Equal-loudness contour - AbsoluteAstronomy.com

An equal-loudness contour is a measure of sound pressure (dB

Decibel

The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

SPL), over the frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of 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

Phon

The phon was proposed in DIN 45631 and ISO 532 B as a unit of perceived loudness level LN for pure tones by S. S. Stevens.-Definition:The purpose of the phon scale is to compensate for the effect of frequency on the perceived loudness of tones...

, 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 appear equally loud to 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are often referred to as "Fletcher-Munson"' curves, after the earliest researchers, but those studies have been superseded and incorporated into newer standards.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

Human

Humans are the only living species in the Homo genus...

auditory system is sensitive to frequencies from about 20 Hz

Hertz

The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

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

Ear canal

The ear canal , is a tube running from the outer ear to the middle ear. The human ear canal extends from the pinna to the eardrum and is about 35 mm in length and 5 to 10 mm in diameter....

and the transfer function

Transfer function

A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

of the ossicles

Ossicles

The ossicles are the three smallest bones in the human body. They are contained within the middle ear space and serve to transmit sounds from the air to the fluid-filled labyrinth . The absence of the auditory ossicles would constitute a moderate-to-severe hearing loss...

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

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...

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

Absolute threshold of hearing

The absolute threshold of hearing is the minimum sound level of a pure tone that an average 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 organism...

. The highest contour is the threshold of pain

Threshold of pain

The threshold of pain is the point at which pain begins to be felt. It is an entirely subjective phenomenon. The intensity at which a stimulus begins to evoke pain is the threshold intensity. So, if a hotplate on a person's skin begins to hurt at 42°C , then that is the pain threshold temperature...

.

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

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, and reported in a paper entitled "A re-determination of the equal-loudness relations for pure tones" in Br. J. Appl. Phys...

(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

International Organization for Standardization

The International Organization for Standardization , widely known as ISO, is an international standard-setting body composed of representatives from various national standards organizations. Founded on February 23, 1947, the organization promulgates worldwide proprietary, industrial and commercial...

(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 function

Head-related transfer function

A head-related transfer function is a response that characterizes how an ear receives a sound from a point in space; a pair of HRTFs for two ears can be used to synthesize a binaural sound that seems to come from a particular point in space. Some consumer home entertainment products designed to...

s (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

Headphones

Headphones are a pair of small loudspeakers, or less commonly a single speaker, held close to a user's ears and connected to a signal source such as an audio amplifier, radio, CD player or portable Media Player. They are also known as stereophones, headsets or, colloquially, cans. The in-ear...

, 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

Anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or electromagnetic waves.They are also insulated from exterior sources of noise...

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

Total harmonic distortion

The total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency...

, 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

A-weighting

A Weighting curve is a graph of a set of factors, that are used to 'weight' measured values of a variable according to their importance in relation to some outcome. The most commonly known example is frequency weighting in sound level measurement where a specific set of weighting curves known as A,...

curve, in widespread use for noise

Noise

In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...

measurement

Noise measurement

Noise measurement is carried out in various fields.In acoustics, it can be for the purpose of measuring environmental noise, or part of a test procedure using white noise, or some other specialised form of test signal....

, 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

Din

DIN or Din or din can have several meanings:* A din is a loud noise.* Dīn, an Arabic term meaning "religion" or "way of life".* Din is one of the ten aspects of the Ein Sof in Kabbalah ....

4550 standard for audio quality measurement

Audio quality measurement

Audio quality measurement seeks to quantify the various forms of corruption present in an audio system or device. The results of such measurement are used to maintain standards in broadcasting, to compile specifications, and to compare pieces of equipment....

, 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

Compact Cassette

The Compact Cassette, often referred to as audio cassette, cassette tape, cassette, or simply tape, is a magnetic tape sound recording format. It was designed originally for dictation, but improvements in fidelity led the Compact Cassette to supplant the Stereo 8-track cartridge and reel-to-reel...

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

Pink noise

Pink noise or 1/ƒ noise is a signal or process with a frequency spectrum such that the power spectral density is inversely proportional to the frequency. In pink noise, each octave carries an equal amount of noise power...

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

ITU-R 468 noise weighting

ITU-R 468 is a standard relating to noise measurement, widely used when measuring noise in audio systems. The standard defines a weighting filter curve, together with a quasi-peak rectifier having special characteristics as defined by specified tone-burst tests...

curve, originally proposed in CCIR

CCIR

CCIR is a four-letter abbreviation that may stand for:*Campaign for Comprehensive Immigration Reform, a Washington, DC organization for immigrant rights...

recommendation 468, but later adopted by numerous standards bodies (IEC

International Electrotechnical Commission

The International Electrotechnical Commission is a non-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology"...

, BSI

BSI

BSI is a three letter acronym that can stand for:* Backside illumination, a type of digital image sensor* The Baker Street Irregulars, a fictional group featured in Sherlock Holmes stories* Banca della Svizzera Italiana* Bentley Systems Inc....

, JIS

JIS

JIS is a three letter acronym that can stand for:*Japanese Industrial Standards**JIS encoding**Shift JIS**Horsepower*Jakarta International School*Jeddah International School*Jerudong International School*Jabriya Indian School*Just in Sequence...

, ITU

Itu

Itu is an old and historic municipality in the state of São Paulo in Brazil. The population in 2009 was 157,384 and the area is 641.68 km². The elevation is 583 m. This place name comes from the Tupi language, meaning big waterfall. Itu is linked with the highway numbered the SP-75 and are flowed...

) 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.

External links

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