Atonal Embellishment: An Application of Subaggregate Chains

partition lists provide us with much useful information. This one tells us, for example, that some trichords combine with more than one pentachord and some pentachords with more than one trichord: within the sc 8-20 norm, sc 3-11 combines with four different pentachords and sc 5-21 combines with three different trichords. Sc 8-20 has relatively few such multiple combinations. Other norms have many, and some also have successions of partition pairs that lead away from a given combination of set classes and then loop back. The trichord/pentachord abstract partition list for sc 8-19 [01245689] (see Example 4.2) reveals many such loops. Among the paired set classes are sc 3-3 and sc 5-13, sc 5-13 and sc 3-4, sc 3-4 and sc 5-9, and finally sc 5-9 and sc 3-3, which complete the loop.13 The abstract partition list for the trichord/ pentachord partitions of sc 8-19 is the maximum of fifty-four twopartitions in length because there are no duplicates to be eliminated.