(but then I still wonder why the tutorial doesn't show it like that).
Because pitches.h belongs in the same directory as the sketch, so the double quotes are correct, not <>.
And indeed, the .ccp file is missing.
Because there is no code to put in it.
But the pitches.h file as shown in the tutorial is not a proper library at all
Exactly. Only you thought it might be.
As I stated, I use IDE version 1.0.4.
I just fired it up. Looks exactly like 1.0.3.
I don't know what you mean by "dialog",
What else would you call the window that pops up? In computer program parlance, that's a dialog.
but just above the window in which you type the statements of the program there are 5 buttons on the left side and 1 at the utmost right side.
On the top row, yes. There is also a tab where you enter the sketch, and on the same level as the tab, on the far right (just under the serial monitor icon) there is an icon with a downward triangle (the tutorial is showing an old icon). Click that icon.