An equal-loudness contour is a measure of sound pressure (dB SPL), over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones. The unit of measurement for loudness levels is the phon, and is arrived at by reference to equal-loudness contours. By definition two sine waves, of differing frequencies, are said to have equal-loudness level measured in phons if they are perceived as equally loud by the average young person without significant hearing impairment.
Equal-loudness contours are often referred to as "Fletcher-Munson"' curves, after the earliest researchers, but those studies have been superseded and incorporated into newer standards. The definitive curves are those defined in the international standard ISO 226:2003 which are based on a review of several modern determinations made in various countries.
Experimental determination 
The human auditory system is sensitive to frequencies from about 20 Hz to a maximum of around 20,000 Hz, although the upper hearing limit decreases with age. Within this range, the human ear is most sensitive between 2 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. 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.
A second determination was carried out by Churcher and King in 1937, but these two investigations showed considerable discrepancies over parts of the auditory diagram.
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 (ISO 226) which was considered definitive until 2003, when the standard was revised on the basis of recent assessments by research groups worldwide.
Recent revision aimed at more precise determination - ISO 226:2003 
Because of perceived discrepancies between early and more recent determinations, the International Organization for Standardization (ISO) recently revised its standard curves as defined in ISO 226, in response to the recommendations of a study coordinated by the Research Institute of Electrical Communication, Tohoku University, Japan. The study produced new curves by combining 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 a new set of curves standardized as ISO 226:2003. The report comments 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.
Side versus frontal presentation 
Equal-loudness curves derived using headphones are valid only for the special case of what is called 'side-presentation', which is not how we normally hear. Real-life sounds arrive as planar wavefronts, if from a reasonably distant source. If the source of sound is directly in front of the listener, then both ears receive equal intensity, but at frequencies above about 1 kHz the sound that enters the ear canal is partially reduced by the masking effect of the head, and also highly dependent on reflection off the pinna (outer ear). Off-centre sounds result in increased head masking at one ear, and subtle changes in the effect of the pinna, especially at the other ear. This combined effect of head-masking and pinna reflection is quantified in a set of curves in three-dimensional space referred to as head-related transfer functions (HRTFs). Frontal presentation is now regarded as preferable when deriving equal-loudness contours, and the latest ISO standard is specifically based on frontal and central presentation.
The Robinson-Dadson determination used loudspeakers, and for a long time the difference from the Fletcher-Munson curves was explained partly on the basis that the latter used headphones. However, the ISO report actually lists the latter as using "compensated" headphones, though how this was achieved is not made clear.
Headphones versus loudspeaker testing 
Good headphones, well sealed to the ear, can provide a very flat low-frequency pressure response measured at the ear canal, with low distortion even at high intensities, 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. Headphone testing is therefore a good way to derive equal-loudness contours below about 500 Hz, although reservations have been expressed about the validity of headphone measurements when determining the actual threshold of hearing, based on observation that closing off the ear canal produces increased sensitivity to the sound of blood flow within the ear which appears to be masked by the brain in normal listening conditions. It is at high frequencies that headphone measurement gets unreliable, 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. Until recently it was not possible to achieve high levels at frequencies down to 20 Hz without high levels of harmonic distortion, and even today the best speakers are likely to generate around 1 to 3% of total harmonic distortion, corresponding to 30 to 40 dB below fundamental. This is not really good enough, given the steep rise in loudness (rising to as much as 24 dB per octave) with frequency revealed by the equal-loudness curves below about 100 Hz, and a good experimenter must ensure that trial subjects really are hearing the fundamental and not harmonics, especially the third harmonic which will be especially pronounced as speaker cones become limited in travel as their suspensions reach the limit of compliance. A possible way around the problem is to use acoustic filtering, such as by resonant cavity, in the speaker setup.
A flat free-field high-frequency response up to 20 kHz, on the other hand, 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.
Relevance to sound level measurement and noise measurement 
Although the A-weighting curve, in widespread use for noise measurement, is said to have been based on the 40-phon Fletcher–Munson curve, research in the 1960s demonstrated 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 analyzes sounds in terms of spectral content, each "hair-cell" responding to a narrow band of frequencies known as a critical band. The high-frequency bands are wider in absolute terms than the low frequency bands, and therefore "collect" proportionately more power from a noise source. However, when more than one critical band is stimulated, the outputs of the various bands are summed by the brain to produce an impression of loudness. For these reasons Equal-loudness curves derived using noise bands show an upwards tilt above 1 kHz and a downward tilt below 1 kHz when compared to the curves derived using pure tones.
Various weighting curves were derived in the 1960s, in particular as part of the DIN 4550 standard for audio quality measurement, which differed from the A-weighting curve, showing more of a peak around 6 kHz, and these were found to give a more meaningful subjective measure of noise on audio equipment; especially on the newly invented compact cassette tape recorders with Dolby noise reduction which were characterised by a noise spectrum dominated by high frequencies.
BBC Research has conducted listening trials in an attempt to find the best weighting curve and rectifier combination for use when measuring noise in broadcast equipment, examining the various new weighting curves in the context of noise rather than tones, confirming that they were much more valid than A-weighting when attempting to measure the subjective loudness of noise. This work also investigated the response of human hearing to tone-bursts, clicks, pink noise and a variety of other sounds which, because of their brief impulsive nature, do not give the ear and brain sufficient time to respond. The results were reported in BBC Research Report EL-17 1968/8 entitled The Assessment of Noise in Audio Frequency Circuits.
The ITU-R 468 noise weighting curve, originally proposed in CCIR recommendation 468, but later adopted by numerous standards bodies (IEC, BSI, JIS, ITU) was based on the research, 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 audio professionals when measuring noise on broadcast paths and audio equipment, enabling subjectively valid comparisons of different equipment types to be made even though they have different noise spectra and characteristics.
See also 
- D W Robinson et al., "A re-determination of the equal-loudness relations for pure tones", Br. J. Appl. Phys. 7 (1956), pp.166–181.
- Yôiti Suzuki, et al., "Precise and Full-range Determination of Two-dimensional Equal Loudness Contours".
- Bauer, B., Torick, E., "Researches in loudness measurement", IEEE Transactions on Audio and Electroacoustics, Vol. 14:3 (Sep 1966), pp.141–151.
- Ken’ichiro Masaoka, Kazuho Ono, and Setsu Komiyama, "A measurement of equal-loudness level contours for tone burst", Acoustical Science and Technology, Vol. 22 (2001) , No. 1 pp.35–39.
- Audio Engineer's Reference Book, 2nd Ed., 1999, edited Michael Talbot Smith, Focal Press.
- An Introduction to the Psychology of Hearing 5th ed, Brian C.J. Moore, Elsevier Press.
- ISO Standard
- Precise and Full-range Determination of Two-dimensional Equal Loudness Contours
- Fletcher-Munson is not Robinson-Dadson (PDF)
- Full Revision of International Standards for Equal-Loudness Level Contours (ISO 226)
- Test your hearing - A tool for measuring your equal-loudness contours
- Equal-loudness contour measurements in detail
- Evaluation of Loudness-level weightings and LLSEL JASA
- A Model of Loudness Applicable to Time-Varying Sounds AESJ Article