Double sharp or Triple sharp?

Are you reading the music correctly? I don't recall any D double sharps in Moonlight Sonata. There are F double sharps, which would played on the piano as G, but no D from what I remember. Either way, you don't add up the accidentals with what is in the key signature - you simply play what is written next to the note. Also, you have worked it out wrongly in your examples. D sharpened three times would be F natural not F sharp, and twice would be E (natural).

It's a double-sharp. A while back, a zealot here decided to poke us with a sharp stick, about the incidence of triple sharps and triple-flats in music. Yes, he found some. You can find anything loony if you look long enough. I suppose that if you wrote a passage in d-double-sharp major, that your third and your leading tone would be triple sharps - so? You can find every aberration of notation that is possible - and most were written by people who did it *just because they felt like it*. As a life-long teacher with a 2nd BM and a MM in Music Theory, I can tell you that there is NO theoretical reason to utilize triple sharps or flats, except for the puerile *gotcha!* that this other responder used. I also know of a Russian composer who wrote his music in his own notational system and his own BLOOD, and kept it in an *altar* he built for it in his home. Nah - I think Finale or Sibelius will do just fine . . .

You are always going to find loonies out there. The real stuff requires enough attention and patience.

Double.

... if there were a single sharp sign (# not the X thing) it would only be considered cautionary.