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I loaded the three that I could find on the Ubuntu repositories: Lilypond (with Denemo), NoteEdit, and NtEd. Yes, they're all in the repositories!
After trying them out, I ultimately settled on NtEd. Lilypond seems to be the most full-featured, but for what I need right now, NtEd fits the bill. (NoteEdit also comes from the same author of NtEd).
Some things about NtEd: it's small and light, compared to the other two; it's completely graphical; it plays out the music from the notes; and it's intuitive enough for a non-music-reader like me to use. In fact, I'm learning to read music just by using this software.
I've never been a musically inclined person, forced electric organ lessons notwithstanding. Now I'm beginning to think things might have turned out differently if I had software like this before. The notes and the measures make so much more sense now.