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A function that can be used in Formulas.
phonToDifferenceLimens (x)
x in phon units into an intensity difference limen level.phonToDifferenceLimens (phon) = 30 · ((61/60) phon − 1) |
phonToDifferenceLimens is the inverse of differenceLimensToPhon.
In first approximation, humans can detect an intensity difference of 1 phon, i.e. if two sounds that differ only in intensity are played a short time after each other, people can generally detect their intensity difference if it is greater than 1 phon.
But the sensitivity is somewhat better for louder sounds. According to Jesteadt, Wier & Green (1977), the relative difference limen of intensity is given by
| DLI = ΔI / I = 0.463 · (I / I0)−0.072 |
In this formula, I is the intensity of the sound in Watt/m2, I0 is the intensity of the auditory threshold (i.e. 10−12 Watt/m2 at 1000 Hz), and ΔI is the just noticeable difference.
Boersma (1998: 109) calculates a difference-limen scale from this. Given an intensity I, the number of difference limens above threshold is
| ∫I0I dx ΔI(x) = (1 / 0.463) ∫I0I dx I0−0.072 x0.072−1 |
| = (1 / (0.463 · 0.072)) ((I / I0)0.072 − 1) |
The sensation level in phon is defined as
| SL = 10 log10 (I / I0) |
so that the number of difference limens above threshold is
| (1 / (0.463 · 0.072)) (10(0.072 / 10) (10 log (I / I0)) − 1) = 30 · (1.0167SL − 1) |
© Paul Boersma 2002, 2023