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y axis of waveforms and different fades
I was performing some tests with long fades to check if my theoretical knowledge matches what I'm hearing in Pro Tools and sometimes it seems it doesn't. My reasoning starts with the following statement: In Pro Tools, the y axis reflects a linear scale of samples (and not a dB scale). It's the pure scale of samples, which can be thought as an interval from -1 to 1 (actually we can see in the Main Counter that the interval ranges from -8388607 to 8388607, which is the maximum storable value available in some computer-stuff-specification, as I found). There are ticks in the 0, 0.25, 0.5, 0.75 and 1 positions and it can be verified that the intermediate values represent approximately -12dBFS, -6dBFS and -3dBFS as expected (a sine wave peaking at these levels).
Now to the fades ... Our ear responds logarithmically to the sound (physical pressure), meaning that the graph perception vs. stimulus (y vs. x) is a logarithmic function. Applying a linear fade out in the scale of the stimulus (the pure number of samples in Pro Tools, that mimics voltages that mimic the displacement of a microphone membrane that mimics pressures/densities) should reflect in a log sensation function: a sound that decays slowly at first and then really fast (the opposite in the case of a fade in, where the sound rises fast but keeps rising slower and slower) and not a linear sensation (stimulus = straight line x; perception = logx). If the shape of the fade is an exponential decay (it seems that some people call the image of an exponential function a "logarithmic fade" instead of an exponential fade. I do not follow this convention in this post), then when applying the log function we would have a linear sensation of the drop/rise of the volume (stimulus = e^x; perception = log(e^x) = x) If the shape of the fade is logarithmic then the sensation would be an exaggerated logarithmic sensation (behaving as an exaggerated linear fade, because perception = log(logx)) If the y axis were in a dB scale, it would mimic the way the ear responds (since the decibel formula already contains a log inside) and a linear fade would sound natural as a linear volume drop/rise. Is this correct? Are there wrong assumption here? Also, are all of the fades I mentioned described as "Equal Gain" fades in Pro Tools and "Equal Power" are another thing? I hope I posted on the most appropriate forum :) Feel free to correct any terrible english mistake. |
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