Playing samples with equal volume accros the keyboard range

I want to add a VCA after a sample player (played with a CV source) and control the gain with the same CV as the Pitch CV so it corrects the amplitude according to the pitch, in order to have a constant output.
I managed to have some decent results by setting the VCA bias to 1 and the gain to -0.5.
But this seems not mathematically true. What would be (if possible with a linear VCA) the correct settings ?

Are you talking about how we hear some frequencies louder than others? If so, there is the equal-loudness curve: Loudness - Wikipedia

Well, unless I am wrong, I was talking about the fact that pitching a sample one octave up makes it peaks +3dB over the original. Result is : high notes are louder than low notes.
Am I tripping ?

I think you are being influenced by the level meters which are excited more by higher frequencies due to the HPF inside of it.

Easiest way to verify if the change in loudness is happening in the ER-301 or after, is to check signal peak-to-peak amplitude in the scope, I think you will see that it does not change.

Ok, I was not describing correctly the situation. You absolutely right in the case of, for instance, a varispeed sample player.
But this is not the case for the manual grains unit, which seems to work more like a classical tape or vinyl.

There should be no changes in gain with respect to pitch in the Manual Grains unit either. However, there is a gain compensation that depends on the number of active grains (i.e. grains already playing):

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Well, with just one grain, it’s obvious to me that the lower it is, the quieter.
Both my ears and eyes tell this.