API Enhancement: PerceivedLinear that casts to Decibels

[j-ac]

In my project, I created an abstraction over Decibels called PerceivedLinear which uses a psychoacoustic principle that an increase of 10 decibels is roughly equivalent to a doubling in perceived volume.

With this abstraction 0.0 corresponds to -60 dB and 1.0 corresponds to 0 dB. 0.5 will sound "half as loud" as 1.0. Working with this unit is very useful because it allows me to consider the user's experience first rather than the physical reality of sound waves. Including something like this in Kira natively might be a good idea.

The equation that relates a PerceivedLinear value to a Decibel value is shown in the screenshot. I can share the derivation if necessary.

#[derive(Copy, Clone)]
pub struct PerceivedLinear(pub f32);

impl From<PerceivedLinear> for Decibels {
    fn from(l: PerceivedLinear) -> Self {
        let db = 10. * ((1. / 64. + l.0 * (1. - 1. / 64.) as f32).log2()); // Equation from the screenshot
        Decibels(db)
    }
}

impl From<PerceivedLinear> for kira::Value<Decibels> {
    fn from(a: PerceivedLinear) -> Self {
        kira::Value::Fixed(a.into())
    }
}

impl Mul<f32> for PerceivedLinear {
    type Output = PerceivedLinear;

    fn mul(self, rhs: f32) -> Self::Output {
        PerceivedLinear(self.0 * rhs)
    }
}

[tesselode]

Thanks, this is a cool idea! Where does the 64 come from in the equation?

[j-ac]

Because every 10 decibels is approximately doubling of perceived loudness (S) we can define it as:
S = 2^(dB/10)

At 0 dB:
S = 2^(0/10) = 1

At -60 dB:
S = 2^(-60/10) = 2^-6 = 1/64

This means that our values are on the range [1/64, 1], which we obviously don't want because we want to use [0, 1]

So we linearly interpolate a 0-1 loudness value (L) to the range 1/64 to 1:
S = 1/64 + L * (63/64)

And then we convert it back into decibels by rearranging S = 2^(dB/10):
dB(L) = 10 * log2(S)

Or, substituting S in:
dB(L) = 10 * log2(1/64 + L * (1-1/64))

[j-ac]

PerceivedLinear is a bit of an awkward name. Perhaps it should be called ApparentVolume