Mark,
I hadn't stumbled across that one about the Rats but it makes sense though. Whilst 'mojo' may defy the laws of physics, fortunately I can guess at an explanation of this one with science
I need to make a couple of assumptions to get this to all work, but here goes..
Lets say the 9V adapter is rated to supply 9V @ 300mA. Using Ohms law that means that adapter can supply (9v x 0.3A) 2.7W of power.
Lets then say that the Rat draws >300mA when driven. For sake of example say it draws a hefty 400mA. As per the above example, that means the pedal needs 3.6W of power to work as intended.
So what happens? Well the first thing you're going to notice is your power supply is going to get warm.
Electronically though what I'd expect is the voltage is gong to drop. If (P)ower = (I)current X (V)oltage then V=P/I so if I have this right (and this is real rusty for me so I might not), then V= 2.7W (what the adapter can supply) divided by 0.4A (being the current required by the pedal) meaning you'd see 6.75V under full load instead of 9.
Big difference huh.
Based on the above you might have already worked out that even if the 10V adapter has the same current rating as the 9V one, it's power capabilities are higher. (10 X 0.3= 3W as opposed to the 2.8W of the 9V version) so under load the voltage drop isn't as severe.
It's also a pretty fair assumption that the 10V adapter has a higher current rating though, and that would increase the power rating and.....well I guess by now you see where I'm going....
@Marnold.
Why would ya? In practice, changing the supply voltage will change the overall tonal characteristics of any audio circuit meaning it's going to sound different at 10V than it does at 9V. Some people may dig that, some might not.
Remember that what we do to guitar amps breaks a LOT of the "rules" of amplifier design too. Talk to a HiFi amp guy about distortion and they'll be horrified. Amplifiers were never originally designed to distort the source signal. The fact that it can be musical when they do was a total fluke accident.
Anyway, I was going to do a bit about internal resistance of batteries too but I'd better do -some- work before lunch

If anyone cares, post back and I'll try and explain that too
