The tone row f can be constructed from its first segment, if all the q segments of f can be constructed from the first segment by applying suitable combinations of transposition, inversion and retrograde.
(f(1),…,f(d)), (f(d+1),…,f(2d)), …, (f((q-1)d+1),…,f(12))...
The tone row f is called a derived row if it can be partitioned into 12/d segments, where d∈ {2,3,4,6}, so that f can be constructed from its first segment.
If f is a derived row, then all elements in the orbit (D12 × ⟨R⟩)(f) are derived rows. We want to generalize this notion for D12 × D12-orbits.
The D12 × D12-orbit of f is called derived, if there exist representatives which are derived rows. Thus, the segment from which the row f can be constructed need not be the segment (f(1),…,f(d)). It can be any segment of the form (f(1+j),…,f(d+j)) for 0≤ j<d.
In order to search for derived rows decide which values of d are interesting. It is possible to choose any combination of the four possible values of d and to indicate by choosing AND/OR/EXACT whether the tone rows must be derived from each of these d's, at least one of these d's, or exactly from all these d's and no other d's.