Well there is this new Lana's song and I can't understand the grammar of the title at all. What does the title mean in whole and what does the last "to" mean?
Thanks in advance.
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The particular wording of the title suggests that Lana may be acquainted with a 1967 song called "Music to Watch Girls By" by Bob Crewe Generation (1966). Andy Williams released a version of the song with lyrics in 1967.
In any event, idiomatic English allows you to watch boys (or girls) to music, just as as it allows you to do chores to music: the music plays, and you watch (or work).
Whether you can watch girls (or boys) by music—analogously to the way you can color a picture by number, for example—is more problematic. But in this case Bob Crew's song title might have been echoing an even earlier song—"Standing on the Corner (Watching All the Girls Go By)"—a show tune by Frank Loesser from The Most Happy Fella, released as a 45-rpm single that same year by the Four Lads.
It's an odd grammatical structure, in the form of:
which means, essentially,
nounis good to use when doing this
So, for example, if we make a play list with a lot of upbeat songs, we might entitle it:
Music to Exercise To
Or, we could burn our favorite dance songs onto a CD, and write on the jewel case:
Songs to Dance To
If we made a list of self-help books that offered good time management tips, we might entitle the list:
Books to Manage Your Time With
A rather common one of these is:
Words to Live By
which refers to maxims and proverbs promoting a safe or healthy lifestyle (this one even gets its own entry in The Free Dictionary).
So, in the song title, Lana is referring to music she likes to hear while she is watching boys.
As the lyrics says, "Putting on my music while I’m watching the boys", so the meaning of the title is quite clear. As to the question 'what does the last "to" mean?', well, if you can "dance to the music" (that is while the music is being played), so you can "watch boys to the music" (though it sounds somehow weird). Of course, you can put it as "watch boys (while listening) to the music", but in fact that is not necessary.
P.S. By the way, Lana herself used to babysit, even after she got famous:
"... during a 2012 interview with the Huffington Post, Del Rey admitted she still babysat just as she had before the release of "Video Games" and the successes that followed. Lana discussed the gig as an example of the quiet life she prefers to lead."