Neutron multiwave interference phenomena based on Ramsey's resonance method of "separated oscillating fields" are studied. The neutron passes through N successive resonant coils (with DC field B₀) which flip the neutron spin with a probability ρ (written as ρ = sin²ξ) smaller than 1. These coils are separated by path lengths l over which a homogeneous field B₁ is present. Because the spin-flip probability ρ is smaller than 1, the number of states is doubled after each flipper, so as to produce 2^N neutron waves at the end of the set-up. The phase difference between any pair of waves is a multiple of a "phase quantum" equaled to the line integral over length l of the field difference B₁ - B₀. Highly regular patterns of the quantum mechanical probability R in (B₁,ξ)-space appear due to pair interference between individual waves.