The title is a play on Izayoi Sakuya's name and Japanese names for phases of the moon .
Nanokagetsu (七日月) is the 7th day of the lunar phase, i.e. the first quarter moon.
Izayoi (十六夜) refers to the 16th day -- the first day of the waning moon after the full moon.
This might also have something to do with Sakuya being a child in the comic.
See also: http://en.wikipedia.org/wiki/Lunar_phase

Kenn's Comment: You can read it over @ Danbooru, or the Pixiv link under the OP image. It's by the same guy who did KoaCORE, and follows a similar story. It's how Sakuya, a human, ended up working at the Scarlet Devil Masnion. It's significantly darker than KoaCORE, and has quite a bit of blood in it too.

On another note, did everyone appreciate the Arakune styled speech before the jump?