It's no secret that a lot of Jack White's songs are heavily sourced from the blues but interestingly enough when it comes to his guitar riffs he kind of ignores the traditional blues scale. He still places a heavy emphasis on the I, IV, V chord structure, the blues' bread and butter, but when it comes to his riffs he's unlikely to pop out with something resembling Smoke On The Water (I'm mentioning this song because it's the best example of the blues scale in rock 'n' roll riffage). Take a handful of riffs throughout the bands career (when I say riff I mean a concrete melody played on guitar so guitar parts such as Let's Shake Hands and The Hardest Button To Button aren't being included) Offend In Every Way, Truth Doesn't Make A Noise and I Think I Smell A Rat. They're all written around major and minor scales that don't often appear in rock 'n' roll. My knowledge of musicology is limited so I can't analyze this very well but Jack had no music degree so I doubt he sat in his upholstery shop thinking to himself: "wouldn't I be clever if I wrote my songs unconventionally scalic and then performed them in an understated garage rock sound". In fact I'd put good money on that not being the case. I don't quite know what name to give this style of music (and by now you must be wondering how this relates to Look Me Over Closely) but whatever you want to call it, this aspect of the White Stripes sound comes from his appreciation for tradition pop music and the first signs of this are in Look Me Over Closely. This love for artists like Patti Page or in this case Marlene Dietrich gives his songwriting an unconventional edge, one that he himself has acknowledged and while Look Me Over Closely is a cover the riff is his own and it's a good indicator of things to come.
The traditional pop influence is not limited to the guitar, on a regular basis Jack will sing in a sultry style almost trying to do his own version of the female singers of the 50s. However his voice is so different that it's hard to pick that up unless your looking for it but it lends a dramatic quality to his vocals. It becomes less noticeable later on but it's an important development here because his voice needs power when he's not shrieking and this theatrical technique is the best way to achieve it. What's more commendable is that in conjunction with his never-dying loyalty to truth he manages to put all this drama into his voice without ever sounding hammy or dishonest, something incredibly difficult.
It may seem odd to think of Jack White as a 1940s songstress but his appreciation for a sense of class in his music is one of the things that have kept The White Stripes interesting after all these years. Discounting Conquest, today this influence is almost untraceable in his music but it's importance is not lost. If another garage basher had been the b-side than maybe every foray into musical richness by Jack would never have happened. Without this bizarre influence of the sultry sounds of traditional pop we might never of had the lush tracks on De Stjil or the marimba on Get Behind Me Satan. Hell, maybe even The Raconteurs would not exist. I'm probably being overdramatic here but after hearing Look Me Over Closely I feel like being dramatic!