Example 12 from Stockhausen's article "... wie die Zeit vergeht ...", illustrating with a version of the series from Gruppen für drei Orchester that, "if you start from the intervals of a proportion series, then with every step forward the register of each duration is also already chosen".[1] There are "a number of basic durations, indicated in metronome marks and corresponding with the pitch proportions within the series, reaching far as the octave positions (basic duration units)",[2] or "a duration scale which changes its 'time register' ... corresponds to a twelve-tone scale that extends over more than one octave".[3]
Gruppen (German: Groups) for three orchestras (1955–57) is amongst the best-known compositions of German composer Karlheinz Stockhausen, and is Work Number 6 in the composer's catalog of works. Gruppen is "a landmark in 20th-century music ... probably the first work of the post-war generation of composers in which technique and imagination combine on the highest level to produce an undisputable masterpiece".[4]
