So, the TS 451 is a celeron and below the recommended cpu specs. There are really two questions,
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Will it load and function? And the answer is probably yes. I have not tried it so I can’t answer completely with authority. But, I don’t see why it wouldn’t work.
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Will it provide you with a good software experience? That is something that is hard for others to answer for you. The required processing power is very dependent on your use case for Roon, how big is your collection, are you using DSP, how many zones will you be using, etc etc. Depending on things, it might just manifest as a slower response in the interface, when searching, when starting things up. OR, it could reach a limit rather quickly and drop outs and other audio artifacts could appear.
If anything I’ve mentioned in the above paragraph sounds is confusing, take a read on the Roon forums about how Roon works (Roon - How Roon works), or feel free to ask :D.
As long as the computer is an i3 or better; some would argue that this is the better solution. If this is easier and cheaper, then you could use it as a a temporary setup first to get a feel for how you will use Roon. Might let you make a more informed decision.
Also, there is ROCK coming down the line which would arguably provide an even more set it and forget it option for the less technically inclined.
See, this…