions correspond preferentially to different frequencies.
Temporal information comes from the timing patterns of neural activity. At lower frequencies, neurons can synchronize their firing patterns with particular phases of the sound waveform, a behavior known as phase locking.
Together, these mechanisms help explain the remarkable ability of human hearing to distinguish frequencies and identify musical pitches.
Human Hearing Range and Pitch
A commonly quoted hearing range for young humans is approximately:
20 Hz to 20,000 Hz (20 kHz)
This range varies considerably among individuals. Sensitivity to high frequencies generally decreases with age and can also be affected by noise exposure and other factors.
Sounds below approximately 20 Hz are called infrasound, while sounds above approximately 20 kHz are called ultrasound.
These boundaries describe approximate human hearing limits, not limits on the existence of sound waves. Many other animals detect frequencies outside the typical human range.
Hearing a sound and perceiving a clear musical pitch are also different abilities. Some sounds within the audible range do not produce a strong or definite pitch.
Pitch Perception Is Not Perfectly Determined by Frequency
Although frequency is the dominant physical factor controlling pitch, other characteristics of a sound can alter its perceived pitch slightly.
Intensity
Changing sound intensity can cause small changes in the perceived pitch of some tones. The effect depends on frequency and listening conditions.
Duration
Very short sounds can produce uncertain pitch perception because the auditory system has limited information from which to identify the repeating pattern.
Harmonic Content
The presence and relative strength of harmonics affect how easily the auditory system identifies a fundamental pitch.
Surrounding Sounds
Musical and auditory context can influence pitch judgments. The brain interprets sounds relative to other sounds as well as from their individual acoustic properties.
These effects reinforce the distinction between physical frequency and perceived pitch.
Frequency, Pitch, and Musical Intervals
Musical intervals correspond to frequency ratios, although the exact ratios depend on the tuning system.
Some simple ratios have particular importance in acoustics and traditional tuning systems:
| Interval | Simple Frequency Ratio |
|---|---|
| Octave | 2:1 |
| Perfect fifth | 3:2 |
| Perfect fourth | 4:3 |
| Major third | 5:4 |
| Minor third | 6:5 |
These are just-intonation ratios. Equal temperament slightly adjusts most of them so that an instrument can play consistently in all keys.
For example, the equal-tempered perfect fifth has a ratio of:
2^(7/12) ≈ 1.4983
which is very close to the simple 3:2 ratio of 1.5.
This connection between numerical ratios and musical intervals forms one of the most important links between physics and music theory.
Frequency, Pitch, and Resonance
Musical instruments produce sustained tones using resonance.
A resonating object or air column has particular frequencies at which it naturally vibrates. These are its natural frequencies or resonant frequencies.
For a string fixed at both ends, the fundamental frequency is:
f₁ = v/(2L)
where:
- f₁ = fundamental frequency
- v = wave speed along the string
- L = vibrating length of the string
Shortening a guitar string by pressing it against a fret decreases L, increasing its fundamental frequency and therefore raising its pitch.
Increasing string tension increases the wave speed along the string and also raises the pitch. Increasing the string’s linear mass density lowers the wave speed and pitch.
Similar principles govern standing waves in organ pipes, flutes, clarinets, brass instruments, and other resonating systems, although the allowed harmonics depend on the geometry and boundary conditions.
Other Attributes of Musical Tones
Pitch is only one property that describes how a musical tone sounds.
Loudness
Loudness is the perception associated mainly with sound intensity and sound pressure level.
Increasing the amplitude of a sound wave generally makes the sound seem louder rather than higher in pitch.
This distinction is fundamental:
Frequency primarily affects pitch. Amplitude primarily affects loudness.
Human loudness perception also depends strongly on frequency, so equal physical intensities do not necessarily sound equally loud.
Timbre
Timbre is the quality or character that distinguishes sounds having similar pitch and loudness. It allows a listener to distinguish a violin from a trumpet or piano even when all three instruments play the same note.
Factors affecting timbre include:
- harmonic spectrum
- relative harmonic amplitudes
- attack and decay
- changes in spectrum over time
- noise components
- resonance
Timbre is sometimes informally called tone color.
Duration
Duration is the length of time a sound lasts. The duration contributes directly to rhythm and musical phrasing. It can also affect whether a listener perceives a definite pitch, particularly for extremely short sounds.
Envelope
The envelope describes how the amplitude of a sound changes with time.
A commonly used model divides the envelope into:
Attack → Decay → Sustain → Release
The envelope contributes strongly to the identity of musical instruments. A piano note begins with a rapid percussive attack and gradually fades, while a bowed violin can sustain a note much more continuously.
Pitch vs Loudness vs Timbre
| Attribute | What It Describes | Main Physical Factors |
|---|---|---|
| Pitch | How high or low a sound seems | Frequency, fundamental frequency, spectrum |
| Loudness | How loud or soft a sound seems | Amplitude, intensity, frequency |
| Timbre | Character or quality of a sound | Harmonics, spectrum, envelope, transients |
| Duration | How long a sound lasts | Time |
These attributes interact perceptually, but they describe different aspects of sound.
Pure Tones, Complex Tones, and Noise
A pure tone is a sinusoidal sound containing essentially one frequency. A tuning fork produces an approximation of a pure tone, although a real tuning fork is not perfectly sinusoidal.
A complex tone contains multiple frequency components. Most musical instrument sounds and human vocal sounds are complex tones.
A harmonic complex tone contains frequency components related approximately by integer multiples of a fundamental frequency.
Noise contains a broad or irregular distribution of frequencies. Noise can still have spectral characteristics, and some noises produce a pitch sensation, but many do not have a single clearly identifiable pitch.
Frequency Spectrum
A sound can be represented in two useful ways.
A waveform shows how a quantity such as sound pressure changes with time.
A frequency spectrum shows the frequencies contained in the sound and their relative amplitudes.
For a pure 440 Hz tone, the ideal frequency spectrum contains one prominent component at 440 Hz.
For a musical instrument playing A4, the spectrum might contain peaks near:
440 Hz, 880 Hz, 1320 Hz, 1760 Hz…
The strengths of these harmonics vary from instrument to instrument.
Mathematically, Fourier analysis provides a way of representing a complex periodic waveform as a combination of sinusoidal components. This makes frequency analysis an important connection between wave physics, acoustics, mathematics, music, and digital signal processing.
Beats and Small Frequency Differences
When two tones with similar frequencies sound simultaneously, they can produce periodic changes in amplitude called beats.
The beat frequency is the absolute difference between the two frequencies:
fbeat = |f₁ − f₂|
For example, suppose two tuning forks have frequencies of 440 Hz and 443 Hz:
fbeat = |443 − 440| = 3 Hz
A listener hears the combined sound grow louder and softer approximately three times each second.
Musicians use beats when tuning instruments. As two frequencies approach one another, the beats become slower. When the frequencies match closely, the beats disappear.
Beats are an especially useful demonstration that frequency difference and pitch difference are related but distinct concepts.
Common Misconceptions
Frequency and pitch are the same thing.
They are closely related but different. Frequency is a measurable property of a wave, while pitch is an auditory perception.
A louder sound has a higher pitch.
Not necessarily. Increasing amplitude mainly increases loudness. Increasing frequency generally raises pitch.
Every sound has one frequency.
Pure tones approach this condition, but most real sounds contain many frequencies.
The lowest frequency present always determines pitch.
Often the fundamental frequency strongly determines pitch, but the missing-fundamental effect demonstrates that the auditory system can infer a pitch even when that frequency is physically absent.
Doubling frequency doubles perceived pitch.
Doubling frequency produces a pitch one octave higher. Pitch perception and musical intervals are more naturally related to frequency ratios than to simple frequency differences.
Humans hear exactly from 20 Hz to 20 kHz.
These values are approximate conventional limits. Hearing range differs among people and changes with factors such as age and noise exposure.
Frequently Asked Questions
What is the difference between frequency and pitch?
Frequency is the number of wave cycles per second, measured in hertz. Pitch is the perception of how high or low a sound seems.
Does higher frequency mean higher pitch?
Generally, yes. Increasing the frequency of a simple tone raises its perceived pitch.
What is the frequency of middle C?
In 12-tone equal temperament with A4 = 440 Hz, middle C (C4) has a frequency of approximately 261.63 Hz.
What frequency is A440?
A440 refers to the musical note A4 tuned to 440 Hz. It is a widely used reference pitch for tuning musical instruments.
What happens to pitch when frequency doubles?
The pitch rises by one octave.
For example, 220 Hz and 440 Hz correspond approximately to A notes separated by one octave.
Does amplitude affect pitch?
Amplitude primarily affects loudness rather than pitch. However, changes in intensity can cause small perceptual shifts in pitch under some conditions.
Why can two instruments play the same pitch but sound different?
They can have the same fundamental frequency but different harmonic spectra, envelopes, and transient characteristics. These differences produce different timbres.
Can a sound have pitch without containing its fundamental frequency?
Yes. With a harmonic series, the auditory system can sometimes infer the missing fundamental from the spacing of higher harmonics.
Why does shortening a string raise its pitch?
A shorter vibrating string has a higher fundamental frequency, assuming other properties remain unchanged. The increased frequency produces a higher perceived pitch.
Glossary
Amplitude: The maximum displacement of an oscillation from equilibrium. In sound, amplitude is related to sound pressure and intensity.
Beat: A periodic variation in amplitude caused by interference between sounds with slightly different frequencies.
Frequency: The number of wave cycles per second, measured in hertz.
Fundamental frequency: The frequency associated with the fundamental vibration of a periodic system and usually the primary frequency associated with perceived musical pitch.
Harmonic: A frequency component that is an integer multiple of the fundamental frequency.
Hertz (Hz): The SI derived unit of frequency, equal to one cycle per second.
Loudness: The perception of the strength or intensity of a sound.
Octave: A musical interval corresponding approximately to a 2:1 frequency ratio.
Period: The time required for one complete oscillation or wave cycle.
Pitch: The auditory perception that orders sounds from low to high.
Pure tone: A sound consisting ideally of a single sinusoidal frequency.
Resonance: An enhanced response of an oscillating system when driven at or near one of its natural frequencies.
Timbre: The perceptual quality that distinguishes sounds having similar pitch and loudness.
Wavelength: The spatial length of one complete wave cycle.
Frequency and Pitch Summary
Frequency and pitch provide a bridge between the physics of waves and the perception of music. The frequency is a physical measurement of oscillation rate, while pitch is the auditory perception of how high or low a sound seems.
For simple tones, higher frequencies generally correspond to higher pitches. Musical intervals depend primarily on frequency ratios rather than frequency differences, with a 2:1 ratio corresponding to an octave. Real musical sounds contain fundamentals and harmonics, and the auditory system analyzes these complex patterns to determine pitch.
Pitch is only one aspect of sound. Loudness, timbre, duration, and the sound envelope combine with pitch to create the rich variety of tones produced by voices and musical instruments.
References and Further Reading
- Hartmann, William Morris (1997). Signals, Sound, and Sensation. Springer. ISBN 978-1-56396-283-7.
- Olson, Harry F. (1967). Music, Physics and Engineering. Dover Publications. ISBN 978-0-486-21769-7.
- Schwartz, David A.; Dale Purves (2004). “Pitch Is Determined by Naturally Occurring Periodic Sounds”. Hearing Research. 194 (1–2): 31–46. doi:10.1016/j.heares.2004.01.019
- Terhardt, E., Stoll, G. and Seewann, M. (1982). “Algorithm for Extraction of Pitch and Pitch Salience from Complex Tonal Signals”. Journal of the Acoustical Society of America. 71: 679–88.