Equal-Loudness Contour Simulator: Fletcher-Munson Curves & Phon Scale

simulator intermediate ~10 min
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60 phon = 4 sone — moderate conversation level at 1 kHz

At 1 kHz reference frequency, 60 dB SPL equals 60 phon by definition and corresponds to 4 sone — the perceived loudness of normal conversational speech at 1 meter distance.

Formula

S = 2^((L_N − 40)/10) (sone from phon)
L_N(f) = SPL + ΔL(f) (equal-loudness correction)
A(f) = 12194² × f⁴ / [(f² + 20.6²)(f² + 12194²)√((f² + 107.7²)(f² + 737.9²))]

The Ear's Uneven Frequency Response

Human hearing is far from a flat microphone. We are exquisitely sensitive around 2–5 kHz — the frequency range of speech consonants and infant cries — yet remarkably insensitive at low frequencies. A 30 Hz bass note must be 60 dB louder than a 3 kHz tone to sound equally loud. Fletcher and Munson first mapped this uneven landscape in 1933, and their curves (refined by Robinson-Dadson and ISO 226) remain foundational to audio engineering.

Phon and Sone: Perceptual Units

Because decibels do not correspond to perceived loudness, psychoacousticians use the phon (equal-loudness level) and sone (linear loudness) scales. The phon anchors to 1 kHz, while the sone scale captures the important finding that perceived loudness doubles every 10 dB — not with every doubling of sound pressure. A 70 dB conversation sounds twice as loud as 60 dB, not 1.12 times.

Loudness at Different Levels

The equal-loudness contours are not parallel — they flatten at higher SPL. At 90+ dB, the ear responds more uniformly across frequency. This is why music sounds 'fuller' at louder volumes and why audio systems include 'loudness' buttons that boost bass and treble at low volumes to compensate for the ear's reduced sensitivity at moderate levels.

Engineering Applications

Equal-loudness data drive A-weighting (the standard noise measurement filter), headphone equalization, hearing aid fitting, loudness normalization in broadcasting (EBU R128, ATSC A/85), and architectural acoustics. Understanding these curves means designing audio systems that account for human perception rather than just physical sound pressure.

FAQ

What are equal-loudness contours?

Equal-loudness contours (ISO 226:2003) are curves showing which combinations of frequency and SPL sound equally loud to the average human listener. Originally measured by Fletcher and Munson in 1933, they reveal that our hearing sensitivity varies dramatically with frequency — we are most sensitive around 2–5 kHz and least sensitive at very low and very high frequencies.

What is the phon scale?

The phon is a unit of perceived loudness. By definition, a 1 kHz tone at N dB SPL has a loudness of N phon. At other frequencies, the SPL required for the same perceived loudness differs according to the equal-loudness contours. For example, a 100 Hz tone must be about 80 dB SPL to sound as loud as a 60 dB tone at 1 kHz (both are 60 phon).

What is the sone scale?

The sone is a linear scale of perceived loudness. By definition, 1 sone = 40 phon. Doubling the sone value means doubling the perceived loudness. The conversion is S = 2^((phon − 40)/10). So 50 phon = 2 sone, 60 phon = 4 sone, 70 phon = 8 sone — perceived loudness doubles every 10 phon.

Why does A-weighting exist?

A-weighting is a frequency filter applied to sound level measurements to approximate human hearing sensitivity at moderate levels (~40 phon contour). It reduces the contribution of low and very high frequencies, correlating better with perceived loudness than unweighted (flat) measurements. It is the standard for noise regulations, workplace safety, and environmental acoustics.

Sources

Embed

<iframe src="https://homo-deus.com/lab/psychoacoustics/equal-loudness/embed" width="100%" height="400" frameborder="0"></iframe>
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