Separating a certain clause with a comma

Hi.

I'm not even sure what this is called, so I can't search usefully for it. I want to write a sentence that ends with a noun followed by a clause that explains what that noun means. One might write something like,

'Plato's description was of a different kind of relationship which we now call a Platonic relationship; that is, a non-sexual form of intimacy',

but for reasons that have to do with what surrounds the actual sentence I'm using (which isn't the above one), I want to write something more like,

''Plato's description was of a different kind of relationship which we now call a Platonic relationship, a non-sexual form of intimacy'.

The comma seems strange to me, however; and I don't want to use an em-dash (again, for reasons of surrounding content). Is this proper use or must I use one of the alternatives that I'd prefer not to?