''Studie II'' () is an
electronic music
Electronic music is a Music genre, genre of music that employs electronic musical instruments, digital instruments, or electronics, circuitry-based music technology in its creation. It includes both music made using electronic and electromech ...
composition by
Karlheinz Stockhausen
Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groundb ...
from the year 1954 and, together with his ''
Studie I'', comprises his work number ("opus") 3. It is
serially organized on all musical levels and was the first published
score
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*Test score, the result of an exam or test
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* Score Digital, now part of Bauer Radio
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of electronic music.
History
The composition was provisionally titled ''Bewegungen'' (Motions), but the name was later changed to ''Studie II''. It was commissioned by what was then the
NWDR
Nordwestdeutscher Rundfunk (NWDR; ''Northwest German Broadcasting'') was the organization responsible for public broadcasting in the German Länder of Hamburg, Lower Saxony, Schleswig-Holstein and North Rhine-Westphalia from 22 September 1945 to ...
, in whose Studio für elektronische Musik in
Cologne
Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of the German western state of North Rhine-Westphalia (NRW) and the fourth-most populous city of Germany with 1.1 million inhabitants in the city proper and 3.6 millio ...
the piece was created. The world premiere took place in Cologne on 19 October 1954 in the concert series Musik der Zeit, together with Stockhausen's ''Studie I'' and works by
Henri Pousseur
Henri Léon Marie-Thérèse Pousseur (23 June 1929 – 6 March 2009) was a Belgian classical composer, teacher, and music theorist.
Biography
Pousseur was born in Malmedy and studied at the Academies of Music in Liège and in Brussels from 1947 to ...
,
Karel Goeyvaerts
Karel August Goeyvaerts (8 June 1923 – 3 February 1993) was a Belgian composer.
Life
Goeyvaerts was born in Antwerp, where he studied at the Royal Flemish Music Conservatory; he later studied composition in Paris with Darius Milhaud and analys ...
,
Herbert Eimert Herbert Eimert (8 April 1897 – 15 December 1972) was a German music theorist, musicologist, journalist, music critic, editor, radio producer, and composer.
Education
Herbert Eimert was born in Bad Kreuznach. He studied music theory and compo ...
, and
Paul Gredinger Paul Gredinger (27 July 1927 – 6 October 2013) was a Swiss architect. Gredinger was one of the leading figures in the German advertising scene. .
In contradistinction to
musique concrète
Musique concrète (; ): " problem for any translator of an academic work in French is that the language is relatively abstract and theoretical compared to English; one might even say that the mode of thinking itself tends to be more schematic, wit ...
, Stockhausen wanted no longer "to use any electronic acoustic sources, with the sound spectra already built up (Melochord, Trautonium), but only produced from the pure tones of a frequency generator ("pure" notes without overtones)" therefore using neither electroacoustic instruments nor other found sounds. The ideal was to produce each sound synthetically and thus separately determined in its details: "The conscious organization of music extends to the micro-acoustic sphere of the sound material itself".
He had previously tried out sound synthesis with pure tones in ''Studie I''. However, an aesthetic problem arose: "Instead of a fusion of the pure tones into new, more complex sounds, the individual pure tone components appeared separately audible and are easily identifiable. Thus, the impression develops of chords formed from pure tones instead of a new sound quality. On the other hand, the individual pure tones receive their own sound quality owing to their easy identifiability, about comparable to the specific sound of a simple music instrument somewhere between a flute and special pipe-organ registers".
Materials and form

Stockhausen's two ''Elektronische Studien'' are amongst the earliest examples of composition with what he called "groups", in contrast to the earlier concept of
punctualism
Punctualism (commonly also called "pointillism" or "point music") is a style of musical composition prevalent in Europe between 1949 and 1955 "whose structures are predominantly effected from tone to tone, without superordinate formal concepti ...
or "point composition", in works like ''
Kreuzspiel
(Crossplay) is a composition by Karlheinz Stockhausen written for oboe, bass clarinet, piano and four percussionists in 1951 (it was later revised for just three percussionists, along with other changes). It is assigned the number 1/7 in the comp ...
''.
The idea at the core of ''Studie II'' was the decision to extrapolate everything from the number 5. Five main sections are each divided into five subsections, and each subsection contains five groups consisting of one to five sounds, called "tone mixtures". Each of these tone mixtures is constructed as five equally spaced, reverberated
sine tone
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in m ...
s. The width of the tone mixtures remains constant within each group, but changes from group to group in five widths derived from an underlying scale. For the pitches, Stockhausen built a scale in which the interval between successive steps consists of the frequency proportion