Introduction to Computer Music: Volume One

15. What is loudness?

Loudness is the way in which we perceive amplitude. As mentioned above, a particular change in amplitude is not necessarily perceived as being a proportionate change in loudness. That is because our perception of loudness is influenced by both the frequency and timbre of a sound. The "just noticeable difference," or JND for amplitude — that is, the minimal perceptible change in amplitude — varies by the starting amplitude and frequency, but in general it ranges between 0.2 and 0.4 dB.

The most famous, well-used measurement for plotting our perception of loudness against the frequency of tones is the Fletcher-Munson curve(s) of equal loudness, published in 1933. The graphs were updated in 1956 by D.W. Robinson and R.S. Dadson. They were refined again in 2003 and adopted by the International Standards Organization as ISO 226. The purpose of the graph is to show that for humans to consider two pitches equally loud, the amount of energy necessary to produce the tone at one frequency may be completely different than at another. The multiple lines, spaced in 10 dB increments, also show that the energy/frequency differences are steeper at lower intensity levels and flatten out at extremely high intensities, though not quite as much as Fletcher and Munson first determined.

Image released into the public domain by copyright holder

The "loudness button" on a stereo amplifier is intended to boost bass frequencies at lower volume levels where the curve is the steepest. In viewing the graph, it immediately becomes apparent that much more acoustic energy is required in the lower frequencies to create sounds of equal loudness to those in higher frequencies. With a minimum around 4000 Hz, some additional energy is also required for equal loudness at higher frequencies. You do not buy a 500 watt amplifier for frequencies in the 5000 kHz range, but you might for equally loud bass in the 20-100 Hz range.

Most natural and instrumental sounds have the majority of their acoustic energy in the lower portion of their spectra—this naturally follows the way we hear. Certain synthesis methods, such as frequency modulation (FM) are prone to creating energy equally distributed across the spectrum, and so sound weighted toward the higher frequencies to us.

Above, there was mention of “weighted” methods of dB measurement that were more closely related to the way in which we hear. The most widely used is the ‘A’-weighted or dBA scale, which rolls off, or progressively filters out, lower frequencies and so creates a measurement in which all audible frequencies are treated equally for sounds of approximately 40 dB. This is a standard option on most dB meters and measurements should be indicated as dBA, not dB. Interestingly, the dBA scale was based on the Fletcher-Munson 40 dB curve, which turned out to be the closest to the ISO 226 curve (pictured above).

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