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Square One: Can You Hear Me Now?

June 1, 2009
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FIG. 1: The Fletcher-Munson Curves, or equal loudness contours, show the degree to which our ears are nonlinear with regard to frequency. They favor upper-mid frequencies and struggle with quiet lows and highs.

FIG. 1: The Fletcher-Munson Curves, or equal loudness contours, show the degree to which our ears are nonlinear with regard to frequency. They favor upper-mid frequencies and struggle with quiet lows and highs.
Illustration: Chuck Dahmer

The human auditory system is a fascinating and complex affair. As sound reaches you, it is in various parts deflected, absorbed, and otherwise filtered by your shoulders and head. It is then collected by your pinnae (the external part of your ears), whose dimensions and geometry further affect the sound on its way to the inner ear. There, vibration is translated into neural signals, which are interpreted by your psyche. In the 1930s, two scientists at Bell Labs tried to objectively measure the linearity of this elaborate affair, and what they discovered has profoundly affected everything from the design and measurement of audio gear to the development of audio data-reduction codecs.

Dangerous Curves

Harvey Fletcher and Wilden Munson discovered that our hearing is decidedly nonlinear with respect to frequency and perceived loudness, and they mapped this data at various levels to produce what have come to be known as the Fletcher-Munson Curves, or more generally the equal loudness contours (see Fig. 1).

The two researchers asked subjects to compare the loudness of sine waves at different frequencies, identifying those that they felt were comparable in loudness to a 1 kHz sine wave at a fixed reference level. In general, tones at the high and low ends of the audible spectrum had to be significantly more powerful than the reference tone to be perceived as the same loudness. For example, to be “as loud as” a 40 dB SPL 1 kHz tone, a 10 kHz tone needs to be about 50 dB SPL, and a 100 Hz tone must be more than 60 dB SPL. The curve actually dips between 1 kHz and 5 kHz, with its nadir between 3 kHz and 4 kHz, depending on the reference level.

At lower SPLs, the variation is greater, while at higher levels, the variations are less significant, coming closest to leveling off at around 90 dB SPL. This is why wise mix and mastering engineers monitor at levels in the 85 to 90 dB SPL range, where our hearing is particularly flat.

The ways in which this nonlinear sensitivity is demonstrated in our audio experiences are myriad. Consider the sound of AM radio, low-bitrate audio codecs and public-address systems, all of which favor the overtones that give clarity to speech above all else. The Loudness button on consumer stereo receivers is an equalization circuit that boosts the highs and lows as the volume is lowered so the music will sound the same whether soft or loud. Noise-shaping circuits filter dither and quantization noise into the extreme upper range, where we will simply notice it less.

More Equal

To describe the concept of equal loudness regardless of frequency, the unit phon was developed. Each curve of the equal loudness contours defines a single phon level. For example, the curve that is 40 dB SPL at 1 kHz is defined as 40 phons; 40 phons at 10 kHz is therefore approximately 50 dB SPL and at 100 Hz slightly more than 60 dB SPL. Phons and decibels SPL are the same for a 1 kHz tone — an increase of 10 phons is equal to an increase of 10 dB at 1 kHz, but it may be more or less at other frequencies.

Many audio measurements are made using weighting curves that attempt to skew the results in favor of the way we actually hear. For example, the signal-to-noise ratio of a microphone preamp might be listed as 108 dB A-weighted, or sometimes just 108 dB(A). This means that the noise was filtered before measurement to exclude the extreme lows and highs to approximately the same degree our ears do at 40 phons. The rationale is that if we listen to the device at that level, then we will perceive the noise floor to be very low, even if there is significant noise in the low end of the spectrum because our ears are too insensitive to notice it. It's a reasonable proposition, except manufacturers sometimes use A-weighting for measurements at which a 40-phon reference level is of debatable relevance. Other weighting curves exist, but only C-weighting, whose curve resembles the 100-phon contour, and Z-weighting (zero-weighting), which is really no filter at all, are in common use.

Since the 1930s, other scientists have validated Fletcher and Munson's work, most notably D. W. Robinson and R. S. Dadson in the 1950s. The collective wisdom has been codified by the International Organization for Standardization as ISO 226:2003.


Brian Smithers, author of Mixing in Pro Tools: Skill Pack, from Cengage, teaches at Full Sail University in Winter Park, Fla.

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