The Silicon Valley Insider, based on speculation from one person, says that it might be 27 million tracks thus far:

[E]Music CEO David Pakman, an Amazon rival, says he thinks Amazon has 4% to 5% of the U.S. digital music market.

That doesn’t sound bad for a store that didn’t exist last fall. But put in unit sales, it looks awfully modest: Nielsen Soundscan says Americans bought 532.7 million digital tracks in the first half of the year. If Pakman’s estimates are right, that would mean Amazon (AMZN) has sold up to 27 million tracks so far this year — during the same period where Apple (AAPL) has sold more than 1 billion (worldwide). Amazon sells each track for up to 89 cents, and the labels take about two-thirds of that, which would leave Jeff Bezos with…perhaps $7 million of revenue.

(Link via The Daily Swarm.) A lot of caveats, though:

Could these numbers be off? Absolutely. Pakman says he gets his estimate by talking to the music labels, who tell him that his company is selling up to 3x as many tracks as Amazon is; he pegs his market share at 10% to 15%.* As we said, Pakman isn’t a neutral observer here, and has been tangling with Amazon for the right to call his company the second-biggest online music store in the business. And beyond that, his sample is skewed: eMusic works primarily with smallish indie labels, not the Big Four labels that almost certainly power most of Amazon’s sales.

And the item has this trenchant comment:

Here’s a data point, I’ve ‘purchased’ more than 10 mp3s on amazon.com. With bottlecaps. Given their target market and the availability of bottlecaps (and it only takes 5), this is probably a large part of their mp3 ‘business’.
[…]
The music industry is killing itself with CD sales (which are DRM free and go straight to hard drives and get sold used for less and less money each year) and trying to kill Apple. You know what a song is worth now? 5 bottlecaps.