Within the recently formulated composite fermion hierarchy the filling fraction of a spherical quantum Hall system is obtained when it can be expressed as an odd or even denominator fraction. A plot of ␯(2S/NϪ1) as a function of 2S for a constant number of particles ͑up to Nϭ10 001͒ exhibits a structure of the fractional quantum Hall effect. It is confirmed that ␯eϩ␯hϭ1 for all particle-hole conjugate systems, except systems with NeϭNh and NeϭNhϮ1. ͓S0163-1829͑97͒03132-9͔