|Combine sugar, water, corn syrup and salt in a large heavy pan. Heat and stir until sugar crystals are dissolved, then stop stirring. Bring to a rolling boil and wash down the crystals, then add the cream of tartar. Boil rapidly to the hard crack stage on a candy thermometer.
Pour two-thirds of the syrup out quickly onto a slab or greased flat pan. Pour the rest into a buttered glass pie pan, and do not move until partly set. Turn the edges in on each portion and add flavoring to each - about 6 drops of oil to the large portion and 3 to the small. Add food coloring to the small dish. As soon as possible, start to pull the portion in the large container until pearly-colored. (It will be very hot - butter your hands and set it down when it gets too hot!) Form it into a ball.
Meanwhile gather up the colored portion and form it into a rope and wrap it around the ball. With one person on each end, start to stretch and twist the ball in opposite directions to form a long rope with the traditional stripe. Cut into lengths as necessary. When the desired diameter is achieved, cut and form into canes (roll it on the board to get it smooth). If it gets too cold to work with, put on a wooden breadboard in a warm oven to soften.