The invention relates to a balance spring (1, 1′) including a first hairspring (3, 3′) the curve of which extends in a first plane, a second hairspring (5, 5′) the curve of which extends in a second plane parallel to the first plane, an attachment member (4, 4′) securing one end of the curve of the first hairspring (3, 3′) to one end of the curve of the second hairspring (5, 5′) so as to form a dual balance spring (1, 1′) in series. According to the invention, the curve of the first hairspring (3, 3′) and the curve of the second hairspring (5, 5′) each include a continuously variable pitch and are symmetrical relative to a straight line (A) parallel to the first and second planes and passing through the median plane of projection of the attachment member (4, 4′) and in that each curve respects the relations. Px(0)=0 and Py(1)=2Py(0) in order to reduce displacements of the centre of mass thereof during contraction and expansion. The invention concerns the field of sprung balance resonators.