Equal-loudness contour

An equal-loudness contour is a measure of sound pressure (dB SPL), over the frequency spectrum, for which a listener perceives a constant loudness. The unit of measurement for loudness levels is the phon, and by definition two sine waves that have equal phons are equally loud.



The human auditory system is sensitive to frequencies from 20 Hz to a maximum of around 20,000 Hz, although the hearing range decreases with age. Within this range, the human ear is most sensitive between 1 and 5 kHz, largely due to the resonance of the ear canal and the transfer function of the ossicles of the middle ear.

Equal-loudness contours were first measured by Fletcher and Munson using headphones (1933). In their study, listeners were presented with pure tones at various frequencies and over 10 dB increments in stimulus intensity. For each frequency and intensity, the listener was also presented with a reference tone at 1000 Hz. The reference tone was adjusted until it was perceived to be of the same loudness as the test tone. Loudness, being a psychological quantity, is difficult to measure, so Fletcher and Munson averaged their results over many test subjects to derive reasonable averages.

A new experimental determination was made by Robinson and Dadson (1956) which was believed to be more accurate, and this became the basis for a standard (ISO226) which was considered definitive until 2003.

Because of perceived discrepancies between early and more recent determinations, the International Organization for Standardization (ISO) recently set out to revise its standard curves as defined in ISO 226, referring to the results of several studies, by researchers in Japan, Germany, Denmark, UK, and USA. (Japan was the greatest contributor with about 40% of the data.) This has resulted in the recent acceptance of new curves standardized as ISO 226:2003. The committee responsible for this revision has commented on the surprisingly large differences, and the fact that the original Fletcher-Munson contours are in better agreement with recent results than the Robinson-Dadson, which appear to differ by as much as 10–15 dB especially in the low-frequency region, for reasons that are not explained.

Equal loudness curves derived using headphones are valid only for side-presentation. Frontal presentation, from a single central loudspeaker, can be expected to show reduced sensitivity to high frequencies, which are partially masked by the head, and presentation using two loudspeakers, as for stereo will reveal more complicated differences related the HRTF (head related transfer function) which is also dependent on elevation of the sources and plays a major role in our ability to locate sounds. The Robinson-Dadson determination used loudspeakers, and for a long time the difference from the Fletcher-Munson curves was explained on this basis. However, the ISO report actually lists the latter as using 'compensated' headphones.

Good headphones, well sealed to the ear, can provide a very flat low-frequency pressure response measured at the ear canal, and at low frequencies the ear is purely pressure sensitive and the cavity formed between headphones and ear is too small to introduce any modifying resonances. It is at high frequencies that things get dubious, and the various resonances of pinnae (outer ear) and ear canal are severely affected by proximity to the headphone cavity. With speakers, exactly the opposite is true, a flat low-frequency response being very hard to obtain except in free space high above ground or in a very large and anechoic chamber free from reflections down to 20 Hz. A flat free-field response up to 20 kHz though is comparatively easy to achieve with modern speakers on-axis. These facts have to be borne in mind when comparing results of various attempts to measure equal loudness contours.

The lowest equal loudness contour represents the quietest audible tone and is also known as the absolute threshold of hearing. The highest contour is the threshold of pain.

Although the A-weighting curve, in widespread use for noise measurement, is said to have been based on the 40-phon Fletcher-Munson curve, it should be noted that determinations of equal loudness made using pure tones are not directly relevant to our perception of noise. This is because the cochlea in our inner ear analyses sounds in terms of spectral content, each 'hair-cell' responding to a narrow band of frequencies. The high-frequency bands are wider in absolute terms than the low frequency bands, and therefore 'collect' proportionately more power from a noise source. Equal loudness curves derived using noise bands therefore show an upwards tilt above 1 kHz and a downward tilt below 1 kHz.

The 468-weighting curve, originally proposed in CCIR recommendation 468, but later adopted by numerous standards bodies (IEC,BSI,JIS) was based on BBC Research using a variety of noise sources ranging from clicks to tone bursts to pink noise, and incorporates a special Quasi-peak rectifier to account for our reduced sensitivity to short bursts and clicks. It is widely used by Broadcasters and is by far the preferred weighting to use for all forms of noise measurement, enabling subjectively valid comparisons of different equipment types to be made even though they have different noise spectra and characteristics.