Loudness

Loudness is the sensory scale of sound intensity. It was built experimentally based on the extensive research work in the field of psychophysics in the late 19th century (E. Weber, G. Fechner) and in the 1950s (S. S. Stevens). Loudness was then measured by asking listeners to give to a sound a number reflecting its perceived loudness, sometimes in comparison to another reference sound, to which an arbitrary value had been assigned. One important outcome of this research was that the perceived loudness of a one-kHz pure tone was related to its acoustic pressure by a power law, with an 0.6 exponent. This made it possible to define the loudness scale in sone. By this definition:

  • A sound perceived twice as loud as another has double the loudness value in sone.

  • A one-kHz pure tone at 40 dB SPL has a loudness value of one sone.

Other researchers adopted another approach to loudness measurement, by asking listener to set the physical level of a test sound to match the perceived loudness of a reference sound (most often a one-kHz pure tone). This approach yielded another loudness unit, the phon (more frequently considered as the unit of loudness level, rather than that of loudness), which is homogeneous to decibel scales. A loudness level value of X phon is given to any sound that is perceived as equally loud as a one-kHz pure tone at X dB SPL.

By combining these works, along with the power law relating the loudness and the acoustic pressure of a one-kHz pure, an approximate analytic relation was defined between loudness N in sone and loudness level LN in phon:

LN =40+10*log2(N)

This relationship means that doubling the loudness value in sone (doubling the loudness sensation) corresponds to adding ten phons to the loudness level.

From a more practical standpoint, loudness does not depend only on the sound intensity but also on its frequency, its duration and other phenomena such as critical bands and masking. From the 1950s, a major part of the research work in this field was dedicated to defining computation models for the calculation of loudness and loudness level, by integrating these different factors. Ultimately, three main models, associated to international standards, were defined:

  • Stevens’ model (ISO532A), now considered obsolete,

  • Zwicker’s model (ISO532-1),

  • Moore’s model (ANSI S3.4).

Zwicker’s and Moore’s models mainly follow the same principles, roughly matching the path of the acoustic wave in the human ear, from the pinnae up to the basilar membrane and the auditory nerve in the cochlea. These principles correspond to 5 consecutive computation steps:

  1. Outer- and middle-ear equivalent filtering,

  2. Decomposition of the spectrum in critical bands,

  3. Calculation of the excitation level in each critical band (excitation pattern),

  4. Calculation of the specific loudness from the excitation level,

  5. Calculation of the overall loudness by summation of the specific loudness over all critical bands.

In Sound: Analysis and Specification, different types of model of loudness are proposed depending on the type of sounds under consideration, and can be found in distinct computation profiles:

Sound: Analysis and Specification also enables you to calculate and display the loudness colormap of a sound.