Syrtaki is a media invention. When Anthony Quinn taught Alan Bates to dance in Zorba the Greek, he was performing a combination Vari Hasapiko and fast Hasapiko, choreographed by Giorgios Provias, to match the musical score written by Mikis Theodorakis. Starting slow and building up to a frenetic climax, it was a triumphant way to end a movie. Quinn had learned a more difficult dance, but sprained his ankle before shooting, so the final product is hardly a Greek dance at all.
When non-Greeks saw it, they thought it was a real Greek dance and soon tourists were demanding to be taught ‘Zorba’s Dance’. Since no such dance existed, everyone was free to do anything vaguely Greek that started slow and ended fast. Google ‘Zorba’ and ‘dance’ and look at the variations.
Someone started calling the dance Syrtaki, which means “little syrto” – a catchy name, even though the dance has nothing to do with a traditional Greek Syrto. It did however give the impression that Syrtaki was a real Greek dance, not just something from a movie.
If you want to dance a Syrtaki there are many printed dance notes you can learn. A better use of energy would be to learn Vari Hasapiko, Hassaposerviko, and fast Hasapiko. Then, instead of trying to perform someone else’s choreography, do what Zorba would do and dance as the spirit moves you!
Start slow, doing variations on Vari Hasapiko, including the basic step if you can. Sometimes the music gradually increases to a tempo suitable for Hassaposerviko. Sometimes it jumps abruptly to fast Hasapiko speed. Sometimes it even slows and speeds several times. Have fun with it. More than any other dance, with Syrtaki there is no right way or wrong way.