Mantra is a composition by the German composer Karlheinz Stockhausen. It was composed in 1970 and premiered in autumn of the same year in Donaueschingen. The work is scored for two ring-modulated pianos; each player is also equipped with a chromatic set of crotales (antique cymbals) and a wood block, and one player is equipped with a short-wave radio producing morse code or a magnetic tape recording of morse code. In his catalogue of works, the composer designated it as work number 32.
This work involves the expansion and contraction of a counterpointed pair of melodies, which the composer calls a "formula" (Stockhausen 2003, 3 and 6). In this particular work (the first of a long succession of compositions to use formula technique), Stockhausen chose the term "mantra" in order "to avoid the words theme, row or subject, as in a fugue" (Stockhausen 2003, 2), and "Mantra" also became the title of the entire work. In Mantra, the two-strand formula is stated near the outset of the piece by piano I. According to the composer, the mantra "has thirteen notes, and each cymbal sound occurring once in the piece indicates the large sections—you hear the cymbal whenever a new central sound announces the next section of the work" (Cott 1973, 220–22). Although "the cymbals have the same pitches as the mantra and can thus mark the 13 form cycles of the two pianists … they are not identical", and "there are also some sections in which a larger number of cymbal strokes occurs” (Stockhausen 2003, 9). Though this mantra recurs constantly, the structure of the composition is not a theme and variations as found in classical composers such as Beethoven and Bach, because the material is never varied, only expanded and contracted (both in duration and in pitch) to different degrees; not a single note is ever added, it is never "accompanied" or embellished (Stockhausen 1978, 155). The comparatively strict predetermination of the form plan is occasionally broken and altered through the use of insertions, additions, and small deviations and exceptions (Blumröder 1976, 102). Near the end of the composition there is an extremely fast section that is a compression of the entire work into the smallest temporal space; in this section, all of the expansions and transpositions of the mantra formula are summarized as fast as possible and in four layers (Stockhausen 1978, 155).
The "mantra" (melody formula) is made of an upper and lower voice; it is divided temporally into 4 segments with rests of 3, 2, 1, and 4 crotchets' duration following the segments. The 13 notes of the mantra's upper voice form a 12-tone row where the 13th note returns to the first note A. The lower voice consists of an intervallic inversion of the upper voice with transposed segments: the first segment of the lower voice corresponds to the inversion of second segment of the upper voice and vice versa; similarly, the third and fourth segments in the inverted voice are also exchanged (Blumröder 1976, 96–97).
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