page_title: Telemusik
section_title: Form
hierarchical_section_title: Telemusik / Form
caption_attribution_description: Klangschale / Singing bowl. Bought in Heidelberg.
context_page_description: Telemusik is an electronic composition by Karlheinz Stockhausen, and is number 20 in his catalog of works.
context_section_description: The principal forming element of Telemusik is duration (Kohl 2002, 100). The work consists of thirty-two structures, called "moments" by the composer (Stockhausen 1971a, 77). Each begins with the stroke of a Japanese temple instrument. These six instruments are each associated with a moment duration according to their natural decay time: the taku (a high-pitched sandalwood clapper with almost instantaneous decay) with the shortest duration, the bokushō (a larger clapper with longer decay time) with the next longer duration, then a hollow-sounding mokugyo ("wooden fish"), higher and lower-pitched cup gongs called rin and keisu, ending with a group of four large temple bells for the longest of the six durations used (Kohl 2002, 102). The durations in seconds of these moments are taken from the six Fibonacci numbers between 13 and 144. The numbers of occurrences of these steps are also drawn from Fibonacci numbers, from 1 to 13 (Erbe 2004, 132; Kohl 2002, 100). The longer the step, the fewer times it occurs, and vice versa:
  However, the actual duration values used in the score are systematically varied above these base values so that from longest to shortest there are 1, 2, 3, 4, 3, and 2 variants (144, 89/91, 55/56/57, 34/35/36/37, 21/22/23, and 13/14). In order to achieve the specified numbers of moments, the variants of the shorter values are duplicated, again according to the Fibonacci series (13 × 5, 14 × 8; 21 × 3, 22 × 3, 23 × 2; 34 × 2, and the rest with single instances) (Kohl 2002, 101).
  Each of the 32 moments is then subdivided into from two to thirteen subsections, again using Fibonacci numbers, in most cases with some values repeated. For example, one of the composer’s sketches (reproduced in Erbe 2004, 146) shows that moment 22, with a total duration of 91 seconds, has subdivisions of 34 + 21 + 13 + 8 + 5 + 3 + 2 + 1 + 2 + 1 + 1, though not used in that order in the composition itself (Toop 1981, 190–91).
  The moments' durations are distributed over the length of the composition as follows (Kohl 2002, 103):
  The "extra" moment marked "7 Fortsetzung" (7 continued) is an insertion which repeats the long composite of descending glissandos from the two preceding moments, ring modulated with a 12,000 Hz sine wave, briefly "notched" with a dip to 2,000 Hz at the point corresponding to the division between moments 6 and 7. This insert is marked at the beginning by a stroke on a Japanese temple instrument found nowhere else in Telemusik: a gong called a kane (鐘) (Kohl 2002, 104–05). Of the six resulting structural layers, or "formant rhythms" (Harvey 1975, 101) four—the second, third, fourth, and fifth—are internally symmetrical. However, their centres of symmetry, marked in the table by the symbol "↕", do not coincide, so that the composite structure is not itself symmetrical. The keisu layer is centred on the overall form, while the rin, mokugyo, and bokusho layers are phase-shifted by incrementally increasing distances to the left, right, and left again (Kohl 2002, 102).
  Moments are often more or less casually grouped together into successions of two or more moments, similar to the Hauptgruppen Stockhausen conceived as early as Klavierstück I in 1952 (Kohl 2002, 110). Opinions on these groupings differ somewhat. Robin Maconie describes moments 15, 16 and 17 as a "structural episode" consisting of a sustained "resonance of consciousness", superimposing and transforming material taken from moments 1, 4, 5, 6, 7, 9, and 14 (Maconie 1976, 211–12; Maconie 2005, 267). Others variously regard as groupings:
  moments 1–3 (Fritsch 1999, 177–78; Kohl 2002, 110)
  moments 5–7 Forts., 10–11, 17–23, and 27–31 (Kohl 2002, 110)
  moments 12–14 and 24–26 (Erbe 2004, 147–48; Kohl 2002, 110)
  moments 16–21, 22–23, and 27–30 (Erbe 2004, 147–48).
caption: A Japanese rin marks the beginning of moments 8, 16, and 24.
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