Pitch Discrimination

Abstract

Pitch discrimination, the facet of pitch perception that MeSH indexes as its own descriptor, is the ability to tell two tones apart by pitch — operationally, the smallest change in frequency a listener can reliably detect. That threshold, the frequency difference limen, is remarkably fine: a trained listener near 1 kHz resolves a change of a few hertz, far smaller than a musical semitone. The limen stays a roughly constant fraction of frequency through the low and middle range, then worsens above about 4–5 kHz, where the auditory nerve can no longer lock to the waveform. This pattern is the central evidence in the long contest between place and temporal theories of how the ear codes frequency. Discrimination also localises to the right auditory cortex and fails selectively in congenital amusia.

Keywords: pitch discrimination, frequency difference limen, place and temporal coding, mel scale, congenital amusia

What Pitch Discrimination Is

Pitch discrimination is the ability to detect a difference in pitch between two sounds. Pitch is the perceptual attribute by which sounds are ordered from low to high; for a pure tone it is governed almost entirely by frequency, the number of cycles of the waveform per second. Discrimination is therefore measured by presenting two tones in succession and asking the listener which is higher, then shrinking the frequency difference between them until performance falls to a criterion level.

The resulting threshold is the frequency difference limen (FDL), the smallest change in frequency Δf that a listener can reliably tell apart. It is the auditory counterpart of the just-noticeable difference studied throughout psychophysics, and like other difference thresholds it is best expressed relative to the baseline frequency: the Weber fraction Δf/f. A small Weber fraction means fine discrimination.

Two features of the FDL make it a central measurement in hearing science. First, it is extraordinarily small — near 1 kHz a practised listener resolves a change of only two or three hertz, a fraction of a percent, finer than one-twentieth of a musical semitone (Wier, Jesteadt, & Green, 1977). Second, the way the FDL changes with frequency, level, and tone duration constrains every theory of how the cochlea and auditory nerve represent a sound's frequency, which is why the measurement recurs throughout this article.

The Frequency Difference Limen

The classic map of the FDL was drawn by Wier, Jesteadt, and Green (1977), who measured it across the audible range and at several sensation levels. Their result is usually plotted as the Weber fraction against frequency: discrimination is finest — the Weber fraction smallest and roughly constant — from the low hundreds of hertz up to about 2 kHz, then deteriorates sharply at higher frequencies. Discrimination also improves with level, a tone well above threshold being easier to discriminate than a faint one.

The FDL depends on duration as well. Moore (1973) showed that the limen for very short tones is larger than for long ones and shrinks as the tone is lengthened to about 200 milliseconds, after which further duration buys little. A tone must last long enough for the auditory system to accumulate the evidence a fine frequency judgement needs — a constraint any coding theory must reproduce.

The FDL is not fixed by the ear's wiring alone; it is trainable. Micheyl, Delhommeau, Perrot, and Oxenham (2006) found that musicians discriminate far finer than untrained listeners, but that a few hours of practice bring untrained listeners most of the way to the musicians' thresholds, so much of the musician advantage is learned rather than innate. Discrimination is thus a perceptual skill shaped by experience, not only a hard limit of the cochlea.

Place and Temporal Coding of Frequency

How does the ear represent the frequency a listener is discriminating? Two mechanisms have competed since the nineteenth century, and the FDL is the evidence that adjudicates between them (Oxenham, 2012).

The place mechanism derives from the mechanics of the cochlea: each frequency peaks at a particular position along the basilar membrane, so frequency is coded by which neurons fire. On this account the FDL reflects how precisely the listener can register a shift in the location of the excitation pattern. The temporal mechanism instead uses when neurons fire: the auditory nerve phase-locks to the waveform, firing in time with its cycles, so the intervals between spikes carry the frequency directly.

The decisive datum is the breakdown of discrimination above about 4–5 kHz. Phase locking in the auditory nerve weakens across this region and is effectively gone by 5 kHz, and this is precisely where the Weber fraction worsens steeply (Sek & Moore, 1995). That the loss of fine discrimination coincides with the loss of phase locking is the strongest evidence that temporal information underlies fine frequency discrimination at low and middle frequencies, with the place mechanism taking over, more coarsely, above the phase-locking limit. Physiological measures such as the frequency-following response, whose fine structure tracks the stimulus waveform, give a direct window on this temporal code (Tichko & Skoe, 2017).

The Mel Scale and Perceived Pitch

Discrimination measures the resolution of pitch; a separate question is how the magnitude of pitch grows with frequency. Stevens, Volkmann, and Newman (1937) answered it by asking listeners to adjust tones to perceptual halves and doubles of a standard, building the mel scale of perceived pitch. By convention a 1 kHz tone at a moderate level is 1000 mels; the scale then rises roughly linearly with frequency at low frequencies but compresses at high ones, so equal steps in perceived pitch correspond to ever-larger steps in hertz as frequency climbs.

The mel scale and the FDL are distinct but related: both reflect a nonlinear mapping from frequency to perception rooted in the cochlea, and both compress the high-frequency end, where a given change in hertz is both harder to discriminate and smaller in perceived pitch. Modern work complicates the picture, showing that pitch is not a single quantity: how finely and along what dimension listeners discriminate depends sharply on the task they are given (McPherson & McDermott, 2017).

Cortical Localisation and Congenital Amusia

Pitch discrimination is not only a cochlear feat; its finest form depends on the cerebral cortex, and asymmetrically so. Lesion and imaging studies implicate the right auditory cortex specifically: Johnsrude, Penhune, and Zatorre (2000) found that patients with right-side excisions of Heschl's gyrus were impaired at judging the direction of a pitch change while their simple detection of a change was spared, and Zatorre, Belin, and Penhune (2002) related this to a general division in which the right auditory cortex has finer spectral resolution and the left finer temporal resolution.

The sharpest evidence that fine pitch discrimination is a specific faculty comes from congenital amusia, a lifelong deficit in music perception that is not explained by hearing loss, low intelligence, or lack of exposure. Amusic listeners have abnormally large pitch difference limens — Hyde and Peretz (2004) showed they fail to detect small pitch changes that control listeners hear easily, yet detect timing changes normally, so the deficit is specific to pitch and not to auditory change in general. Peretz and Hyde (2003) argued from this double dissociation that fine-grained pitch processing is a dedicated, dissociable component of cognition, and later work located the disorder in a fronto-temporal network rather than in the ear (Peretz, 2016).

Table 1

Factors That Govern the Frequency Difference Limen

Note. The frequency effect is the central datum constraining theories of frequency coding (Wier et al., 1977; Sek & Moore, 1995; Oxenham, 2012).

Worked Example

How fine is a frequency difference limen of 2 Hz at 1 kHz, expressed in the musical units that make its size vivid? The natural unit is the cent, defined so that an octave (a doubling of frequency) spans 1200 cents and a semitone spans 100. The interval in cents between a tone f and a tone f + Δf is 1200 × log₂((f + Δf)/f).

With f = 1000 Hz and Δf = 2 Hz, the ratio is 1.002, and log₂(1.002) = ln(1.002)/ln(2) = 0.0019980/0.693147 = 0.0028824. Multiplying by 1200 gives 3.46 cents. Because a semitone is 100 cents, this limen is about one twenty-ninth of a semitone (100 / 3.46 = 28.9) — a listener near 1 kHz can hear a pitch change twenty-nine times smaller than the smallest step on a piano.

The corresponding Weber fraction is Δf/f = 2/1000 = 0.002, or 0.2 percent. Now carry the same fraction up to 8 kHz, above the phase-locking limit, where measured limens give a Weber fraction closer to 0.02. There Δf = 0.02 × 8000 = 160 Hz, which in cents is 1200 × log₂(8160/8000) = 34.3 cents — a full tenfold coarsening of discrimination relative to 1 kHz. The collapse of fine discrimination once phase locking is lost is exactly what the place-versus-temporal account predicts. These numbers match the Frequency Difference Limen demonstration above.

Current Directions

Three fronts are active. The first asks what pitch is: rather than a single perceptual axis with one threshold, pitch appears to be several task-dependent representations, so that the measured limen depends on whether the listener judges direction, matches a standard, or recognises a melody (McPherson & McDermott, 2017). The second uses physiological measures of the temporal code — notably the frequency-following response, whose fine structure tracks the stimulus waveform — to test directly how phase-locked information limits discrimination across the range (Tichko & Skoe, 2017).

The third links discrimination to memory and learning. Listeners rapidly form long-term implicit memory for arbitrary sequences of pitches, recognising a once-heard random pattern weeks later, which shows that fine pitch discrimination feeds a statistical-learning system rather than a momentary sensory comparison alone (Bianco et al., 2020). Across all three, the modern synthesis treats pitch as a construction of the central auditory system, reviewed against the cochlear evidence by Oxenham (2018).

Discussion

Pitch discrimination holds a central place in hearing science because a single, easily measured quantity — the frequency difference limen — bears on questions at every level of the auditory system. Its sheer fineness, a fraction of a percent at middle frequencies, sets a demanding target that any account of cochlear and neural coding must explain. Its orderly dependence on frequency, and in particular its steep worsening once auditory-nerve phase locking fails above 4–5 kHz, is the strongest single piece of evidence that the ear codes frequency temporally where it can and by place where it cannot.

Above the cochlea, the measurement continues to pay off. Its dependence on duration and level constrains how neural evidence is integrated; its improvement with training shows discrimination to be a learned skill and not only a fixed limit; its lateralisation to the right auditory cortex and its selective failure in congenital amusia show that fine pitch discrimination is a specific faculty with its own neural substrate, separable from the perception of timing and from general intelligence. That one threshold reaches from the mechanics of the basilar membrane to a developmental disorder of music is why pitch discrimination remains a workhorse of auditory cognition.

Common Misconceptions

Pitch is the same thing as frequency.

Frequency is a physical property of the sound; pitch is the perception it evokes, and the mapping between them is nonlinear, as the mel scale shows. Equal steps in hertz are not equal steps in perceived pitch, and perceived pitch depends on level and context as well as frequency (Stevens, Volkmann, & Newman, 1937).

Discrimination is equally fine across the whole range of hearing.

The Weber fraction is small and roughly constant only up to about 2 kHz; above 4–5 kHz discrimination deteriorates sharply as auditory-nerve phase locking fails, which is why the highest notes of an instrument are hard to tune by ear (Sek & Moore, 1995).

Poor pitch discrimination just means poor hearing.

Congenital amusics have normal audiograms yet abnormally large pitch difference limens, while their discrimination of timing is intact. The deficit is a specific, central one, not a loss of audibility (Hyde & Peretz, 2004; Peretz, 2016).

Musicians are simply born with finer pitch discrimination.

Much of the musician advantage is learned: a few hours of practice bring untrained listeners most of the way to musicians' thresholds, so discrimination is a trainable perceptual skill rather than a fixed endowment (Micheyl et al., 2006).

Glossary

Basilar membrane.

The coiled membrane within the cochlea whose stiffness varies along its length, so that each place responds best to a particular frequency; the anatomical substrate of the place mechanism.

Cent.

A logarithmic unit of pitch interval in which an octave is 1200 cents and a semitone 100; used to express a difference limen in musically meaningful terms.

Congenital amusia.

A lifelong deficit in music perception, marked by abnormally large pitch difference limens, that is not explained by hearing loss, low intelligence, or lack of exposure.

Frequency difference limen (FDL).

The smallest change in frequency a listener can reliably detect; the operational measure of pitch discrimination.

Frequency-following response.

A scalp-recorded neural response that tracks the fine structure of a sound's waveform, giving a physiological window on the temporal code for frequency.

Frequency.

The number of cycles of a sound waveform per second, measured in hertz; for a pure tone it is the main physical determinant of pitch.

Mel scale.

A scale of perceived pitch magnitude built from listeners' judgements of perceptual halves and doubles, on which 1000 mels is fixed to a 1 kHz tone.

Phase locking.

The tendency of auditory-nerve fibres to fire in step with the cycles of a sound's waveform; it carries temporal frequency information and fails above about 4–5 kHz.

Pitch perception.

The perception of how low or high a sound is; the parent faculty of which pitch discrimination is the resolution, indexed by MeSH as the parent descriptor.

Place mechanism.

The coding of frequency by position along the basilar membrane, so that frequency is represented by which neurons fire; the dominant code above the phase-locking limit.

Pure tone.

A sound consisting of a single sinusoidal frequency, with no harmonics; the standard stimulus for measuring the frequency difference limen.

Semitone.

The smallest interval in the Western twelve-tone scale, a frequency ratio of about 1.059 (100 cents); a reference against which the difference limen is strikingly small.

Temporal mechanism.

The coding of frequency by the timing of neural firing relative to the waveform; the dominant code for fine discrimination at low and middle frequencies.

Weber fraction.

The difference limen divided by the baseline value, Δf/f for frequency; a dimensionless measure of relative discrimination, small when discrimination is fine.

Key Researchers

Georg von Bekesy

(1899–1972). Hungarian-American biophysicist whose travelling-wave measurements of the cochlea established the place basis of frequency analysis, work recognised by the 1961 Nobel Prize in Physiology or Medicine. See his Wikipedia biography.

Josh H. McDermott

(living). Associate professor in brain and cognitive sciences at MIT, whose Laboratory for Computational Audition showed that pitch discrimination depends sharply on the task, revealing multiple underlying representations. See the McDermott Lab.

Brian C. J. Moore

(living). Emeritus professor of auditory perception at the University of Cambridge whose measurements of the frequency difference limen anchor the modern account of temporal versus place coding. ORCID 0000-0001-7071-0671.

Andrew J. Oxenham

(living). Distinguished McKnight University Professor of Psychology at the University of Minnesota, whose reviews frame the place-versus-temporal debate and whose training studies quantify how discrimination sharpens with experience. ORCID 0000-0002-3676-8316.

Isabelle Peretz

(living). Professor of psychology at the University of Montreal and co-director of the BRAMS laboratory, whose work on congenital amusia established fine pitch discrimination as a specific, dissociable faculty. ORCID 0000-0003-3572-0262.

Christopher J. Plack

(living). Ellis Llwyd Jones Professor of Audiology at the University of Manchester and professor at Lancaster University, author of standard texts on hearing and of psychophysical and physiological studies of pitch coding. ORCID 0000-0002-2987-5332.

Stanley Smith Stevens

(1906–1973). American psychophysicist at Harvard who built the mel scale of perceived pitch magnitude and founded the modern theory of psychophysical scaling. See his Wikipedia biography.

Robert J. Zatorre

(living). Professor of neuroscience at the Montreal Neurological Institute, McGill University, whose lesion and imaging studies localised pitch-direction perception to the right auditory cortex. See the Zatorre Lab.

Frequently Asked Questions

What is pitch discrimination?

Pitch discrimination is the ability to tell two sounds apart by their pitch. It is measured as the frequency difference limen, the smallest change in frequency a listener can reliably detect, usually expressed relative to the baseline frequency as the Weber fraction.

How small a pitch difference can people hear?

Near 1 kHz a trained listener resolves a change of only two or three hertz — about a fifth of a percent, or roughly 3.5 cents, which is less than one-twentieth of a musical semitone. Discrimination is finest in the low and middle frequency range.

Why does discrimination get worse at high frequencies?

Fine discrimination relies on the auditory nerve phase-locking to the waveform, firing in step with its cycles. Phase locking weakens above about 4–5 kHz and is effectively gone by 5 kHz, and the frequency difference limen worsens steeply over the same range, which is why high notes are hard to tune by ear.

What is the difference between place and temporal coding?

The place mechanism codes frequency by position along the basilar membrane — which neurons fire. The temporal mechanism codes it by when neurons fire, using the phase-locked intervals between spikes. The evidence from the difference limen suggests temporal coding underlies fine discrimination at low frequencies and place coding takes over, more coarsely, at high ones.

Is pitch the same as frequency?

No. Frequency is the physical rate of the waveform; pitch is the perception it produces. The mel scale shows the mapping is nonlinear, so equal steps in hertz are not equal steps in perceived pitch, and perceived pitch also depends on level and context.

Can pitch discrimination be improved with practice?

Yes. Musicians discriminate much more finely than untrained listeners, but a few hours of practice bring untrained listeners most of the way to musicians' thresholds, so discrimination is largely a trainable perceptual skill rather than a fixed endowment.

What is congenital amusia?

Congenital amusia is a lifelong deficit in music perception, found in people with normal hearing, intelligence, and musical exposure. Amusics have abnormally large pitch difference limens while their discrimination of timing is intact, which shows that fine pitch discrimination is a specific, dissociable faculty.

Which part of the brain is involved in pitch discrimination?

Fine pitch discrimination, and especially judging the direction of a pitch change, depends particularly on the right auditory cortex. Damage there impairs pitch-direction judgements while sparing simpler detection, consistent with the right auditory cortex having finer spectral resolution than the left.

References

Bianco, R., Harrison, P. M. C., Hu, M., Bolger, C., Picken, S., Pearce, M. T., & Chait, M. (2020). Long-term implicit memory for sequential auditory patterns in humans. eLife, 9, e56073. https://doi.org/10.7554/eLife.56073

Hyde, K. L., & Peretz, I. (2004). Brains that are out of tune but in time. Psychological Science, 15(5), 356–360. https://doi.org/10.1111/j.0956-7976.2004.00683.x

Johnsrude, I. S., Penhune, V. B., & Zatorre, R. J. (2000). Functional specificity in the right human auditory cortex for perceiving pitch direction. Brain, 123(1), 155–163. https://doi.org/10.1093/brain/123.1.155

McPherson, M. J., & McDermott, J. H. (2017). Diversity in pitch perception revealed by task dependence. Nature Human Behaviour, 1, 0052. https://doi.org/10.1038/s41562-017-0261-8

Micheyl, C., Delhommeau, K., Perrot, X., & Oxenham, A. J. (2006). Influence of musical and psychoacoustical training on pitch discrimination. Hearing Research, 219(1–2), 36–47. https://doi.org/10.1016/j.heares.2006.05.004

Moore, B. C. J. (1973). Frequency difference limens for short-duration tones. The Journal of the Acoustical Society of America, 54(3), 610–619. https://doi.org/10.1121/1.1913640

Oxenham, A. J. (2012). Pitch perception. The Journal of Neuroscience, 32(39), 13335–13338. https://doi.org/10.1523/JNEUROSCI.3815-12.2012

Oxenham, A. J. (2018). How we hear: The perception and neural coding of sound. Annual Review of Psychology, 69, 27–50. https://doi.org/10.1146/annurev-psych-122216-011635

Peretz, I., & Hyde, K. L. (2003). What is specific to music processing? Insights from congenital amusia. Trends in Cognitive Sciences, 7(8), 362–367. https://doi.org/10.1016/S1364-6613(03)00150-5

Peretz, I. (2016). Neurobiology of congenital amusia. Trends in Cognitive Sciences, 20(11), 857–867. https://doi.org/10.1016/j.tics.2016.09.002

Sek, A., & Moore, B. C. J. (1995). Frequency discrimination as a function of frequency, measured in several ways. The Journal of the Acoustical Society of America, 97(4), 2479–2486. https://doi.org/10.1121/1.411968

Stevens, S. S., Volkmann, J., & Newman, E. B. (1937). A scale for the measurement of the psychological magnitude pitch. The Journal of the Acoustical Society of America, 8(3), 185–190. https://doi.org/10.1121/1.1915893

Tichko, P., & Skoe, E. (2017). Frequency-dependent fine structure in the frequency-following response: The byproduct of multiple generators. Hearing Research, 348, 1–15. https://doi.org/10.1016/j.heares.2017.01.014

Wier, C. C., Jesteadt, W., & Green, D. M. (1977). Frequency discrimination as a function of frequency and sensation level. The Journal of the Acoustical Society of America, 61(1), 178–184. https://doi.org/10.1121/1.381251

Zatorre, R. J., Belin, P., & Penhune, V. B. (2002). Structure and function of auditory cortex: Music and speech. Trends in Cognitive Sciences, 6(1), 37–46. https://doi.org/10.1016/S1364-6613(00)01816-7