The rhythm machine takes AC at 120 and 220 through two separate figure eight female jacks. It's from India.
Then there is a transformer that outputs ~6.2v from my 120v AC (don't know what it would be from 220). It would make sense if the transformer was sourced off a shelf at the cost of a voltage regulator which there appears to be.
Since this is older gear, it is probably a 6.3V transformer, 6.3 and 12.6 volt transformers were some of the most common and cheapest voltages before the rise of cheap switcher supplies. 6.3 and 12.6 were the optimum voltages for powering the filaments of vacuum tubes and became standard voltages in transistor gear since they were cheap and available, even today transformers in these voltages are easy to find cheaply on the surplus market.
*Edit: Nevermind, I read that as you had 120 and 220VAC transformers followed by a 6.3VAC transformer, you have one transformer with 120/220 primaries and a 6.3VAC secondary. Not odd at all.
Common switch mode power supplies are not picky about input voltages and generally have a wide range of operating voltages, having the switch on 230 likely just knocked 20 volts or so off the input voltage to keep the 230 below the max voltage, not half it. The reason this eventually started causing problems is probably because your wall voltage has dropped and/or components in the supply aging and drifting from spec meant it could no longer maintain good clean output which triggered a safe guard in the computer.