Volume control - multiplication factor versus percent

I assume that the recording volume control works by multiplying the input signal by some factor. I would like to know what the factor is versus the percentage on the volume control. For example, is the factor 1 at 50% and greater than 1 at >50%? Seems as if that information should not be hard to find with out going through the code.

Amplification is a multiplication factor (less than 1.0 for attenuation) but the meter and volume slider are in decibels. -6dB is 50%.

By default, the waveform display is linear (not decibels) and the scale shows 0 to +/- 1, where zero is silence (or the waveform zero-crossing) and +1 & -1 are 100% positive & negative peaks (the highest you can go with integer data). 100% positive & negative peaks represent 0dB. -6dB is 50%.

Decibels are used because our hearing is logarithmic (or proportional). This is logical because a change from 1 watts to 2 watts is a doubling of power (but barely noticeable so it doesn’t sound like doubling) whereas a change from 10 watts to 11 watts is a smaller percentage and not noticeable.

If you amplify an electrical signal by a factor of 2 (+6dB) the voltage is doubled. (The voltage of quiet sounds is doubled and the voltage of louder sounds is doubled.) It’s the same with digital, all of the sample values are doubled.

With digital or electrical (voltage) amplitude, 0dB is a factor of 1.0 (no change), 6dB is a factor of 2, 12dB is a factor of 4 and 20dB is a factor of 10.

The formula for amplitude is:
dB = 20 x log (A/Aref), where A is the amplitude and Aref is the reference or starting amplitude.

For power (wattage) the formula is:
dB = 10 x log(P/Pref).

…A 20dB change is a voltage (or digital) factor of 10. With 10 times the voltage (or digital value) you get 100 times the wattage. (It’s the same dB or loudness change but the formulas are different.)

On the digital scale 0dBFS (0 decibels full scale) is the “digital maximum” for integer formats… It’s the highest you can “count to” with a given number of bits so digital dB levels are normally negative. (Everything is scaled during playback so a 24-bit file isn’t louder than an 8-bit file.)

Audacity uses floating-point internally so there is essentially no maximum (or minimum) but if you go over 0dB you’ll hit the 0dB limit of your digital-to-analog converter and clip (distort).

The reference for acoustic loudness of 0dB SPL (sound pressure level) is approximately the quietest sound you can hear so dB SPL levels are positive.

There is no calibration between digital and acoustic levels (because it depends on the volume control, etc.). But there is a direct correlation - If you are listening at 80dB SPL and you reduce the digital level by -3dB (3dB more negative), the loudness will drop to 77dB SPL.

Thanks. I guess my question was not clear. I understand decibels so I was not asking for an explanation. My quetion relates to the multiplicaton factor corredponding to different percentages on the volume scale on the record setting. If all internal calculations are done in floating point, I assume that the volume setting will not affect the output resolution. That implies to get the highest resolution, the digital input should be set as high as possible without clipping.

I still hope to get an answer from someone. Thanks

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