Intervals

One familiar ``Ligeti motif'' immediately captures attention. The motif:

Figure: Motif widely used by Ligeti in many of his pieces.

21#21

This ``favorite'' motif by Ligeti is the main structural element of his First String Quartett (Métamorphoses nocturnes 1953-54). It is the pc-set 22#22, Forte Code: 4-1, interval vector: 23#23; a highly versatile set.

Figure: String Quartett N.1, First Movement, bars:7-8

24#24

It is interesting to note that this motif is actually the famous B.A.C.H. set.

Figure: Motif B.A.C.H. very widely used in the music history

25#25

This motif is the main building block of the whole 48-voice (micro)polyphony. Below are some examples from its occurrences in the beginning of the examined section. Rhythms are removed to show only the pitches.

Figure: Atmosphères Sample microstructure. Bars: 44-46 Violins I-1 to I-6

26#26

The intervals of the prime form of the set (whole-tone, semi-tone, whole-tone) are used in the form of permutations throughout the section.

It is interesting to note that the whole section (bars: 44-48; up to the re-entrance of the Double Basses at bar: 49, rehearsal letter: I) is composed exclusively with neighbor tones, half and whole.

The few ``jumps'' which occur at bars 48 (cello 10 Violin II-14) or 49 (Violin I-14) are clearly for shifting the line back into the range of the instrument. The shift at the second half of the bar 44, Violin II-12-13 and 14 are all marked imperceptible attack on the score.

At the beginning of the section; bar: 44-45, violins I and II are moving together in a generally descending motion while violas and cellos are set in an upward motion

Figure: Motion of the violins I and II (14 + 14, 28 solo parts). Bars: 44-45. A general descending motion.

27#27

Figure: Overview of bars 44-45. Strings section all solo 48 parts. Violins I and II are in descending motion while violas and cellos are ascending. At the point where the graph ends the ascending motion of the violas and cellos parts will extend to the violins.

28#28

The upward motion of the viola and cello parts creates a ``rising wave motion'' which gradually expands to the violin parts starting from bar 47.

The graph, figure:3.13 (page: ) shows the overall evolution of the sound-cloud.

Figure: A sketch drawing of the evolution from bar 44 to 49. It should be noted that the widening of the boxes is to represent an augmentation in the density of the parts

29#29