Normally, when you power up electronics (like a TV, PC, Video, DVD Player) it's harmful because the electronics get a "burst" since the transformers in them are not yet at their default when first powered up.

In the case of the PSR's however, the transformer stays on (that is, if you leave it in the wall outlet) and the ON/OFF switch on the board only allows regulated DC to flow through, which makes it way easier on the electronics.

Now as far as the Tyros goes, I believe the power regulator is inside, so I would presume the power switch there is on the AC side, which is more harmful to the electronics each time you power on.

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