I could easily try to find excuses to avoid writing about NieA under 7, but instead I'll just grit my teeth and do it.
So what is it? Well, it's the most puzzling anime I've yet seen. It has a large element of slice-of-life (Miyuko's day-to-day existence and concerns), a little romance (the taciturn Genzo, who never does anything more exciting than coming over with a bag of rice), with added comedy (NieA's perpetual demand for food, and making UFOs that need to be plugged in to fly), ineffectual aliens (they're sort-of integrated into Earth society, and do nothing alienish aside from having antennae, apart from NieA who is perpetually building her UFOs), a mystery that could be deep but is never explained (the alien mothership, which talks only to NieA, says "sayonara" - we suppose, because NieA says it back - and then disappears by turning into fireflies that remind Miyuko of her father).
All this adds up to something and nothing. Nothing, because there is no discernible plot or moral to be found (a few hints at a concern with discrimination are not built up into anything meaningful); something, because the characters themselves have appeal, and keep you coming back to follow them even though they don't really develop. The realism of some of them - Miyuko the most - is satisfying; but the lack of development, or lack of explanation when something does happen (disappearance of the mothership), is unsatisfying to the same degree.
And why is the next episode preview actually an Indian talking about India?
In many ways the series seems unplanned, an experiment looking into how to write... something. Some of the gentleness feeds into Haibane Renmei; and I even briefly thought that there might be a message about acceptance of one's lot in NieA under 7 which could have been an earlier version of that in Haibane Renmei.
I did actually enjoy watching it - there are so many details that are wonderful: anything to do with Miyuko; the range of NieA's expressions; the omnipresence of the mothership; the tension when NieA herself disappears for a whole episode. But would I recommend it to anyone else? Well, that's a really hard one - I'll just say, read what I've written and make your own choice.
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PS - the music. The background music is unobtrusive and appropriate, a lot of it simply acoustic guitar. The OP is an acquired taste, which I was only beginning to acquire when the series ended. The ED is sweet and jaunty, and quite hummable.
PPS - I should explain, for those who don't know, that NieA under 7 was made by ABe and the team that had just made Serial Experiments Lain, as a sort of relaxation. It is far less known than the trio of Lain, Texhnolyze and Haibane Renmei, and kind of hard to discover anything about.