Abstract of DisclosureA transmission system provided for a bicycle, including a primary transmission sub-assembly having a set of rear sprockets, whose number of teeth, from one sprocket to the next sprocket in the ascending order, varies according to a ratio of the numbers of teeth that is greater than or equal to a value n such as n greater than 1. The invention also includes a control of the transmission system, as well as a bicycle that includes the transmission system and the control for same. The transmission system includes a single chain wheel for driving the chain, associated with a bottom bracket assembly, and a secondary transmission sub-assembly having at least two drive output ratios, whose ratio of the highest drive speed to the lowest drive speed is equal to a value R between 1 and n so as to introduce at least one intermediate transmission ratio between two successive sprockets.