What is a vacil?

Fluctuation strength is similar to roughness, though at much lower modulation frequencies. Fluctuation strength is measured in vacils (from vacilare in Latin or vacillate in English). Police sirens are a good example of sounds with high fluctuation strength.

Fluctuation strength reaches its maximum at a modulation frequency of around 4 Hz. For much higher modulation frequencies, one perceives roughness rather than fluctuation. The reference value for one vacil is a 1 kHz tone, fully modulated at 4 Hz, at a sound pressure level of 60 decibels. In other words

(1 + sin(8πt)) sin(2000πt)

where t is time in seconds.

Since the carrier frequency is 250 times greater than the modulation frequency, you can’t see both in the same graph. In this plot, the carrier is solid blue compared to the modulation.

1000 Hz signal fully modulated at 4 Hz

Here’s what the reference for one vacil would sound like:


See also: What is an asper?

3 thoughts on “What is a vacil?

  1. Great reminder on psychoacoustic metrics, but John do you know sources, where to find algorithms to calculate these all?

  2. That’s tricky. The literature in this area is exceptionally hard to read and lacking sufficient detail to implement in software without some guesswork.

    One reference is Daniel and Weber’s paper Psychoacoustical Roughness: Implementation of an Optimal Model, Acta Acoustica, vol 83 (1997) 113–123. It has some errors and ambiguities, but with persistence and experimentation you can code it up.

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