The begin set of a row P is the note set formed by taking the first n notes of P; the end set of P the note set formed by taking the last n notes of P; the set of notes not in the begin set or end set is the midset of P.

There are two cases of this kind of combinatoriality:

Case 1. The begin set remains the same under some transformation X. Then the row P will produce combinatoriality with the row RXP.

Case 2. The end set under some transformation X is the same as the begin set.

Then the row P will produce combinatoriality with the row XP. Hexachordal combinatoriality is just a special case of 2-row combinatoriality where the begin set and end set are hexachords (so the midset is empty). Note also that X can be any one-to-one and onto pitch-class transformation whatsoever.

If a row has a begin set that satisfies case 1 under TmI, and case 2 under two transformations, Tn and TpI, then the row is all-combinatorial. The set-classes that fulfill these requirements are the 2-row all-combinatorial source-sets. We know that there are 6 hexachordal source-sets; there are also 5 dyadic, 5 trichordal, 14 tetrachordal, and 9 pentachordal all-combinatorial source-sets.