The equal-loudness contour is the measurement of sound pressure over a range of frequencies in the spectrum where each is perceived at the same volume as the next.
‘Phon’ is the measurement for these loudness levels in reference to these equal-loudness contours. A pair of sine waves with different frequencies, by definition, have an equal level of phons if both are perceived at the same level by the average listener, assuming that the person is not hearing impaired.
Another name often given to the equal-loudness contour is the Fletcher-Munson Curve. A modern review of a variety of determinations on definitive curves, otherwise known as ISO 226:2003, has shown that this alternative name is actually incorrect.
20Hz to 20,000Hz is the range in which the human auditory system can pick up frequencies. As we get older, the top part of this range will decrease. In terms of sensitivity, humans can hear best within the 1kHz to 5kHz range. We can give credit to the transfer function of the middle ear’s ossicles, as well as the resonance of the ear canal, for this bump in our frequency pickup ability.
Fletcher and Munson were the first to measure equal-loudness contours back in 1933 with a pair of headphones. They gave listeners a variety of different tones using varying frequencies with over 10 dB increments in stimulus intensity. The tones were played back to back with 1kHz reference tones, which were each adjusted in level until the listener felt that the intensity or loudness was perceived to be the same as the test tone. Of course, because the idea of loudness is purely psychological, Fletcher and Munson found it difficult to measure. To measure most accurately, they created a graph with reasonable averages. The highest contour was the pain threshold, while the lowest contour represented the quietest audible tone.
Another determination was given in 1937 by Churcher and King, though there were plenty of discrepancies with the diagram Fletcher and Munson had made.
Finally, Robinson and Dadson made a brand new experimental determination in 1956. This became the basis for ISO 226 because it was believed to be the most accurate. It wasn’t until 2003 that a series of worldwide research assessments made new discoveries that called for a revision of their determination.
A More Precise Measurement
The ISO (International Organization for Standardization) recently revised the standard curves that we knew in ISO 2006 due to the perceived discrepancies that were found between recent and early determinations. The study was coordinated by a group from Tohoku University in Japan known as the Research Institute of Electrical Communication. By combining a variety of studies from countries such as the United States, Germany, Denmark, and the UK, as well as a majority of data from Japan, the institute was able to produce new curves.
This was the reason why we came to accept ISO 226:2003 as we now know it. The report was able to show that the Fletcher-Munson Curves from the first study were in fact a lot closer to the data collected than the recent Robinson-Dadson study. The Robinson-Dadson study had 10-15dB discrepancies in the lower frequency ranges, but we do not know why.
Front Presentation vs. Side Presentation
Using headphones to find equal-loudness curves is only valid if we consider the fact that it uses side presentation. Of course, as we know, we don’t actually hear the world with side presentation. Sounds in the real world arrive from a reasonably distant source as planar wavefronts. Both ears will perceive a sound at equal intensity if that sound comes from directly in front of the listener. However, the masking effect of the head will partially reduce frequencies at 1kHz or above from coming into the ear canal.
This is also dependent on the reflection on the outer ear, otherwise known as the pinna. Sounds that are off-center can cause subtle changes in the reflection on the pinna, which can change the perception at the other ear. We use head-related transfer functions (HRTFs) to quantify the set of curves with the combined effects of pinna reflection and head-masking when in a three-dimensional space. When deriving equal-loudness contours, we now prefer to use frontal presentation. In fact, the most recent ISO standard is based on audio presentation from the front and center.
The differences between the Fletcher-Munson study and Robinson-Dadson study were attributed to the fact that the Robinson-Dadson study used loudspeakers. However, we now understand that the Robinson-Dadson study used compensated headphones thanks to the ISO report, but exactly how they did this was not clarified.
Headphones vs. Loudspeakers
Well-sealed, high-quality headphones have the ability to provide even, low-frequency pressure when placed atop the ear canals. This is even the case when there is little distortion at very high frequencies. With low frequencies, the ear is most sensitive to pressure, and because the ear canal is so small, we don’t have to worry about resonances being created. If we’re looking to test equal loudness contours that fall below 500Hz, headphones are a great tool. With that said, many have questioned the ability to determine the hearing threshold with headphone measurements.
This is because we experience increased sensitivity to the blood flow within our ears when we close the canals off. The sound of this blood flow is typically canceled out during regular listening thanks to the cleverness of the brain. High-frequencies, however, are a different story. This is because we now need to account for the proximity between the headphone cavity and ear canal.
The opposite is true with speakers. It is extremely difficult for us to obtain a low-frequency response that is flat unless we are in a large anechoic chamber that is free from 20Hz and above reflections or a space that is very high above the ground. Achieving high levels of distortion-free frequencies down to 20Hz was not something we could do until very recently. Look at the top-of-the-line speakers these days and you’ll see that most of them have 1-3% of harmonic distortion. This distortion corresponds to about 40dB below the fundamental.
With the steep rise in loudness, which can be anywhere from 6-10dB per octave, this isn’t the best method for measuring equal loudness curves < 50Hz. To properly produce the experiment, administrators must make sure that their subjects are picking up the fundamentals rather than the harmonics. The speaker cone will typically produce the third harmonic in a pronounced fashion when it reaches its compliance limits. One way to avoid this is to use a resonant cavity or some other form of acoustic filtering that sits alongside the loudspeaker setup.
On the other hand, high-quality speakers that are on-axis are wonderful for creating a flat, free-field frequency response up to 20kHz. It is very important that all of these facts are taken into consideration when comparing the results from multiple tests dealing with equal-loudness contours.
Noise Measurement and Sound Level Measurement Relevance
The 40-phon Fletcher-Munson Curve is said to have been the basis for the A-weighting curve, which many use in noise measurement today. However, it was found through a series of studies in the 1960s that our perception of noise to equal-loudness made by pure tones is quite off. This has to do with our inner ear cochlea, which uses spectral content to analyze sound. A narrow band of frequencies, called the critical band, causes our hair cells to respond.
When we compare the high-frequency bands to the low-frequency bands, we find that the high-frequency bands are, in absolute terms, wider. This means that the high-frequency bands proportionately pick up more power from a noise source. With that said, the stimulation of multiple bands are summed up by the brain, which increases our loudness perception. When we look at equal-loudness curves using noise bands above 1kHz, we see an upward tilt, while a downward tilt is seen for frequencies below 1kHz. This is much different when comparing pure tones.
In the 1960s, researchers developed a variety of weighting curves. One that was derived from the A-weighting curve was known as the German DIN 4550 audio quality measurement standard. This provides us with a subjective measurement of noise audio that is a bit more meaningful. It showed a peak around 6kHz.
In order to find the best combination of rectifiers and weighting curves for noise measurement in the broadcast realm, the BBC research department conducted a variety of listening trials. Instead of examining the weighting curves in the context of tones, they examined them in the context of noise. They used an array of different sounds, including clicks, pops, tone-bursts, pink noise, and more. They didn’t give the brain very much time to respond due to the fact that they were impulsive in nature. The BBC’s Report EL-17 1968/8 gave the results, and the study was titled the Assessment of Noise in Audio Frequency Circuits.
BBC research was the basis for the ITU-R 468 noise weighting curve, even though the CCIR Recommendation 468 originally proposed the idea. A number of standard bodies, including the IEC, JIS, BSI, and ITU, would eventually adopt this curve. This standard incorporates and accounts for the fact that we have a reduced sensitivity when it comes to these short noises. Nowadays, audio professionals and broadcasters use this standard when making noise measurements for audio equipment and broadcast paths. This allows us to take different types of equipment and make subjectively valid comparisons, even if the characteristics and spectra of noise varies.
- ISO Standard
- 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
- A Model of Loudness Applicable to Time-Varying Sounds AESJ Article
- Researches in loudness measurement by CBS using noise bands, 1966 IEEE Article