On Partial Ordering

Babbitt 1 has formulated the highly suggestive notion of considering a twelve-tone (or other species of) row as a family of what one might call "protocol pairs" (x,y). Each such pair might be interpreted as a rule: "do not state y before stating x." From such a point of view, one characteristic feature of serial structure is that, given a specified row and distinct objects x and y, either (x,y) or (y,x) will be a protocol pair for the row, but not both. Babbitt then goes further to discuss some other protocol systems, ones in which, given a distinct x and y, neither (x,y) nor (y,x) need necessarily be a protocol pair. Figure 1 below symbolizes one such system.