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I am working in an engine that encodes sound as decibels (dB). Let's assume the decibel range of human hearing is -60dB to 0dB.

Audibility is not linear across this range.

So my question is...

How does one map a decibel range to a set of numbers (for example, 1-10), such that each number corresponds to (roughly) one linear step up in audibility?

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  • \$\begingroup\$ I have updated my answer. I hope it helps. \$\endgroup\$
    – Vaillancourt ♦
    Dec 6, 2019 at 16:21
  • \$\begingroup\$ Are you asking simply for a mathematical formula to convert a number from (1, 10) to (-60, 0)? \$\endgroup\$
    – Tom Tsagkatos
    Dec 6, 2019 at 16:23
  • \$\begingroup\$ @TomTsagk, no. That would help if audibility was linear across (-60, 0) dB, but it is not. \$\endgroup\$
    – DyingIsFun
    Dec 7, 2019 at 5:39

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We use dBvalue = 20 * log10( volumeAsPercent ) where volumeAsPercent is in the range of [0.001 .. 1]. dbValue will be in the range of [-60 .. 0].

(That's a bit annoying because the actual engine - OpenAL - uses 0..1 for its gain, so we have to convert that back using volumeAsPercent = 2^(dBvalue/6). It will not exactly give the same result as the input but will give an approximation to volumeAsPercent = 10^(dBvalue/20) which is close enough (I don't know why we use that formula, and we can't change it at this point).)

I'm not a sound engineer, I don't play music and I don't have a sound studio to test this, but testing this formula with increments of 10%, seems to give a nice progression in making the sound louder (from completely muted at 0, up to what is in the original wav file at 1).

Here are the plotted curves.

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