“Kathinkas Gesang” ("Kathinka's Chant") by Karlheinz Stockhausen is a composition for flute and electronic music. With the help of new technological means we are experiencing a new orientation of musical logic in the field of harmonics.
Since my early compositions of electronic music I have always been searching for technical possibilities to produce phase-synchronous spectrums, with controlled phase shifts of individual partial tones. Usually you learn in acoustics that the phase position of partial tones does not matter for hearing, which is only partially true. Some phase rotations achieved by myself in the Cologne Studio in really adventurous ways were very encouraging for continuing research in this direction, (for instance, recording a spectrum on two tape recorders near to each other and pressing the tape on one of them slowly in between the recording and playing heads, and recording the result of the two tapes on a third recorder). You can achieve wonderful spectral “rotations”, in which a spectrum undergoes all possible shifts of its partial tones on itself.
In May 1983 I first wrote for the electronic music on “Kathinka's Chant”, a form scheme with explanations of the symbols. It contains the information for the theoretical programming. This I discussed with Marc Battier, a musical/technical colleague from IRCAM (Paris), with whom I wanted to collaborate.
In December 1983 and August 1984 I realised the electronic music in 2 x 7 days at IRCAM. Battier, using a PDP11 computer, programmed the 4X according to my score.
During the time spent in the studio there came about working notes containing the data for the particulars (chosen by ear) of the timbres and relative dynamics. Finally they were summarised in a four-page synchronisation scheme with 2 x 6 tracks for copying from the 4X onto a 16-track tape. A supplemented form scheme with meter-level numbers is the result of the mix-down in the auditorium “Espacede Projection” from the 16-track tape recorder to an eight-track tape recorder, for the production of a performance master-copy. In this scheme I added the numbering (above each K) of the K1 to K6 sounds.
The most essential aspect is the six-layered space-polyphony of controlled phase-rotations of the harmonic spectra. A new orientation of musical logic in the realm of the harmonic stands out, which was not possible with the technical means available, until now. Simultaneous phase-rotations of phase-synchronous partial-groups of rich overtone spectra (with wholy determined fundamental tones and durations of each rotation, above all, with very long durations and with certain intensity-relations of the partial groups amongst themselves), can be of a beauty never before experienced. The changes of slow phase-rotations have suchan intense temporal logic, that one can accurately follow quarter, third, and, above all, half-phases; while the coinciding of the maxima of all overtones (where a sharp explosion occurs at the point of phase synchronisation) is perceived each time as a liberating new beginning. (Karlheinz Stockhausen)

Comments on the score-example:

At the beginning of each new stage the tracks in which the sound occurs is indicated by roman numerals. The six types of K-sounds are marked with K1 – K 6. Right before the track in which the fundamental and first overtones occur, the pitch of the fundamental tone is notated, marked with an arrow; the note with a staccato dot ist he concluding explosion of the preceding fundamental tone.
The original numbers of the overtones appear in the ellipses (thus in stage 5: track II the 1st – 9th overtone, track III the 10th – 36th, track IV the 37th – 82nd, track V the 83rd – 118th, track VI the 119th – 136th, and track I the 137th – 192nd).
The diagram to the right next to the overtone numbers shows with dots, from which speakers the sound comes
IV III
V II
VI I
A dot in a small rectangle indicates a K-sound

Technical background:

“Kathinkas Gesang” for Flute and Electronic Music, 1983 / 84, 33 min.
Mandalas with steps, hexagon cloth, black curtain (for entrance and exit) behind which a hidden corridor at the left leads outside the hall to the dressingrooms.

Karlheinz Stockhausen (D), born 1928. After his studies at the State Music College (piano and educational music) and at Cologne University (germanistics, philosophy, musicology), he worked as a permanent staff member at the Studio for Electronic Music of WDR Cologne. Besides his research work and composition at the Studio for Electronic Music, Stockhausen studied phonetics and communication research at Bonn University. Apart from his numerous activities as composer, he was co-editor of the serial music magazine “Die Reihe” In 1970 he was nominated Professor for Composition at Cologne Music College, a post he held until 1977.