Equal loudness contours — how hearing shapes what we measure

The Fletcher-Munson curves

In 1933, Harvey Fletcher and Wilden Munson published measurements of the sound pressure levels required at different frequencies to produce equal perceived loudness. Subjects were presented with a reference tone at 1 kHz and a comparison tone at various frequencies; the level of the comparison tone was adjusted until it matched the loudness of the reference. The resulting curves — contours of equal perceived loudness across the frequency range — became known as the Fletcher-Munson curves.

These curves were revised by Robinson and Dadson in 1956 and again in ISO 226:2003, which remains the current standard. The ISO 226 contours differ from the original Fletcher-Munson data, particularly at low frequencies, and should be used in preference to the older measurements.

The phon scale

The unit of loudness level is the phon. By definition, a sound at any frequency has a loudness level of N phons if it sounds equally loud as a 1 kHz pure tone at N dB SPL. The equal loudness contours are therefore lines of constant phon level.

At 1 kHz, phons and dB SPL are equivalent by definition. At other frequencies, the two diverge: at 50 Hz, the 60-phon contour occurs at approximately 75 dB SPL — meaning a 50 Hz tone must be 15 dB louder in sound pressure to be perceived as equally loud as a 1 kHz tone at 60 dB SPL.

Key features of the equal loudness contours

Low-frequency sensitivity drops sharply at low SPL. At moderate listening levels (60–70 phons), the ear requires roughly 10–15 dB more SPL at 50 Hz than at 1 kHz to perceive equal loudness. At low listening levels (20–30 phons), this deficit increases to 30 dB or more. Bass content that is clearly audible at high levels may be almost inaudible at low levels.

The ear is most sensitive around 3–4 kHz. The equal loudness contours dip in this region, meaning less SPL is required here to achieve a given loudness level. This corresponds to the resonance of the outer ear canal (approximately 3.4 kHz for a typical adult ear canal length of 25 mm). A flat loudspeaker frequency response does not produce a flat perceived response.

At high SPL, the contours flatten. At 100 phons, the difference in SPL required between 50 Hz and 1 kHz is much smaller than at 40 phons. This means that as listening level increases, bass and treble become perceptually louder relative to the midrange.

A-weighting

A-weighting is an electrical filter applied to measurements to approximate the frequency-dependent sensitivity of the ear at moderate listening levels (roughly 40 phons). The A-weighting curve broadly mirrors the inverse of the 40-phon equal loudness contour.

A-weighted SPL (dBA) is widely used in noise measurement, occupational health standards, and product specifications because it correlates better with perceived loudness than unweighted SPL for broadband noise at typical listening levels. It significantly attenuates low frequencies — at 50 Hz, attenuation is approximately 30 dB relative to 1 kHz — and applies a modest attenuation above 6 kHz.

A-weighting is appropriate for general broadband noise assessments at low to moderate levels. It is less suitable for:

• High-level noise where the 100-phon contours (the basis for C-weighting) are more appropriate
• Low-frequency noise assessment, where A-weighting's aggressive attenuation can seriously understate audibility
• Loudspeaker frequency response evaluation, where the goal is to measure what the loudspeaker does, not what the ear does with it

Practical implications

Mixing level consistency. If music is mixed at high SPL, bass and treble will be perceived as louder relative to the midrange than they will sound during quieter playback. This is a common cause of mixes that sound bass-heavy or harsh at low volumes. Professional mixing practice typically involves working at a consistent, moderate SPL (often 83 dB SPL per channel for film work, somewhat lower for music) and checking at multiple levels.

Loudspeaker measurement. Acoustic measurement of a loudspeaker captures the SPL frequency response — not the perceived response. A loudspeaker with a flat anechoic response does not sound flat in a room; the combination of the loudspeaker's power response, the room's directional reflections, and the ear's frequency-dependent sensitivity all contribute to the perceived sound. Understanding equal loudness contours helps explain why measurements and listening impressions sometimes diverge.

Subwoofer integration. The steep rise in required SPL at low frequencies means that subwoofers must produce substantially higher sound pressure levels than main loudspeakers to sound balanced, particularly at low listening levels. Level matching a subwoofer at high SPL and then listening quietly typically results in a perceived lack of bass.

Hearing damage assessment. A-weighted SPL measurements underestimate the energy content of low-frequency noise sources. High-level low-frequency noise — industrial machinery, for example — may cause hearing damage despite appearing relatively benign in dBA terms. Unweighted or C-weighted measurements are more appropriate for such assessments.

The sone scale

The phon scale measures loudness level (in dB-equivalent units). The sone scale measures perceived loudness as a linear quantity. One sone is defined as the loudness of a 1 kHz tone at 40 dB SPL. Doubling the number of sones corresponds to a doubling of perceived loudness — an increase of approximately 10 phons (10 dB at 1 kHz).

The sone scale is used in product noise specifications (fan noise, appliance noise) where communicating perceived loudness differences in terms a non-specialist can interpret is more important than the logarithmic precision the phon provides.

End of acoustics foundational article drafts.