The early sketches for
Trans show that Stockhausen initially considered using the
formula technique he had recently (and very successfully) developed for
Mantra. In the end, however, he decided against it, and settled instead on a simple pitch sequence of thirty-six notes without formal or rhythmic implications, which is "treated with inspired flexibility", first a
twelve-tone row in a sharply falling contour, and then a gradually rising, winding chromatic line. The music consists of three main layers, differentiated by audible characteristics, but in part by the visual aspects as well. The first layer is played back invisibly on tape in the theatre, and consists of the loudly amplified sound of a
loom shuttle crossing the room, left-to-right and right-to-left, at first occurring at nearly periodic intervals of about 20 seconds. Over the course of the piece the intervals between these sounds deviate increasingly from this average, following a systematic process. These sounds mark off segments of the music similar to the
colotomic percussion signals used in some Asian musics, such as Japanese
gagaku. Stockhausen had used this device previously in
Mantra and
Telemusik. There are 33 of these smaller subsections, grouped into six large sections, with a clear evolutionary process. The shuttle-loom sounds also indicate the structural levels, according to whether they occur singly, in pairs, or—at the dividing points between the six main sections of the work—in threes. Each of the four concealed wind groups consists of a bass instrument, which plays either a fundamental tone or a second or fourth harmonic above a virtual fundamental, and four treble instruments that provide a cluster of higher harmonics. For example, the first subsection has the central tone E, initially expressed as a fundamental tone on the second E below the bass clef (41.25 Hz), which is the lowest note of the contrabass. Above this the four flutes of group I play harmonics 14, 15, 16, and 18, giving way to a second chord in the four oboes of group II, playing harmonics 13, 15, 16, and 19. The fundamental note then drops by an octave, so that the sounding bass E becomes a second harmonic, with the four clarinets of group III playing harmonics 16, 17, 21, and 22. The low E then becomes a fourth harmonic of an implied fundamental yet another octave lower, at 10.3 Hz, and the cup-muted trumpets in group IV play harmonics 20, 21, 23, and 28. The behaviour of these harmonic tones, which roughly parallel the bass-tone fundamentals, resembles early medieval
organum, but appears to be modelled on
organ mixture stops, rather than on the formant resonances of the human voice, which remain in the same frequency zone while the fundamentals change below. Because the winds and percussion are concealed from view (apart from the brief appearances of the solo trumpet and the military drummer), Stockhausen wondered whether people could tell the difference if those parts were just played back on tape. Even though he believed that it matter, at least during inspired interpretations, he authorised performances in which the wind-instrument parts are played back from a recording. Understandably, given the economics of rehearsals and tight deadlines, orchestras have overwhelmingly opted for the pre-recorded winds. Such performances are not entirely without their dangers, however. In 1987, Stockhausen criticised one of them for over-amplification, distorted playback, poor balance, and unnaturally strong high frequencies. The technicians in charge complained bitterly that the tape was defective, possibly due to copies made without using the correct noise-reduction equalisation, though they had taken no steps to obtain a better copy. Stockhausen also considered it possible that the inputs to the sound-mixing board may have been over-driven.) ==Reception==