Stockhausen's Rhythm System


• uses system similar to that of Structures 1a

Studie I


• uses a system based on ratios derived from the harmonic series

• serial procedure used to determine elements of additive synthesis of sine-wave tones
1) series of frequencies is generated from an original
2) original frequency is divided by a second series of frequencies of ratios derived from the harmonic series
3) resulting collection is subjected to the same process
4) this process results in a tone table; tones grouped into ‘groups’, consisting of five intervals each

"Group Form"

a) tone mixtures (vertical tone groups) make up
b) sequences horizontal sound groups; in turn make up
c) structures (horizontal and vertical sequence groups); groups form a unified proportion of the whole composition

Rhythm (time and structure)

• durations of each mixture are measured as 1/10 the frequency of the loudest tone

• each tone may be preceded or followed by a rest, determined by a six-member row; each divided by 6; provides sound-to-rest ratios (6/6 = no rest)

• durational structures are organized similarly:
1) tone mixture durations proportional to frequency of loudest tone;
2) sequence duration is sum of tone mixtures;
3) structure duration equal to sum of sequence duration;
4) duration of piece is sum of structures