Orthogonal interval class to a 7-limit temperament

Here's a trick to finding that, starting from two monzos for a comma
basis. If |a b c d> is a 7-limit monzo, then |-b-c-d b c d> is the
corresponding class representative perpendicular to |1 1 1 1>. Now
take either the triple wedge product of |1 1 1 1> (represeting 210)
with the
two class representatives, or the determinant of the three with the
monzo of indeterminants |a b c d> (ths comes to the same thing.) The
resulting val <w x y z|, can be cleared of common factors and
converted to the corresponding monzo |w x y z>, which now is the class
representative for the intervals perpendicular to the temperament.

This all works because the 7-limit lattice in 3-space of classes can
be identified with the lattice in 4-space of class representatives
perpendicular to |1 1 1 1>.