Harmonic conjugation in harmonic matroids

We study a generalization of the concept of harmonic conjugation from projective geometry and full algebraic matroids to a larger class of matroids called harmonic matroids. We use harmonic conjugation to construct a projective plane of prime order in harmonic matroids without using the axioms of projective geometry. As a particular case we have a combinatorial construction of a projective plane of prime order in full algebraic matroids.