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An equal-loudness contour is a measure of
sound pressure level 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 ...
, 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. The Fletcher–Munson curves are one of many sets of equal-loudness contours for the human ear, determined experimentally by
Harvey Fletcher Harvey Fletcher (September 11, 1884 – July 23, 1981) was an American physicist. Known as the "father of stereophonic sound", he is credited with the invention of the 2-A audiometer and an early electronic hearing aid. He was an investigator in ...
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''. Fletcher–Munson curves have been superseded and incorporated into newer standards. The definitive curves are those defined in ISO 226 from the International Organization for Standardization, which are based on a review of modern determinations made in various countries.
Amplifier An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
s often feature a "loudness" button, known technically as
loudness compensation Loudness compensation, or simply loudness, is a setting found on some hi-fi equipment that increases the level of the high and low frequencies. This is intended to be used while listening at low-volume levels, to compensate for the fact that as t ...
, that boosts low and high-frequency components of the sound. These are intended to offset the apparent loudness fall-off at those frequencies, especially at lower volume levels. Boosting these frequencies produces a flatter equal-loudness contour that appears to be louder even at low volume, preventing the perceived sound from being dominated by the mid-frequencies where the ear is most sensitive.


Fletcher–Munson curves

The first research on the topic of how the ear hears different frequencies at different levels was conducted by Fletcher and Munson in 1933. Until recently, it was common to see the term ''Fletcher–Munson'' used to refer to equal-loudness contours generally, even though a re-determination was carried out by Robinson and Dadson in 1956, which became the basis for an ISO 226 standard. It is now better to use the generic term ''equal-loudness contours'', of which the Fletcher–Munson curves are now a sub-set, and especially since a 2003 survey by ISO redefined the curves in a new standard.


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 The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...
, largely due to the resonance of the ear canal and the transfer function of the
ossicles The ossicles (also called auditory ossicles) are three bones in either middle ear that are among the smallest bones in the human body. They serve to transmit sounds from the air to the fluid-filled labyrinth ( cochlea). The absence of the audit ...
of the middle ear. Fletcher and Munson first measured equal-loudness contours using
headphones Headphones are a pair of small Electrodynamic speaker driver, loudspeaker drivers worn on or around the head over a user's ears. They are electroacoustics (acoustical engineering), electroacoustic transducers, which convert an electrical signa ...
(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 absolute threshold of hearing (ATH) is the minimum sound level of a pure tone that an average human ear with normal hearing can hear with no other sound present. The absolute threshold relates to the sound that can just be heard by the organis ...
''. 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. 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 the US. (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. According to the ISO report, the Robinson–Dadson results were the odd one out, differing more from the current standard than did the Fletcher–Munson curves. The report states that it is fortunate that the 40- phon Fletcher–Munson curve on which the
A-weighting A-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured ...
standard was based turns out to have been in agreement with modern determinations. The report also comments on the large differences apparent in the low-frequency region, which remain unexplained. Possible explanations are: * The equipment used was not properly calibrated. * The criteria used for judging equal loudness at different frequencies had differed. * Subjects were not properly rested for days in advance, or were exposed to loud noise in traveling to the tests which tensed the tensor tympani and stapedius muscles controlling low-frequency mechanical coupling.


Side versus frontal presentation

Real-life sounds from a reasonably distant source arrive as planar wavefronts. 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 head shadow, 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. Because no HRTF is involved in normal headphone listening, equal-loudness curves derived using
headphones Headphones are a pair of small Electrodynamic speaker driver, loudspeaker drivers worn on or around the head over a user's ears. They are electroacoustics (acoustical engineering), electroacoustic transducers, which convert an electrical signa ...
are valid only for the special case of what is called ''side-presentation'', which is not how we normally hear. 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 the 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 becomes 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 An anechoic chamber (''an-echoic'' meaning "non-reflective") is a room designed to stop reflections of either sound or electromagnetic waves. They are also often isolated from energy entering from their surroundings. This combination means t ...
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 In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
. 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 and noise measurements

The
A-weighting A-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured ...
curve—in widespread use for
noise measurement In acoustics, noise measurement can be for the purpose of measuring environmental noise or measuring noise in the workplace. Applications include monitoring of construction sites, aircraft noise, road traffic noise, entertainment venues and neighb ...
—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. 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 In audiology and psychoacoustics the concept of critical bands, introduced by Harvey Fletcher in 1933 and refined in 1940, describes the frequency bandwidth of the "auditory filter" created by the cochlea, the sense organ of hearing within the inne ...
. 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 DIN or Din or din may refer to: People and language * Din (name), people with the name * Dīn, an Arabic word with three general senses: judgment, custom, and religion from which the name originates * Dinka language (ISO 639 code: din), spoken by ...
4550 standard for
audio quality measurement Audio system measurements are a means of quantifying system performance. These measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment. Maintenance engineers make ...
, 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 The Compact Cassette or Musicassette (MC), also commonly called the tape cassette, cassette tape, audio cassette, or simply tape or cassette, is an analog magnetic tape recording format for audio recording and playback. Invented by Lou Otten ...
tape recorders with Dolby noise reduction, which were characterized by a noise spectrum dominated by the higher frequencies.
BBC Research BBC Research & Development is the technical research department of the BBC. Function It has responsibility for researching and developing advanced and emerging media technologies for the benefit of the corporation, and wider UK and European m ...
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 The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
, BSI, JIS,
ITU The International Telecommunication Union is a specialized agency of the United Nations responsible for many matters related to information and communication technologies. It was established on 17 May 1865 as the International Telegraph Union ...
) was based on the research, and incorporates a special Quasi-peak detector to account for our reduced sensitivity to short bursts and clicks.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.
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

*
A-weighting A-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured ...
*
Audio quality measurement Audio system measurements are a means of quantifying system performance. These measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment. Maintenance engineers make ...
*
Audiogram An audiogram is a graph that shows the audible threshold for standardized frequencies as measured by an audiometer. The Y axis represents intensity measured in decibels and the X axis represents frequency measured in hertz. The threshold of hear ...
* CCIR (ITU) 468 Noise Weighting *
dB(A) A-weighting is the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. A-weighting is applied to instrument-measured s ...
* ITU-R 468 noise weighting *
Listener fatigue Listener fatigue (also known as listening fatigue or ear fatigue) is a phenomenon that occurs after prolonged exposure to an auditory stimulus. Symptoms include tiredness, discomfort, pain, and loss of sensitivity. Listener fatigue is not a clini ...
* Luminosity function, the same concept in vision * Mel scale * Pure tone audiometry *
Robinson–Dadson curves The Robinson–Dadson curves are one of many sets of equal-loudness contours for the human ear, determined experimentally by D. W. Robinson and R. S. Dadson. Until recently, it was common to see the term 'Fletcher–Munson curves, Fletcher–Muns ...
* Sound level meter *
Weighting filter A weighting filter is used to emphasize or suppress some aspects of a phenomenon compared to others, for measurement or other purposes. Audio applications In each field of audio measurement, special units are used to indicate a weighted measure ...


Notes


References

* ''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


ISO Standard

Precise and Full-range Determination of Two-dimensional Equal Loudness Contours

Fletcher–Munson is not Robinson–Dadson (PDF)


* ttp://www.phys.unsw.edu.au/~jw/hearing.html 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
{{Acoustics Psychoacoustics Audio engineering ISO standards Sound Acoustics