there is described a tool as well as a method for machining a workpiece made of a hard material by means of a geometrically determined blade . in order to obtain an improved surface quality of the machined workpiece when machining such a hard and brittle material , a tool is provided which has a cutting angle of less than 10 °. according to the associated machining method , rotational speeds exceeding 1300 rpm are used . there is further described a machine that is to be used in such a tool and is utilized in such a method .