Practical Methods for Identifying Perle Arrays

While both the theory and the practical implementation of twelve-tone tonality in the music of George Perle are challenging, devising a comprehensive method of analysis presents a greater task. Because the six-note "axis-dyad chords" from the array are the fundamental harmonic elements in twelve-tone tonality, the identification of arrays is an essential entryway to analysis. Part of the significance of Perle 's arrays is that they can be derived from the score itself, and that derivation is guided by aural and intuitive clues. Indeed, shouldn't we be skeptical of a system that cannot be deduced from the music? What are the aesthetic consequences of a generative theory so impenetrable that it can only be revealed by consulting the composer's sketches? The analyses comprising this study may not exactly match Perle's original designs, as there are occasional instances of ambiguous or inconclusive array structures. However, tonality is filled with ambiguities as well, as Perle might argue, and the beauty of a passage might well be enhanced by the possibility of multiple interpretations. However, the elegantly self-contained and "verifiable" nature of Perle's pitch mechanisms permit a persuasive case to be made for the analytical schemes shown here. Using short excerpts from the Six New Etudes (1984) for piano, this study aims to decipher Perle's arrays through two principal methods: sum pairings within tetrachords and semitonal surface voice leading between hexachords.1