In a familiar scene, Google (Nasdaq: GOOG) is staging a retreat out of China, and Baidu (Nasdaq: BIDU) is positioned to be its biggest beneficiary.

Google said on Friday that it will be shutting down Google Music Search in China next month. It seemed like a good idea when the world's biggest search engine introduced the service four years ago.

After seeing Yahoo! (Nasdaq: YHOO) lose a legal battle in China in 2007, and seeing homegrown search stars Baidu and Sohu.com's (Nasdaq: SOHU) Sogou come under fire for making it too easy to find pirated MP3 files on their sites, Google tried to take the high road. Big G negotiated with the record labels to roll out a licensed music service.

A free ad-supported music downloading service was probably never supposed to be a permanent solution. As China's economy evolved and piracy was curbed, a more traditional premium music service would be the better solution. However, Google Music Search stuck around even after Google officially backed out of China in traditional search two years ago.

"We have decided we are no longer willing to continue censoring our results on Google.cn, and so over the next few weeks we will be discussing with the Chinese government the basis on which we could operate an unfiltered search engine within the law, if at all," Google argued in 2010.

Some argue that Google was merely saving face at the time. It may have been leaving China on principle, but even at its peak, its market share in search was only just a little more than half of what Baidu was commanding.

It remains to be seen what effect this will have on Baidu, which rolled out its own legal music service last year. Obviously having one less rival around will make life easier. Baidu went from commanding nearly two-thirds of China's search market when Google was around to as much as 80% recently.

Obviously, music search will never be as lucrative as traditional search. There's only so much that advertisers are willing to pay for young users looking for free tunes. It's still something that will help Baidu, and possibly even as it wages a war in traditional search with Qihoo 360's (NYSE: QIHU) emerging challenge.

And the beat goes on.

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