Log pots are built with geometrically created values of different resistance in order to keep down the cost, instead of creating nice curved shape resistance material.
Different mfg make those resistance values for each "leg" different.
I'd scan one of my books to give a picture, but the simple phrase is "as high impedance as possible, maximum voltage transfer, minimum current, middle value, equal volt/current, low value impedance maximum current transfer, minimum voltage".
The circuits inside a box or a guitar depend on a certain level of current flowing around the output area. If there's less resistance to ground, there's more ability for current to go that way rather than be deflected into the output loop trying to find ground. The reason highs get louder with a larger ohmic value pot is because resistance has more effect on high frequencies than on low frequencies. Remember that even if you cant hear the guitar or keyboard in a club, you'll still here the wump wump of bass coming through that brick wall.
Caps are the opposite. they have more effect on lows than highs in terms of resisting passage of frequencies.
This stuff is why a high pass filter (passes highs along to the output more than lows) consists of a resistor to ground, while a low pass consists cap to ground
With a much larger resistance, as you increase the volume, you're "getting back" a lot more mid-high freqs, which makes it louder.
You may notice that with all volume knobs, you lose highs more than lows as you turn it down.
There are "sweet spots" of resistance values to have for pots.
