[Rincewind]

The word "Tintos" is capitalised. This implies it's a name; possibly a person's or place's name. I would guess that an apostrophe has been omitted and it should be "Tinto's".

"the piece" is commonly use to refer to music. "meditations" means deep thinking. So, I would guess, we have someone thinking deeply about some music written by a person called Tinto. Though I could be completely wrong. Is there any other reference to Tintos in other lines of the passage?

"handglass" is an old fashioned word for a small mirror. So the man is looking at himself. "scrutinised" means, look at carefully and critically. "ivorybacked" is an old fashioned adjective and describes the material the back of the handglass is made out of. That is, the back of the handglass is made of ivory (elephant tusks). So in short, he looked at himself in a mirror with an ivory back.