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 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contours are often referred to as "Fletcher-Munson" curves, after the earliest researchers, but those studies have been superseded and incorporated into newer standards.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 modern determinations made in various countries.

ISO equal-loudness contours with frequency in Hz.

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.

Fletcher and Munson first measured equal-loudness contours using headphones (1933). In their study, test subjects listened to pure tones at various frequencies and over 10 dB increments in stimulus intensity. For each frequency and intensity, the listener also listened to a reference tone at 1000 Hz. Fletcher and Munson adjusted the reference tone until the listener perceived that it was 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—the absolute threshold of hearing. The highest contour is the threshold of pain.

Churcher and King carried out a second determination in 1937, but their results and Fletcher and Munson's showed considerable discrepancies over parts of the auditory diagram.[1]

In 1956 Robinson and Dadson produced a new experimental determination that they believed was more accurate. It became the basis for a standard (ISO 226) that was considered definitive until 2003, when ISO revised the standard on the basis of recent assessments by research groups worldwide.

Recent revision aimed at more precise determination – ISO 226:2003

Perceived discrepancies between early and more recent determinations led the International Organization for Standardization (ISO) to revise the standard curves in ISO 226. They did this in response to recommendations in 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 not explained.[2]

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 it doesn't make clear how Robinson-Dadson achieved "compensation".

Headphones versus loudspeaker testing

Good headphones, well sealed to the ear, provide a flat low-frequency pressure response to the ear canal, with low distortion even at high intensities. At low frequencies the ear is purely pressure-sensitive, and the cavity formed between headphones and ear is too small to introduce modifying resonances. Headphone testing is therefore a good way to derive equal-loudness contours below about 500 Hz, though 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 the brain appears to mask in normal listening conditions. At high frequencies, headphone measurement gets unreliable, and the various resonances of pinnae (outer ears) and ear canals are severely affected by proximity to the headphone cavity.

With speakers, the opposite is true. A flat low-frequency response is hard to obtain—except in free space high above ground, or in a very large and anechoic chamber that is 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. 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 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. A good experimenter must ensure that trial subjects really hear the fundamental and not harmonics—especially the third harmonic, which is especially strong as a speaker cone's travel becomes limited as its suspension reaches 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 effects must be considered when comparing results of various attempts to measure equal-loudness contours.

Relevance to sound level measurement and noise measurement

The A-weighting curve—in widespread use for noise measurement—is said to have been based on the 40-phon Fletcher–Munson curve. However, research in the 1960s demonstrated that determinations of equal-loudness made using pure tones are not directly relevant to our perception of noise.[3] 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 signals to the brain add the various bands to produce the impressions 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. These gave 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 the higher frequencies.

BBC Research 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 that, 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 detector to account for our reduced sensitivity to short bursts and clicks.[4] It is widely used by Broadcasters and audio professionals when they measure noise on broadcast paths and audio equipment, so they can subjectively compare equipment types with different noise spectra and characteristics.

See also


  1. ^ 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.
  2. ^ Yôiti Suzuki, et al., "Precise and Full-range Determination of Two-dimensional Equal Loudness Contours" Archived 2007-09-27 at the Wayback Machine.
  3. ^ Bauer, B., Torick, E., "Researches in loudness measurement", IEEE Transactions on Audio and Electroacoustics, Vol. 14:3 (Sep 1966), pp.141–151.
  4. ^ 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.

External links

Fletcher–Munson curves

The Fletcher–Munson curves are one of many sets of equal-loudness contours for the human ear, determined experimentally by Harvey Fletcher and Wilden A. Munson, and reported in a 1933 paper entitled "Loudness, its definition, measurement and calculation" in the Journal of the Acoustical Society of America.

Headroom (audio signal processing)

In digital and analog audio, headroom refers to the amount by which the signal-handling capabilities of an audio system exceed a designated nominal level. Headroom can be thought of as a safety zone allowing transient audio peaks to exceed the nominal level without damaging the system or the audio signal, e.g., via clipping. Standards bodies differ in their recommendations for nominal level and headroom.

ITU-R 468 noise weighting

ITU-R 468 (originally defined in CCIR recommendation 468-4; sometimes referred to as CCIR-1k) is a standard relating to noise measurement, widely used when measuring noise in audio systems. The standard, now referred to as ITU-R BS.468-4, defines a weighting filter curve, together with a quasi-peak rectifier having special characteristics as defined by specified tone-burst tests. It is currently maintained by the International Telecommunications Union who took it over from the CCIR.

It is used especially in the UK, Europe, and former countries of the British Empire such as Australia and South Africa. It is less well known in the USA where A-weighting has always been used.M-weighting is a closely related filter, an offset version of the same curve, without the quasi-peak detector. See Present usage of 468-weighting.

Minimum audibility curve

Minimum audibility curve is a standardized graph of the threshold of hearing frequency for an average human, and is used as the reference level when measuring hearing loss with an audiometer as shown on an audiogram.

Audiograms are produced using a piece of test equipment called an audiometer, and this allows different frequencies to be presented to the subject, usually over calibrated headphones, at any specified level. The levels are, however, not absolute, but weighted with frequency relative to a standard graph known as the minimum audibility curve which is intended to represent 'normal' hearing. This is not the best threshold found for all subjects, under ideal test conditions, which is represented by around 0 phon or the threshold of hearing on the equal-loudness contours, but is standardised in an ANSI standard to a level somewhat higher at 1 kHz [1]. There are several definitions of the minimal audibility curve, defined in different international standards, and they differ significantly, giving rise to differences in audiograms according to the audiometer used. The ASA-1951 standard for example used a level of 16.5 dB SPL at 1 kHz whereas the later ANSI-1969/ISO-1963 standard uses 6.5 dB SPL, and it is common to allow a 10 dB correction for the older standard.

Noise measurement

In acoustics, noise measurement can be for the purpose of measuring environmental noise. Applications include monitoring of construction sites, aircraft noise, road traffic noise, entertainment venues and neighborhood noise.

The word "noise" means any "unwanted sound". Environmental noise monitoring is the measurement of noise in an outdoor environment caused by transport (e.g. motor vehicles, aircraft, and trains), industry (e.g. machines) and recreational activities (e.g. music). The laws and limits governing environmental noise monitoring differ from country to country.

At the very least, noise may be annoying or displeasing or may disrupt the activity or balance of human or animal life, increasing levels of aggression, hypertension and stress. In the extreme, excessive levels or periods of noise can have long-term negative health effects such as hearing loss, tinnitus, sleep disturbances, a rise in blood pressure, an increase in stress and vasoconstriction, and an increased incidence of coronary artery disease. In animals, noise can increase the risk of death by altering predator or prey detection and avoidance, interfering with reproduction and navigation, and contributing to permanent hearing loss.

Various cures are available to combat Environmental Noise; Roadway noise can be reduced by the use of noise barriers, limitation of vehicle speeds, alteration of roadway surface texture, limitation of heavy vehicles, use of traffic controls that smooth vehicle flow to reduce braking and acceleration, and tire design. Aircraft noise can be reduced by using quieter jet engines, altering flight paths and considering the time of day to benefit residents near airports. Industrial noise is addressed by redesign of industrial equipment, shock mounted assemblies and physical barriers in the workplace.

Programme level

Programme level refers to the signal level that an audio source is transmitted or recorded at, and is important in audio if listeners of Compact Discs (CDs), radio and television are to get the best experience, without excessive noise in quiet periods or distortion of loud sounds. Programme level is often measured using a peak programme meter or a VU meter.

The level of an audio signal is among the most basic of measurements, and yet widespread misunderstanding and disagreement about programme levels has become arguably the greatest single obstacle to high quality sound reproduction.

Psophometric weighting

Psophometric weighting refers to any weighting curve used in the measurement of noise. In the field of audio engineering it has a more specific meaning, referring to noise weightings used especially in measuring noise on telecommunications circuits. Key standards are ITU-T O.41 and C-message weighting as shown here.


Psychoacoustics is the scientific study of sound perception and audiology – how humans perceive various sounds. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound (including noise, speech and music). It can be further categorized as a branch of psychophysics. Psychoacoustics received its name from a field within psychology—i.e., recognition science—which deals with all kinds of human perceptions. It is an interdisciplinary field of many areas, including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.

Rumble (noise)

A rumble is a continuous deep, resonant sound, such as the sound made by heavy vehicles or thunder. In the context of audio reproduction rumble refers to a low frequency sound from the bearings inside a turntable. This is most noticeable in low quality turntables with ball bearings. Higher quality turntables use slide bearings, minimizing rumble.

Some phono pre-amplifiers implement a rumble filter, in an attempt to remove the noise. A heavier platter can also help dampen this.

Rumble measurement is carried out on turntables (for vinyl recordings) which tend to generate very low frequency noise originating from the centre bearing and from drive pulleys or belts, as well as from irregularities in the record disc itself.

It can be heard as low-frequency noise and becomes a serious problem when playing records on audio systems with a good low-frequency response. Even when not audible, rumble can cause intermodulation, modulating of the amplitude of other frequencies. The ‘unweighted’ response curve is intended for use in assessing the level of inaudible rumble with such intermodulation in mind.

Smiley face curve

A smiley face curve (also known as "mid scoop") in audio signal processing, is a target frequency response curve characterized by boosted low and high frequencies coupled with reduced midrange frequency power. This curve is often attained by users employing a graphic equalizer which shows a graphic representation of a "smile" using its frequency band faders to describe a curve that sweeps upward at the left and right sides.

Smiley face curves have had a popular appeal with some car audio enthusiasts, disc jockeys, electric bass guitar players, home stereo owners and live sound reinforcement system operators. Though the graphic equalizer was intended to tailor a system's response to match existing venue and performance conditions, the smiley face curve is often applied before the user has heard the system's frequency response.

Sound pressure

Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone. The SI unit of sound pressure is the pascal (Pa).

Super Bit Mapping

Super Bit Mapping (SBM) is a noise shaping process, developed by Sony for CD mastering.Sony claims that the Super Bit Mapping process converts a 20-bit signal from master recording into a 16-bit signal nearly without sound quality loss, using noise shaping to improve signal to noise ratio over the frequency bands most acutely perceived by human hearing.Audible quantization error is reduced by noise shaping the error according to an equal-loudness contour.This processing takes place in dedicated hardware inside the recording device. A similar process is used in Sony's DSD to PCM conversion and is called SBM Direct.


The process of weighting involves emphasizing the contribution of particular aspects of a phenomenon (or of a set of data) over others to a final outcome or result; thereby highlighting those aspects in comparison to others in the analysis. That is, rather than each variable in the data set contributing equally to the final result, some of the data is adjusted to make a greater contribution than others. This is analogous to the practice of adding (extra) weight to one side of a pair of scales in order to favour either the buyer or seller.

While weighting may be applied to a set of data, such as epidemiological data, it is more commonly applied to measurements of light, heat, sound, gamma radiation, and in fact any stimulus that is spread over a spectrum of frequencies.

Weighting filter

A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes.

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