To listen to some examples of alternative Argentine tango music online, check out this link to Jackie Lee Wong's
tangopulse.com!

Dancing Tango to Alternative Music

Opinions vary widely about dancing with Argentine tango steps to music that is not strictly speaking "Argentine tango." Some say the "music is the dance." If you dance Argentine tango steps to Fox trot music, it is still Fox trot.

Sometimes even Argentine tango music is not acceptable to the purists because it doesn't fit into the standard mold for Argentine tango dancing music. They say it is listening and not for dancing. An example is the music by Astor Pizzolla.

Here is a piece published in TANGOReporter (February 2003, Issue # 27), from an interview with Juan Carlos Copes:

"My life with Astor was very profound. I believe that he always considered me a friend and I believe that from the pedestal where I held him I always offered him what I could humbly do. Approaching that music that made me fly so much, it made me fantasize, but also approaching him and feeling like his friend was very satisfying. I had some sort of idolatry towards him.
I remember when I met him. I was a crazy amateur back then. It was the year 1952 and those that have any memory of those days will remember they would kick out the milongueros from all the popular places. And I said, "I have to continue with this in some way, I can't leave it." And besides learning other dances (dances that I was never very good at), like contemporary, acrobatic, choreography, I felt I was very limited with what I knew. So, I began to pay attention to the music.
"A Fuego Lento" by Salgan was one of the first tangos with which a group of inexperienced friends and I worked, then one day I listened to Piazzolla. Then I became a habitue of his concerts, which he often played on the radio with his quartet. And one day I went to the Patagonia Theater and I told him: "Look Astor, I have a small group with amateur dancers and we are doing little stories about BA, not only with couples but also telling stories and I would like you to see one that we did with your tango "Contrabajeando." It seems that was a good introduction, because he came by to see us.
....
He saw it, thanked us, and left. And then I realized that I still have a long way to go to realize what Piazzolla had in mind. That was my first physical contact with him. Until his last words in Rio de Janeiro after a performance, he came, gave me a very strong hug and told me: "Man, who said that Piazzolla could not be danced?"
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NOTE: This article was called to our attention by Gulden Ozen of Tangophilia/North Carolina. It was reprinted with permission of the TANGOReporter