Aspects of pitch organization in György Ligeti's Piano etude no. 8, Fém
AbstraktiGyörgy Ligeti’s Piano Étude No. 8, Fém, is governed by two simultaneous and continuously repeated rhythmic patterns, one of which is for the right hand, the other for the left one. The patterns evoke the medieval concept of Talea, a constant configuration of durations whose repetitions introduce a recognizable element to the piece it is used in. The two Fém taleae are of different lengths, meaning that their starting points coincide only after several cycles. As far as pitch organisation is concerned, Fém contains an element that is as dominant as the Talea patterns are in the realm of rhythm, namely, parallel fifths. It is the purpose of this study to examine how the fifths, and harmonic materials derived from them, govern the pitch organisation of the piece. It is suggested that the fifths form two distinct “harmonic families”. The first one contains collections of notes where the elements can be arranged so that there is a perfect fifth between all pairs of consecutive elements. "Family members" can contain from 2 to 12 elements. The second family contains collections of notes where the elements can be arranged so that in the succession of intervals between pairs of consecutive notes, tritones and fifths alternate. Family members can contain from 3 to 12 elements. Furthermore, the ordering and registral positioning of the elements is free: the family membership of the collection is preserved even if the elements are not in a "pure" interval stack order – the collections are not defined to be chords or other pitch-space objects, but pitch-class sets. It is then examined how the two harmonic families can be utilised in articulating elements of the pitch organization. Among the viewpoints are the relations between the Taleae and the harmonic families, the transpositional relations between family members in controlling the level of dissonance, harmonic-family saturation, completion strategies of incomplete family members, and simultaneous linear instances of family members. The study uses both traditional and pcset-theoretical terminology.