Hello,
When I read the original post yesterday I immediately thought of the logarithmic relationship, but wasn't sure yet what to say about it.
But now that I think of it, VI Labs' Modern U actually offers two curves (which I find excellent):
- A midi response curve;
- A gain curve.
I take the first one as the typical MIDI-to-sample or MIDI-to-timbre curve; while I see the latter one as… the gain or volume curve 🙂.
So, if you @QuasiUnaFantasia happen to have Modern U, take a look at that gain curve. It indeed shows that logarithmic relationship. The "helptext" for that curve says that the default gain curve setting "is how the sampled piano (Yamaha U3) actually behaves" (or something along those lines).
Of course the actual volume completely depends on the gain staging after the VSTi, so the several gain/volume settings in any software that is used, as well as volume/gain controls on the hardware used.
In Modern U, I left the gain curve at default and measured the final volume at the player's head to be approx. 80 dB when MIDI 127 is played (setting the gain chain to get as such). This I assume to be sort of a realistic level for a typical upright piano.
In practice, this works beautifully.
Hope this illustrative example adds something useful to this great discussion.
Cheers and happy gain curves,
HZ