© 2019 by Omer Eilam

This work concerns the realization of an electronic music version of the piece TIERKREIS composed by Karlheinz Stockhausen in 1974. TIERKREIS is a collection of twelve short melodies belonging to the twelve zodiac signs wherein each melody possesses a unique melodic and rhythmic character. So far various arrangements of the composition were published, some by the composer himself, but none of them were made especially for electronic music. The nature of the melodies, namely their focus on a sequence of discreet pitches and rhythmical elements, makes them particularly susceptible to electronic music transformations such as timbral synthesis and spatial movements. The aesthetic choices for this realization were guided by and meant to convey the spirit of the composer.

In 1974 Karlheinz Stockhausen composed TIERKREIS, a cycle of 12 melodies representing the 12 signs of the zodiac. Originally written for music boxes TIERKREIS forms the basis to much of Stockhausen’s later works, most notably in the case of SIRIUS (1976).


The nature of TIERKREIS is unique in the sense that each melody on the one hand has its distinctive characteristics while on the other hand relates to the cycle as a whole, thus achieving a strong compositional unity. This relationship can be more easily understood when examining the diagram below. The first thing to notice is that each melody is based on one important note, called the central tone of the melody. These tones follow the chromatic 12 tones scale, beginning on D# (Aquarius) and ending with D (Capricorn). The tempi also follow a chromatic scale (this time not according to the order of the cycle), with Libra being the slowest at ♩= 71 bpm and Pisces the fastest at ♩= 134 bpm. The two smaller note-heads on each staff represent the highest and lowest tones of each melody, i.e. its range. The durations of each melody also form a 12-member series with a rather narrow range of durations, from 26.66 seconds for Libra to 30.4 seconds for Pisces.

Zooming in from the general diagram Figure 1.2 (Kohl, 1983) shows the series of notes that comprise each melody of TIERKREIS. The central tone is always the first in the series, while the others are called main tones. Each melody utilizes all 12 notes of the chromatic scale while some also include repetition of notes, making the series longer. By examining the different series one can already recognize differences in tendencies. For example, the series of Aquarius is first ascending and then descending in an almost chromatic fashion. On the other hand the melody of Libra begins in the middle range with small  intervals that grow larger in the middle and smaller again towards the end.

To maintain the special relationship discussed above I decided to come up with a few overarching elements that govern the construction of the entire piece. From the perspective of timbral synthesis I decided to limit myself to two synthesis methods which I termed Octaver and Impulser, that repeat in various forms throughout the cycle. I will discuss these two methods in detail in the following chapters. To complement these timbres each melody also contains unique sounds that are identified with it alone and do not occur elsewhere, as in the case of the Tuba in Taurus or the two singers in Pisces. Finally, the sounds of the four classical elements (Air, Fire, Water and Earth) can be heard during several moments in the piece which represent the connections of the zodiac signs to the seasons and triplicities.

With respect to the spatial organization of the sounds a unity is achieved in the form of spatial trajectories within a cubical space, where each melody follows the geometrical path of its corresponding star constellation (as can be seen below). This cube is then projected onto the space of the concert hall. As mentioned above, each of the twelve melodies has a central tone which corresponds to one note of the chromatic scale. This tone is mapped to one of the stars in the constellation and localised to the position of the constellation in the zodiac cycle. For example, the central tone for the Pisces melody is E, located at -30°. The central tone for the Aries melody is F, located at 0°, etc. Once the central tone is localised the orientation of the other stars in the constellation is determined according to their geometrical relation to the chosen star.

At the moment of writing only half of the cycle was completed and performed during my Final Exam Concert in The Institute of Sonology, The Royal Conservatoire, The Hague, in June 2017.

A stereo version of the pieces can be found on soundcloud.

My entire Master's thesis entitled 'Karlheinz Stockhausen's TIERKREIS: An arrangement for electronic music, instruments and voices' can be downloaded from here.