Stockhausen's Rhythm System
Kreuzspiel
• uses system similar to
that of Structures 1a
Studie I
Pitch/timbre
• 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