  A projective rectangle is like a projective plane that has different lengths
in two directions. We develop harmonic conjugation in projective rectangles. We
construct projective rectangles in some harmonic matroids (matroids where
harmonic conjugation is defined on every collinear point triple), such as
Desarguesian projective planes of finite characteristic, by harmonic
conjugation from extended lift matroids based on finite fields. Similar results
follow for countable fields with characteristic $0$. We also show that
projective rectangles are almost harmonic matroids.
