Equal-loudness contour
An equal-loudness contour is a measure of sound pressure level, over the frequency spectrum, for which a listener perceives a constant loudness when presented with pure steady tones.[1] 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 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measurement and calculation" in the Journal of the Acoustical Society of America.[2] Fletcher–Munson curves have been superseded and incorporated into newer standards.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.
Amplifiers often feature a "loudness" button, known technically as loudness compensation, 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.
Experimental determination[edit]
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 had 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.[5]
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.
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.[6]
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 standard was based turns out to have been in agreement with modern determinations.[4]
The report also comments on the large differences apparent in the low-frequency region, which remain unexplained. Possible explanations are:[4]
Relevance to sound level and noise measurements[edit]
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.[7] 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 characterized 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.[8] 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.