Broken and Unbroken Interval Cycles and Their Use in Determining Pitch-Class Set Resemblance

Abstract

HE THIRD SONG of Dallapiccola's Quattro Liriche di Antonio Machado ends with a series of six-note chords in the piano part (Example 1).1 The first chord, repeated and held through measure 80, is a member of set class (SC) 6-Z28 [013569]; the second chord is its literal complement, a member of SC 6-Z49 [013479] (they form the two halves of a twelve-tone series). The third and fourth distinct chords (from the end of measure 81 to the end of the excerpt) reverse this pattern at a different transpositional level. While these chords types all have the same intervalclass (ic) content (as is the nature of Z-related SCs), the subsets and inter-

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