Abstract: A method and apparatus for winding yarn to produce a wound yarn package having a variable density profile. The variable density profile in the wound yarn is produced by variably tensioning the yarn during the winding process by an electrical apparatus which is responsive to a programmed control signal to provide variable tension on the yarn. The density profile thus produced is preferably a progressively variable density profile. In a preferred embodiment, the method is carried out with a precision winding machine with an electromagnetic tensioner. A controlled sequence of control signals is applied to the tensioner to provide a correspondingly varying tension on the yarn. The application of controlled tensioning to dyeing beams by progressively increasing tensioning warping yarn along the length of the beam has also shown improved results in resisting dye liquor channeling and blowout and permitted a beam geometry with a greater capacity.