2 August 2009 - muzikologi

memoire de 3ème cycle d’analyse musicale de mantra de karlheinz stauckhausen – mes. 855-884 [1] – sous la direction du Dr craig ayrey

Historical, stylistic and cultural context
“From the mid-1960s, in West Germany as in many other parts of Europe, cultural thinking was increasingly driven by left-wing ideological agendas”[2] as exemplified in the feminist movement, the opposition to the Vietnam War, the US civil rights movement, or the French student protest of May 1968. In contemporary music, a reaction against Serialism was well under way with the emergence of works based on “repetitive, pulse-driven figures”[3] and of which Steve Reich was becoming the main exponent. Further, with the integrated circuit replacing the cumbersome transistor, “electronic sound generation became the medium in which the ideal of freedom and the aesthetics of the new could be radically realized.”[4] The world wide publishing of pictures of the earth seen from space had underlined the spiritual fragility of humankind, leading to a questioning of the role of ordinary religions. Within that overall context, Stockhausen was pursuing his own unique path of exploration and discovery, whereby “the duty of each new work [is] not just to add to an extant repertory, but to redefine the possibilities of contemporary composition”[5]. Turning away from Catholicism but not from religion itself, “it became increasingly clear that his primary aesthetic motivation was spiritual and cosmic, rather than terrestrially political”[6], drawing from unrelated fields such as information theory, experimental linguistics, evolutionary genetics and quantum mechanics for compositional support.

Compositional intention
“Mantra represents a return to the personal, an assertion of the individual mind rather than a sinking into the collective spirit… the form is more immediately recognisable as stemming from a single idea… It is an expression of Stockhausen’s vibrations within vibrations theory.”[7] That single idea or formula is “a musical object which is recognizable and can be precisely memorized. It must be not too long, not too wide in intervals, not too complicated in rhythm, but it must not be too primitive.”[8] This approach then proceeds to “built entire compositions on the perceivable transformations of one formula into another, or the expansion or condensations of a formula”[9]. Comparing this process to the evolution of life, Stockhausen asserts that “we compose literally whole processes of evolution of forms from sheer matter (which is vibrating masses of vibrations) through processes from simple figures to the most complex, most developed, most personal musical Gestalten, which then meet each other, and we have a new counterpoint in a new way.”[10] The title of the piece denotes an evident emphasis on the spiritual: “The formula is more than a leitmotif or a psychological profile, more than a theme that can be developed further or a generative series: the FORMULA is the matrix and plan of the micro- and the macro-form, while, at the same time, it is the psychic shape and the image of the vibrations of a supra-mental manifestation”[11]. “Mantra, as it stands, is a miniature of the way a galaxy is composed.”[12] This reflects Stockhausen’s preoccupation with “the notion of Geistig-Geistliche [which] emphasizes the balance between reason and religion in Stockhausen’s thinking: to go to the limits of reason (geistig) in order to transcend it towards spirituality (geistlich).”[13] The use of two pianos indicates a return to equal temperament, and this is reinforced by the use of a ring modulator for each piano, whose function is to generate related frequencies. The use of a very precise and traditional notation throughout stems from a concern for the practical aspects of performance, following the disappointment in the way his pieces had been played at the 1970 Osaka World Expo: “where mostly free pieces were played, some of which disgusted me by their amateurish qualities, because the musicians were not always at their best”[14]. In addition, a deep concern about the spatial perception of the resulting sounds is evident in the performance notes and drawings included in the score, with respect to the use and positioning of speakers: “the loudspeakers should be set up in such a way, that from every seat in the hall, one has the impression that the sound is coming only from the directions of the pianos”[15] or the recommended use of towers on which to mount the speakers.

Analytical issues
Although the initial mantra is clearly given in the score, the techniques used to for each of its iterations are not, and my research (JSTOR and Grove Music online) has not come across any poietic material. Concentrating on the last section of the work, it has been a case of seeking patterns (beyond the obvious) which may show a relationship with the initial thirteen notes mantra, either vertically or horizontally. Knowing that Stockhausen had a strong interest for information theory and genetics, it is possible to surmise that he may have used algorithms drawn from those disciplines. What these algorithms may have been remains impossible to determine within the confines of this assignment.

Mantra is for 2 large concert grand pianos, each supplemented by a board with 12 antique cymbals, a wood block, a ring modulator and, for Piano 1 only, a short-wave receiver or a tape recorder with a volume control.

The ring modulator is an electronic device which produces the sum and difference of the frequencies fed into it. This “creates an electronic tonal polarity centred on the sine tone”[16] “such that the notes of the mantra are more or less coloured in proportion to their degree of dissonance with the sine tone. Where the modulating sine tone is of medium or high pitch, additional resonances are created; if, however, the modulating tone is at a low frequency, the intermodulation takes the form of a pulsation agitating the piano tone.”[17] The overall output (pianos and ring modulated tones) are then sent to a set of four speakers. The audience therefore hears a combination of the acoustic sounds of the pianos and its ring modulation treatment.

For Piano 1, each of the antique cymbals is tuned to C#, D, D#, F#, A, A#, B, C, C#, D, G, G (two octaves above Middle C), the wood block being tuned to A5.

For Piano 2, each of the antique cymbals is tuned to A#, B, E, F, F#, G, G#, A, C, D#, E, F (two octaves above Middle C), the woodblock being tuned to C6.

The Mantra itself is based on a thirteen notes series and its inversion (Cf. Fig. 1), which starts and finishes on A. Throughout the work, it is “ornamented, so that each pitch becomes the seed of an expansion process”[18]. It contains all the notes of the chromatic scale. The formal scheme consists of thirteen transpositions of the mantra in twelve different scale forms[19].

“At the outset, it is heard compressed into a fanfare of four chords; following a tremolando on the A, which is the musical compass point on which the entire work turns, it is stated again in open form, but still confined within the space of little more than an octave.”[20]

“By using two pianos, Stockhausen is able to exploit polarities and reciprocities, such as the slowly descending scale of Piano II followed by an equally slow rising scale in Piano I, each accompanied by its modulated mirror image, as in Bar 110.”[21]

Analysis-Last Section: Bar 855-884 (Track 25 on CD).
This section of 30 bars seems to be made of rhythmic oppositions, whereby when one piano plays arpeggiated chords, the other plays single line extended motives (Cf. colour coded Table 1). This is not however systematic as Piano 2 has three bars consisting of both extended motives and chords (bar 855, 859, 872). For both pianos, all arpeggios are to be played upwards from bar 855-866, and downwards for the remaining of the section.

I could not detect any precise pattern as to the rhythmic nature of the extended motives. There is however towards the end a slowing down in the rhythm of Piano 1 (Bar 877-881), with only three notes per bar, framed by Langsam, (slow) Schneller (faster), Rit, Sehr Langsam (very slow) and Rit tempo indications, extending from Bar 875 to 881. Although Bar 881 features sixteen notes, they are to be played very slowly and with a Ritardando towards the end of the bar.

This preceding section is contrasted by two bars of unison tremolo in 32th notes for both cymbals (Bar 882-883), on A (the starting and ending note of the mantra itself), with a return to the intial tempo of Massig Schnell, with a fermata on Bar 883.

In the last bar (Bar 884), Piano 2 enumerate the mantra (in the right hand), as well as its inversion (in the left hand) in four distinct sections (Cf. Table 2), separated by fermatas, at a slow tempo with a Ritardando, while the sound of the cymbal of Piano 1, triggered three bars beforehand, is left to die away (klingen lassen). This could be seen as a kind of recapitulation (in the Sonata Form sense), but with a twist in the number of notes and the note order for the mantra’s inversion:

-In each group, the difference between the number of notes for each hand is always equal to 1.

-There seems to be an interchange of note enumeration order between both hands: 1-2-3 starts Right Hand of Group 1 and Left Hand of group 2, 5-6 starts Left Hand of Group 1 and Right Hand of Group 2, 7-8-9-10 starts Right Hand of Group 3 and Left Hand of Group 4, 11-12-1 starts Left Hand of Group 3 then Right Hand of Group 4.

The chords themselves have a clearer pattern. They are always arpeggiated (upwards then downwards, as noted above), and consists of 2 groups superimposed in close voicing. The intervals of which they are made are quite characteristic (Cf. Table 3) and can be split into two groups:

-Bar 855-866: three note chords, made of a combination of intervals of 5th and/or 4th, with a distance from root note to root note of a 4th or a 5th, except for Bar 866, where the root distance is that of a 2nd.

-Bar 867-880 (when the chords are arpeggiated down): three note chords made of a combination of intervals of 5th and/or 4th, superimposed to four note chords made of intervals 4ths or 5ths and a 2nd, with a distance of root note to root note of a 2nd.

The use of the cymbal does not appear to be structurally significant, and in that section, is only used twice: by Piano Player 1 in Bar 865, and by both piano players in Bar 882-883. The wood blocks are not used at all.

At the time this assignment was written (2007), it is difficult to evaluate the impact this work for acoustic and electronics instruments might have had, as we are so used to the multimedia treatment of sound. There is nowadays an abundance of software plugins capable of manipulating the spectral dimensions of sound in real time, as well as specialist software[22]. At the same time, it is probably Stockhausen’s forays in the electro acoustic domain which sparked a more general interest in such possibilities. In his own words, “Electronic music began in Cologne in 1952-3”[23], and it is likely that Robert Moog, Wendy Carlos and Kraftwerk are in his debt to a considerable extent.

What remains truly original is the application of a systematic and reasoned method to the cross use of acoustic and electronics instruments, as opposed to simply turning the knobs. The effects of the ring modulated tones remain subtle and unobtrusive, supporting and complimenting the pianos, and forcing the ear to question what is actually taking place. It does not announce chaos but a kind of new musical order, possibly bringing to the fore what is actually present in the sympathetic resonance which occur inside a piano’s soundboard, but normally below the threshold of auditory perception. In that sense, Stockhausen can be considered as von Helmholtz’s true heir.

The idea of using a formula which, constantly reiterated, generates new aspects of itself, is also truly original, and prefigures the application of cellular automata to music. Each of the pitches of the mantra seems to be taken as a sonic signifier in itself, rather than being considered as a chain, and the function of creating an effect on the ear comes from the manipulation of their horizontal and vertical permutations. This is not dissimilar to what occur at the genetic human level, whereby different arrangements of the same elements perform different functions.

However, the expected glimpse into the “unified macro-structure of the cosmos”[24] did not occur for me, and I was simply left with an enjoyment of the sounds, rather than an enjoyment of the form itself.

As an aside, it would be highly interesting to recreate a performance of Mantra, using convolution[25] software as well as real time generation of different aspects of the formula, if the form of printouts for the two pianists.



[1] For the CD: Mantra, Andreas Grau & Gotz Schumacher on Pianos, recorded 1993, Wergo, WER 6267-2. For the score: Mantra, ed. Joachim Krist (Kurten:Stockhausen-Verlag).

[2] Toop, Richard: Stockhausen, Karlheinz, Grove Music Online ed. L. Macy (Accessed April 2006), <>.

[3] Griffiths, Paul: Steve Reich, Grove Music Online ed. L. Macy (Accessed April 2006), <>.

[4] Günter Peters & Mark Schreiber in ‘How Creation Is Composed”: Spirituality in the Music of Karlheinz Stockhausen’, Perspectives of New Music, Vol. 37, No. 1. (Winter, 1999), pp. 96-131.

[5] Toop, Richard: Op. Cit.

[6] Toop, Richard: Op. Cit.

[7] Harvey, Jonathan, 1975: The Music of Stockhausen, (London:Faber & Faber), p. 126-128.

[8] Felder, David, 1977: ‘An Interview with Karlheinz Stockhausen’, Perspectives of New Music, Vol. 16, No. 1. (Autumn – Winter, 1977), pp. 85-101.

[9] Felder, 1977, Op. Cit.

[10] Felder, 1977, Op. Cit.

[11] Stockhausen, “Multiformale Musik” Texte 5, 667, quoted by Günter Peters & Mark Schreiber in ‘How Creation Is Composed”: Spirituality in the Music of Karlheinz Stockhausen’, Perspectives of New Music, Vol. 37, No. 1. (Winter, 1999), pp. 96-131.

[12] Cott, Jonathan, 1974: Stockhausen: Conversations with the Composer, quoted by Günter Peters & Mark Schreiber, Op. Cit.

[13] Günter Peters & Mark Schreiber, Op. Cit.

[14] From a conversation with Rudolf Frisius, quoted by Martin Mezger, CD sleeve notes.

[15] Mantra, ed. Joachim Krist (Kurten:Stockhausen-Verlag).

[16] Maconie, Robin, 1990: The Works of Stockhausen (Oxford:Clarendon Press).

[17] Maconie, Robin, 2005: Other Planets, The Music of Stockhausen (London:Scarecrow Press).

[18] Maconie, Robin, 1990: Op. Cit.

[19] Smalley, Roger, Mantra for 2 Pianists by Stockhausen, The Musical Times, Vol. 113, No 1558. (Dec., 1972), pp. 1199-1200.

[20] Maconie, Robin, 1990:, Op. Cit.

[21] Maconie, Robin, 1990: Op. Cit.

[22] Such as the GRM Tools or Max-MSP.

[23] Stockhausen, Karlheinz, 1971: The Origins of Electronics Music, The Musical Times, Vol. 112, No. 1541 (Jul. 1971), pp. 649-650.

[24] Stockhausen, quoted in the CD sleeves notes.

[25] Modern day name for ring modulation.

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