Transformer producing higher voltage than rated

[UserXP]

Hello, people.
i am not sure if this question belongs to this forum section exactly, but since there already are some queries here about power transformer, let's give it a try.

So, I have this old but very well preserved Casio SA-20 ToneBank keyboard. It is powered either by five 1.5V AA bateries, or via a power adapter, so its operating voltage is 7.5V. The power adapter input jack also states 7.5V DC In. Now, since this keyboard was never supplied with a PT, but actually came with test bateries included, I decided to try to buy an adapter for it. I know I could have just gone along with a universal power adapter, but I wanted to make everything original as I still have even the original box for this keyboard and would like to keep it for nostalgic reasons.
So, looking at the SA-20's specs, it says that its power consumption is 1.6W and that the adapter should be 7.5V (outer +, inner - on the plug), model Casio AD-1 (which I found to be 7.5V, 400mA, 7W power adapter, but it works on 120VAC - which wouldn't work where I live).
So, I managed to find an original Casio new old stocke model AD-1GL, which is as in the images, everything regarding the specs corresponds.
The keyboard works with it, BUT, upon measuring the actual DC voltage which this AD-1GL adapter outputs, it is nowhere near 7.5V as rated, but is 12.8V instead. I even asked Casio and they basically wrote almost everything which is in the specs I already have.
So, my question is, is this 12.8V DC, 0,4A and 10W power adapter an overkill for this 7.5V 1.6W keyboard?
Thanks in advance as always, cheers.

[CapLeaker]

Well… try finding a service manual for it and look at the power input section and see how much power it could handle? I am pretty sure I know kinda whats wrong here with your measurements. It’s a transformer based power supply, right? I am pretty sure you plugged the transformer into the wall, took your DMM and checked the output and measured 12.8VDC, right? Well wrong. The transformer has two flaws that changes the DC output voltage.
1: ouput voltage depends on AC input voltage. It’s rated at 220VAC… well if you have 240VAC or so, the output voltage will be higher. Now imaging you get a nice voltage spike through the power line… what goes in, will be reflected on the DC side.
2: output voltage on a transformer based power supply will be higher if there is no load on it. So sizing a transformer based power supply is kinda important. Sure everything is with a certain tolerance in mind. As more load you put on the transformer, the output voltage will drop too.
I found a SM for a SA-21 and looked at the AN8053 that is getting fed from that power rail straight. Its normal rating is 4 to 11VDC. The absolute max rating is 11.5VDC.
You may lower your AC input with an adjustable power supply, an adjustable isolation transformer, or online UPS on which you can adjust the AC voltage, or get a 9VDC wall wart and call it a day.

[Agent24]

It's not overkill, it has the same specifications as the original (aside from being 230v vs 120v), so it should be fine.
And you said the keyboard works with it. Which I would expect.

Unloaded transformers always output higher voltage than the label says.
I assume you measured it unloaded, anyway.

What voltage does it measure when it's powering the keyboard?
That will tell you more useful information.