However I am puzzled by how Allen Forte created his original list of prime forms. Specifically, how was the order of the sequence determined? For example here is the beginning of the list of four note prime forms:
4-1 [0,1,2,3] 4-2 [0,1,2,4] 4-3 [0,1,3,4] 4-4 [0,1,2,5]
This order cannot be created by simply incrementing the final number. Why does [0,1,3,4] intervene between [0,1,2,4] and [0,1,2,5]?
Another example is the beginning of the list of three note prime forms:
3-1 [0,1,2] 3-2 [0,1,3] 3-3 [0,1,4] 3-4 [0,1,5] 3-5 [0,1,6] 3-6 [0,2,4]
Here it appears that the last note in the sequence is being incremented until it reaches the tritone (6) in [0,1,6]. Subsequently [0,2,3] is omitted as it is a mode of [0,1,3], and [0,2,4] follows as the sixth form in the list.
If the list of three note forms followed the same pattern as the list of four note forms then [0,2,4] would follow [0,1,4] and precede [0,1,5]. This pattern would be to increment the highest note, then the next highest etc., skipping over sets which are not prime. However this is demonstrably not the case.
There must be an ordering principle he used to create the list but I can't see it. Any answers?