The most famous full moon in Japan is the harvest moon in September (十五夜, ju-go-ya), but there's an old custom that believes no moon-viewing (お月見, tsukimi) is complete without also looking at the almost full moon in October (十三夜, ju-san-ya).
The latter falls on the 13th night of the 9th month of the old lunar calendar. Ideally you should look at the moon when it's not fully full, because almost perfect is more beautiful than perfect. Isn't that a lovely idea?
Other names for the thirteenth moon is bean moon (豆名月, mame-meigetsu) and chestnut moon (栗名月, kuri-meigetsu).
This year ju-san-ya was on the 27th of October, but I couldn't take photos on that night. Here, instead, is the completely full moon next to Sky Tree on the 29th of October. If you ask me, perfect is good enough.