The flute part in relation to the superformula
The composer’s comments on the 2 x 11 exercises and 2 pauses in 24 stages, which are found in the CD booklet or in the preface of the score, and are reproduced here, should be read in conjunction with the following text. CD track numbers refer to Stockhausen-Verlag CD 28B.
[The 1st, 2nd, . . . 11th tone in the composer’s comments refer to the pitches of the so-called nuclear Lucifer-formula, the formula reduced only to its succession of 11 pitches with their durations, without the ornaments (Akzidenzien), colored pauses and improvisational elements as they are found in the superformula. In KATHINKAs GESANG, these pitches are transposed to E.]
"The 2 x 11 EXERCISES and 2 PAUSES are a 22-fold expansion of the LUCIFER formula on E."
The formula expansion (stretching of the formula in time) takes place as follows: each exercise elaborates on a fragment of the Lucifer formula, and with this it fills the window of temporal expansion allotted for this fragment. One fragment after another is subject of a different exercise until, step by step, the formula is traversed in its entirety.
As in other instances in LICHT (e.g., the electronic music of WELTRAUM (Outer Space)), in KATHINKAs GESANG Stockhausen has chosen for the interesting option of composing an extreme formula expansion as ‘foreground’, not just primarily as background structure, and here this expansion is a mixture of two things:
1) repeated yet varied presentations of formula fragments in relatively ‘normal’ tempo, stretching over the time alotted for each respective fragment within the extreme 22-fold temporal expansion of the formula
2) an extreme temporal stretching of formula notes, so that formula fragments are not necessarily, or not at all, experienced as melodic elements anymore, but – by overlay of other processes including pitch – are transformed into entirely new melodic entities which form the musical fabric.
In almost half of the exercises each dedicated to a specific formula fragment (and in the "Exit") there is a string of repeats of musical gestures.
These gestures mostly consist of the brief phrase of the Lucifer formula – in more or less original tempo – that is subject of the exercise, and that is repeated with variations (see above). Among others, examples for these are the first stage (CD track 21), with the characteristic eleventuplets that commence the formula, the 18th stage (CD track 38), described in the main text, and the 24th stage (CD track 44) described below.
Alternatively, the string of repeats of musical gestures is overlaid on formula phrases presented in great temporal expansion. One example are the tremolos in the 6th stage (CD track 26). They are laid over the pitches of the melody fragment of bar 5 of the Lucifer formula (click here for the superformula of LICHT *)) which is greatly expanded in time – there is just one pass through the fragment during one and a half minutes. Another example would the chases up and down the scale in the 23rd stage overlaid as a process on the 11th tone of the nuclear Lucifer-formula (CD track 43). The up and down chases come to momentary rests on long notes, which are the 11 tones of the Lucifer formula, first backwards and then, as of the middle of the exercise, forwards (Kathinka Pasveer, personal communication).
*) in the pdf file, bar numbers and markings that indicate the different weekday segments are added by A.M. For maximal resolution, save file to computer/print out.
Interestingly, even though the material, with chases up and down the scale, in the 23rd and 24th stage (CD tracks 43 and 44) appears quite similar, nominally it is derived in a different manner from the Lucifer formula. While in the 23rd stage there are "decelerating and accelerating pulses in the 11th tone" of the nuclear Lucifer-formula (the composer), the basis for the 24th stage is the last phrase of the written-out Lucifer formula (in superformula bars 18 and 19). Also here the score prescribes ‘con molto rubato’.
Other than the varied repeats of gestures, there are essentially two other kinds of elaborations of formula fragments.
The first type, equally important as the varied repeats of gestures in terms of number of exercises that it covers (also almost half of all the exercises), are ‘meditations’ on just one or two tones of the nuclear Lucifer formula (e.g., stages 9-12, 14 [CD tracks 29-32, 34]) that lead to variations of timbre and pitch around these tones – as part of the extreme expansion of formula notes in time, see above. These form most of the extended melodic lines in restricted movement as they are described in the main text. Another melodic line of similar character is built on a longer melodic fragment of the Lucifer formula that is greatly stretched out in time, just like the one in the 6th stage (CD track 26) just described. It is the ascending line of the melody fragment of bar 3 of the Lucifer formula, in the 3rd stage (CD track 23). The ascension in its very slow presentation here is played out artfully in a succession of small gestures that venture ever higher in overall pitch.
The other type consists of what we commonly would describe as singing melody, in contrast to the above ‘meditations’ on one or two tones of the nuclear Lucifer formula. This type is concentrated in just three successive exercises (a relatively brief episode compared to the overall length of the work). There is a single, beautiful melody woven that spans all these exercises (stages 20-22 [CD tracks 40-42]), and this melody fuses phrases, presented in normal tempo, from all formulas (MICHAEL, EVE, LUCIFER) that constitute the triple LICHT formula. Interestingly, even though this varied formula melody is heard, according to the composer’s comments these three exercises are based on only one formula tone each as well – just like the ‘meditations’ on single tones.
The other ‘singing melody’ later heard in RELEASE OF THE SENSES is "a 2-fold expansion of the LUCIFER formula, transposed down a minor second lower to E-flat. 7 signals on high F announce the beginnings of the 7 segments" (the composer). The 7 segments are the weekday segments, see my markings in the superformula. The 2-fold expansion of the formula in this segment is clearly informed by elements ‘learned’ in the previous exercises.
The two long ‘pauses’ (tracks 27 and 33) are a part of the extreme expansion of the Lucifer formula stretching over the entire succession of exercises.
© Albrecht Moritz 2014
Back to main article