Stockhausen Tierkreis Score Pdf

Stockhausen into a single score. Nevertheless, the composer has published certain details of his working methods. The following three examples taken from Stockhausen’s notes to his CD of Gesang offer a glimpse into the organization of the piece’s final structure. Example 1 lists the twelve types of elements present in Gesang’s final. TIERKREIS (playing score) Composer: Stockhausen, Karlheinz (1928-2007) Instrumentation: melody + accompaniment: Publisher Ref: Stock: This edition includes an Introduction, Analytical Description and Performance Instructions. This essay analyzes Stockhausen Studie II: Elektronische Musik (1954), focusing on his study of additive synthesis in electronic music. While the first study, Studie I: Elektronische Musik (1953), employs pure sine waves utilizing overtones, the. On November 14th 1994 the Stockhausen Foundation for Music was ratified as a non-profit foundation having as its purpose 'the advancement of musicology including the stimulation of music culture based on the creative oeuvre of Professor Karlheinz Stockhausen' (paragraph 2.2 of the foundation statutes). The Stockhausen Foundation for Music is in a position to fulfil this mandate due to the. Stockhausen Karlheinz Pieces Tierkreis with a inusual partiture by tausigalkan in Types School Work, karlheinz e tierkreis.

• Stockhausen Tierkreis Score Pdf 2017
• Stockhausen Tierkreis Score Pdf Sheets

Carré (Square) for four orchestras and four choirs (1959–60) is a composition by the German composer Karlheinz Stockhausen, and is Work Number 10 in the composer's catalog of works.

History[edit]

Carré was commissioned by the Norddeutscher Rundfunk (NDR) in Hamburg. The essential ideas occurred to Stockhausen in November–December 1958 while on a tour of the United States where, during hours spent each day flying from one location to another, he experienced the slowest temporal rates of change of his life. The work was composed in 1959–60, in collaboration with Stockhausen’s assistant Cornelius Cardew, and was premiered on 28 October 1960 in the Festival Hall of the 'Planten un Blomen' Park in Hamburg, as part of the NDR's concert series Das Neue Werk, with the NDR Chor und NDR Sinfonieorchester, conducted by Mauricio Kagel (orchestra I), Stockhausen (orchestra II), Andrzej Markowski (orchestra III), and Michael Gielen (orchestra IV) (Stockhausen 1964, 102–103). The score is dedicated to the former director of Das Neue Werk, Herbert Hübner.

Material and form[edit]

Carré is a serial composition in which (together with the concurrently composed Kontakte) Stockhausen for the first time treated spatial distribution on the same level of structural importance as properties such as pitch, rhythm, timbre, dynamics, register, density, and others (Stockhausen 2009, 229).

Stockhausen groups Carré with Kontakte (1958–60) and Momente (1962–64/69) as representatives of moment form, in which he tried

to compose states and processes in which each moment is a personal, centred one, that can exist on its own and, as something individual, can also always be related to its surroundings and to the whole; something in which everything that happens does not pursue a determined course from a defined beginning to an inevitable end. (Stockhausen 1963b, 250)

A large orchestra of 80 players is divided into four orchestral units, each of approximately the same scoring and each with its own conductor. A mixed choir of between 12 and 16 singers is attached to each orchestra (Stockhausen 1964, 103).

Carré unfolds 101 'moments' with durations varying from 1.5 to 90 seconds, each of which is characterised by one or several notes and chords (Rigoni 1998, 189). However, Stockhausen originally planned 252 sections in his draft form scheme, where eight basic categories of sound are arrayed, each with four levels (Toop 2005, 172):

1. Type: the four solo instruments used to furnish each of the four orchestras with a characteristic timbre: cimbalom, vibraphone, piano, and harp
2. Attack: four 'attack transient' percussion instruments, also used to differentiate the four orchestras: Indian bells, drums, Alpine cowbells, and cymbals
3. Gestalt variation: four parameters within which transformations are to occur: rhythm, 'height', timbre, and dynamics
4. Density: number of notes present, from one to four
5. Register: four principal octave registers
6. Duration: four generic values from 'short' to 'as long as possible'
7. Amplitude: four basic dynamic levels, notated in the sketch (but not the score) with numerals
8. Colour: four basic timbres: voices, strings, woodwinds, and brass

In contrast to the complex interrelationships of these eight sound categories, the underlying pitch structure of Carré is so simple that Stockhausen was able to write it out on a single sheet of music paper (Toop 2005, 172). The basic pitch series used throughout the work is

Stockhausen Tierkreis Score Pdf 2017

The regular melodic succession of this all-interval row is obscured compositionally, however, through the grouping of some notes into chords—e.g., in the first section, one three-note chord, F♯ B G, and one two-note chord, B♭ A♭ (Frisius 2008, 125).

Instrumentation[edit]

Orchestra I[edit]

• 1 Alto Flute (doubling flute)
• 1 Oboe
• 1 Bass Clarinet in B♭
• Tenor Saxophone in B♭
• 1 Horn (high, in F)
• 1 Trumpet in D
• Bass Trumpet in B♭
• Bass Trombone
• SATB choir (2 or 3 voices per part)
• Piano
• 2 Percussionists:
  • 2 Tomtoms and 1 Bongo
  • 3 Alpine Cowbells [Almglocken]
  • 1 Bass Drum (as large as possible)
  • 1 Snare Drum (very bright)
  • Indian Bells
  • Suspended Cymbals (large and thin)
  • 1 Hihat (as large as possible, thin cymbals)
  • 1 Gong (as large as possible)
  • 1 Tamtam (as large as possible)
• 4 Violins
• 2 Violas
• 2 Cellos

Orchestra II[edit]

• 1 Flute
• 1 Cor anglais
• 1 Clarinet in B♭
• 1 Bassoon
• 2 Horns (1 high, 1 low)
• 1 Trumpet (in C)
• 1 Tenor Trombone
• SATB choir (2 or 3 voices per part)
• Vibraphone
• 2 Percussionists:
  • 2 Tomtoms and 1 Bongo
  • 3 Alpine Cowbells [Almglocken]
  • 1 Bass Drum (as large as possible)
  • 1 Snare Drum (very bright)
  • Indian Bells
  • Suspended Cymbals (large and thin)
  • 1 Hihat (as large as possible, thin cymbals)
  • 1 Gong (as large as possible)
  • 1 Tamtam (as large as possible)
• 4 Violins
• 2 Violas
• 2 Cellos

Orchestra III[edit]

• 1 Oboe
• 1 Clarinet in B♭
• 1 Baritone Saxophone in E♭
• 1 Bassoon
• 1 Horn (low)
• 1 Trumpet (in C)
• 1 Alto Trombone
• 1 Bass Tuba
• SATB choir (2 or 3 voices per part)
• 1 Cimbalom (amplified)
• 2 Percussionists:
  • 2 Tomtoms and 1 Bongo
  • 3 Alpine Cowbells [Almglocken]
  • 1 Bass Drum (as large as possible)
  • 1 Snare Drum (very bright)
  • Indian Bells
  • Suspended Cymbals (large and thin)
  • 1 Hihat (as large as possible, thin cymbals)
  • 1 Gong (as large as possible)
  • 1 Tamtam (as large as possible)
• 4 Violins
• 2 Violas
• 2 Cellos

Orchestra IV[edit]

• 1 Flute
• 1 Clarinet in A
• 1 Alto Saxophone in E♭
• 1 Bassoon
• 2 Horns (1 high, 1 low)
• 1 Trumpet (in C)
• 1 Tenor Trombone
• SATB choir (2 or 3 voices per part)
• 1 Harp (amplified—the harp part may be supplemented by an amplified harpsichord)
• 2 Percussionists:
  • 2 Tomtoms and 1 Bongo
  • 3 Alpine Cowbells [Almglocken]
  • 1 Snare Drum (very bright)
  • Indian Bells
  • Suspended Cymbals (large and thin)
  • 1 Hihat (as large as possible, thin cymbals)
  • 1 Gong (as large as possible)
  • 1 Tamtam (as large as possible)
• 4 Violins
• 2 Violas
• 2 Cellos

Discography[edit]

• 1968. WDR Symphony Orchestra, Cologne, conducted by Karlheinz Stockhausen, Andrzej Markowski, Mauricio Kagel, and Michael Gielen. Recorded May 1965; released with Stockhausen’s Gruppen on Deutsche Grammophon DG 137 002 (LP), DG921022 (Cassette). [N.p.]: Polydor International GmbH.
  • reissued under the same LP disc number, in the first set of Deutsche Grammophon’s Avant Garde series. [Hamburg]: Deutsche Grammophon Gesellschaft, ca. 1972.
  • reissued on reel-to-reel 7½ ips tape, as DGC 7002. Elk Grove Village, Illinois: Ampex/Deutsche Grammophon, ca. 1974.
  • reissued on Stockhausen Complete Edition CD 5. Kürten: Stockhausen-Verlag, 1992.

References[edit]

• Frisius, Rudolf. 2008. Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen, 'Es geht aufwärts'. Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International. ISBN978-3-7957-0249-6.
• Rigoni, Michel. 1998. Stockhausen: ... un vaisseau lancé vers le ciel, 2nd edition, revised, corrected, and enlarged. Lillebonne: Millénaire III Editions. ISBN2-911906-02-0.
• Stockhausen, Karlheinz. 1963a. 'Momentform'. In his Texte zur Musik, vol. 1, 1edited by Dieter Schnebel, 89–210. DuMont Dokumente. Cologne: Verlag M. DuMont Schauberg.
• Stockhausen, Karlheinz. 1963b. 'Erfindung und Entdeckung'. In his Texte zur Musik, vol. 1, edited by Dieter Schnebel, 222–58. DuMont Dokumente. Cologne: Verlag M. DuMont Schauberg.
• Stockhausen, Karlheinz. 1964. 'Nr. 10: Carré (1959/60), für vier Orchester und Chöre'. In his Texte zur Musik, vol. 2, edited by Dieter Schnebel, 102–103. DuMont Dokumente. Cologne: Verlag M. DuMont Schauberg.
• Stockhausen, Karlheinz. 1971. 'Gruppen und Carré'. In his Texte zur Musik, vol. 3, edited by Dieter Schnebel, 22–34. Cologne: Verlag M. DuMont Schauberg. ISBN3-7701-0493-5.
• Stockhausen, Karlheinz. 2009. Kompositorische Grundlagen Neuer Musik: Sechs Seminare für die Darmstädter Ferienkurse 1970, edited by Imke Misch. Kürten: Stockhausen-Stiftung für Musik. ISBN978-3-00-027313-1.
• Toop, Richard. 2005. 'Form Schemes'. In his Six Lectures from the Stockhausen Courses Kürten 2002, 166–207. Kürten: Stockhausen-Verlag, for the Stockhausen Foundation for Music. ISBN3-00-016185-6.

Further reading[edit]

• Cardew, Cornelius. 1961a. 'Report on Stockhausen's Carré' [Part 1]. The Musical Times 102, no. 1424 (October): 619–22.
• Cardew, Cornelius. 1961b. 'Report on Stockhausen's Carré: Part 2'. The Musical Times 102, no. 1425 (November): 698–700.
• Cott, Jonathan. 1973. Stockhausen: Conversations with the Composer. New York: Simon and Schuster. ISBN0-671-21495-0.
• Driver, Paul. 2010a. 'Works of Modern Composers That Move You'. The Sunday Times (28 March).
• Driver, Paul. 2010b. 'Labours of love; Two Contrasting Concerts of Work by Modern Masters Make Paul Driver Mad with Joy'. The Sunday Times (28 March): 30.
• Harvey, Jonathan. 1975. The Music of Stockhausen: An Introduction. Berkeley and Los Angeles: University of California Press.
• Heyworth, Peter. 1971. 'One of the Outstanding Scores of Its Time'. New York Times (28 November): D15.
• Kelsall, John. 1975. 'Compositional Techniques in the Music of Stockhausen (1951–1970)'. PhD diss. Glasgow: University of Glasgow.
• Kurtz, Michael. 1992. Stockhausen: A Biography, translated by Richard Toop. London and Boston: Faber and Faber. ISBN0-571-14323-7 (cloth) ISBN0-571-17146-X (pbk).
• Maconie, Robin. 2005. Other Planets: The Music of Karlheinz Stockhausen. Lanham, Maryland, Toronto, Oxford: The Scarecrow Press, Inc. ISBN0-8108-5356-6.
• Stockhausen, Karlheinz. 1998. 'CARRÉ—Ergänzung 1986 zum Vorwärt der 4 Partituren', in his Texte 7, selected and assembled by Christoph von Blumröder, 41–49. Kürten: Stockhausen-Verlag. ISBN3-00-002131-0.
• Wörner, Karl H. 1961. 'Current Chronicle: Germany'. The Musical Quarterly 47, no. 2 (April): 243–47.

External links[edit]

Media[edit]

Mantra is a composition by the German composer Karlheinz Stockhausen. It was composed in 1970 and premiered in autumn of the same year at the Donaueschingen Festival. 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.

History[edit]

Stockhausen had been interested for several years in writing something for the Kontarsky piano duo, and by early 1969 he had become determined to do so (Blumröder 1976, 94; Toop 1986, 194). On a flight from the Northeastern United States to Los Angeles in September 1969 or shortly before, he had sketched 'a kind of theater piece for two pianos' titled Vision, and in March 1970 began to work out a score, but broke off after just three pages (Cott 1973, 222–23; Toop 1986, 195, 197). During an automobile trip from Madison, Connecticut to Boston, a melody came to Stockhausen, along with the idea of expanding such a musical figure over a very long period of time—fifty or sixty minutes. He jotted the melody down on an envelope at that time, but it only occurred to him after having abandoned Vision that this might become the basis for his new two-piano composition. Stockhausen later recalled that this was early in September 1969 (Cott 1973, 222–23), but the sketch is in fact dated 26 February (Conen 1991, 59–60). Later in the year, on 22 September 1969 at the Couvent d'Alziprato in southern France, he had composed an intuitive music text composition, Intervall, for two pianists playing 'four-hands' (on one piano), but it did not appeal to the Kontarsky brothers—especially to Alfons, who lacked the experience his brother Aloys had gained from performing text-pieces from Aus den sieben Tagen, as a member of Stockhausen's ensemble. Intervall, eventually premiered by Roger Woodward and Jerzy Romaniuk, later became part of Stockhausen's second cycle of intuitive-music compositions, Für kommende Zeiten (Toop 1986, 195–97).

Stockhausen mentioned his wish to write something for the Kontarsky brothers to Heinrich Strobel, director of the Music Division of the SWF Baden-Baden and Artistic Director of the Donaueschinger Musiktage für Zeitgenossische Tonkunst and, toward the end of 1969, Strobel commissioned a work for two pianos for the 1970 Donaueschingen Festival (Blumröder 1976, 94). After abandoning Vision, Stockhausen took up the melody he had jotted down the previous September and on its basis made a form plan and laid out the new work's skeleton between 1 May and 20 June 1970 in Osaka, Japan. He then completed the score in an unbroken stretch of work at his home in Kürten from 10 July to 18 August 1970. Alfons and Aloys Kontarsky gave the premiere of Mantra in Domaueschingen on 18 October 1970, and made the first recording of the work from 10 to 13 June 1971 at the Tonstudio Kreillerstraße 22 in Munich, for Deutsche Grammophon (Stockhausen 1978, 154). The score first appeared in print only in 1975, as one of the first publications of the composer's newly founded Stockhausen-Verlag (Conen 1991, 62).

Structure[edit]

The piece is the first determinate work (that is, the score is completely written down, though there are some passages involving a modest degree of improvisation) that Stockhausen composed after a long phase of indeterminate compositions (Blumröder 1976, 98).

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). The pitches are shown in the example to the right, and the complete formula can be seen at Nordin [n.d.].

Each of the 13 notes of the mantra has an attached characteristic, or 'pitch form' (Cott 1973, 227; Stockhausen 2003, 4); the 13 notes of the upper voice have in order the following characteristics:

Stockhausen Tierkreis Score Pdf Sheets

1. periodic repetition at the beginning (on A in the original transposition)
2. accent at the end of a duration on B
3. G♯ without any characteristic
4. a turn around the beginning of the note E
5. slow tremolo between F and D
6. an accented chord at the end of the F–D oscillation
7. a sharp accent (with a single repetition) at the beginning of a duration on G
8. a descending chromatic scale connecting the G to the following E♭
9. staccato (very short duration) on D♭
10. irregular repetition ('Morse code') of the note C
11. an inverted (upper-note) mordent (trill nucleus) on the beginning of B♭
12. sharp attack with an echo: sfz (fp), on G♭
13. arpeggio connecting the previously articulated pitch (E flat in the other voice, an augmented eleventh lower) upward to A

In addition to its articulative characteristic, each of the thirteen notes is assigned a particular dynamic, in approximate inverse proportion to its duration—that is, the softer a note's dynamic is, the longer is its duration. The very first note is the sole exception to this rule (Blumröder 1976, 97 and 104):

a. with constant intensities:

pp: 5.5 x = character V

p : 6 x = character XIII

p : 4 x = character IV

p : 1 x = character I (exception)

mp : 4 x = character XI

mp : 3 x = character III

mf : 1 x = character VI

f : 1 x = character IX

b. with crescendo or decrescendo:

(m)p > : 7 x = character X

< mf : 2 x = character VIII

sfz (fp) : 2 x = character XII

(p)–f : 2 x = character II, where f = 1 x

ff > : 5 x = character VII, where ff = 1 x

The thirteen cycles of the composition are based on the 13 notes of the mantra and the 13 characteristics detailed above. Each cycle is dominated by its corresponding note and characteristic. In this way, a single statement of the mantra is spread over the length of the entire composition, though the durations of the mantra notes are not incorporated into this overall plan (Conen 1991, 86).

The sounds of each piano are picked up by microphones and fed into an apparatus at the player's left side. This is called a Modul 69 B and was specially built for Mantra to the composer's specification by the Lawo company from Rastatt, near Baden-Baden (Stockhausen 1975, i, iv, and vii). It consists of a microphone amplifier with three microphone inputs, a compressor, a filter, a ring modulator, a scaled sine-wave generator, and a volume control. By means of this device, each piano's sounds are ring modulated with a sine tone tuned to the central pitch corresponding to the note of the mantra formula governing each of the thirteen large segments of the composition, and the modulated sound is played over loudspeakers placed behind and above the performers. The first pianist presents the upper thirteen tones, the second pianist the lower thirteen tones. Because the starting/ending pitch of the mantra is successively transposed onto these central pitches, they sound completely 'consonant', like ordinary piano tones. The other mantra pitches sound 'dissonant' to varying degrees, and differ also from a normal piano to varying degrees in their timbre. 'Hence one perceives a continual 'respiration' from consonant to dissonant to consonant modulator sounds, resulting from the precisely tuned relationships between the modulating sine tones and the modulated piano notes' (Stockhausen 1978, 155–56).

Recordings[edit]

• Rosalind Bevan, Yvar Mikashoff, Ole B. Ørsted (sound engineer: Mats Claessen; producer: Geir Johnson; executive producer: Foster Reed). CD recording. New Albion Records NAR 025. 1990.
• Andreas Grau, Götz Schumacher, Bryan Wolf (Tonmeister: Udo Wüstendörfer; sound engineer: Rüdiger Orth; producer: Ernstalbrecht Stiebler) – 1995, 'Mantra, für 2 pianisten'. Wergo WER 62672. Archived from the original on 2012-12-16. Retrieved 2016-07-25.CS1 maint: BOT: original-url status unknown (link)
• Janka Wyttenbach, Jürg Wyttenbach, Thomas Kessler (enregistrement: Jürg Jecklin; montage: Malgorzata Albinska; producer: Samuel Muller; mastering: Tritonus Studio [Peter Länger]) – 1997, Karlheinz Stockhausen: Mantra. Accord 4642692 (202252)
• Pascal Meyer, Xenia Pestova, Jan Panis (engineer and editor: Jarek Frankowski; recording supervisor: Andrew Lewis; producer: Remy Franck) – 2010, 'Karlheinz Stockhausen: Mantra'. Naxos 8.572398. Retrieved 2010-09-27.
• Mark Knoop, Roderick Chadwick, Newton Armstrong (producer and sound engineer: David Lefeber; executive producers: Berhard 'Benne' Vischer and Werner X. Uehlinger). Recorded 5 and 6 January 2013, Hall Two, Kings Place, London. CD recording. Hat[now]Art 190. Basel: Hat Hut Records, Ltd., 2014.

Two recordings were supervised by the composer:

• Aloys and Alfons Kontarsky, Karlheinz Stockhausen (sound engineer: Klaus Hiemann; producer: Rudolf Werner) – 1971, Karlheinz Stockhausen: Mantra DG LP 2530 208. Reissued 1991, 'Stockhausen Complete Edition no. 16: Mantra'. Karlheinz Stockhausen Official Website. Retrieved 2008-09-04.
• Ellen Corver, Sepp Grotenhuis, Hans Tutschku (sound engineers: Bert Kraaijpoel, Jan Panis; producer: Maarten Hartveldt; digital editing: Chapel Studio Tilburg [Jan Panis, Hans Tutschku, Maarten Hartveldt]) – [1995], Stockhausen: Mantra, Supervised by Karlheinz Stockhausen TMD 950601. This recording received an Edison Classical Award in 1996.

References[edit]

• Blumröder, Christoph von. 1976. 'Karlheinz Stockhausens Mantra für 2 Pianisten. Ein Beispiel für eine symbiotische Kompositionsform.' Melos 43, no. 2/Neue Zeitschrift für Musik 137 (March–April): 94–104.
• Conen, Hermann. 1991. Formel-Komposition: Zu Karlheinz Stockhausens Musik der siebziger Jahre. Kölner Schriften zur Neuen Musik 1, ed. Johannes Fritsch and Dietrich Kämper. Mainz: Schott's Söhne. ISBN3-7957-1890-2.
• Cott, Jonathan. 1973. Stockhausen: Conversations with the Composer. New York: Simon and Schuster. ISBN0-671-21495-0.
• Febel, Reinhard. 1998. Musik für zwei Klaviere seit 1950 als Spiegel der Kompositionstechnik, 2nd revised edition. Saarbrücken: Pfau-Verlag. ISBN3-930735-55-5.
• Frisius, Rudolf. 2008. Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen, 'Es geht aufwärts'. Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International. ISBN978-3-7957-0249-6.
• Harvey, Jonathan. 1975. The Music of Stockhausen. Berkeley and Los Angeles: University of California Press. ISBN0-520-02311-0.
• Kelsall, John. 1975. 'Compositional Techniques in the Music of Stockhausen (1951–1970)'. PhD diss. Glasgow: University of Glasgow.
• Nordin, Ingvar Loco. n.d. 'Stockhausen Edition no. 16 (Mantra)' (review of the Kontarsky recording). Sonoloco Record Reviews (Accessed 22 February 2010).
• Stockhausen, Karlheinz. 1975. Mantra für 2 Pianisten (1970), Werk Nr. 32 (score). Kürten: Stockhausen-Verlag.
• Stockhausen, Karlheinz. 1978. 'Mantra, für 2 Pianisten (1970)'. In Karlheinz Stockhausen, Texte zur Musik 4, edited by Christoph von Blumröder, 154–66. DuMont Dokumente. Cologne: DuMont Buchverlag. ISBN3-7701-1078-1.
• Stockhausen, Karlheinz. 2003. Introduction to Mantra. Kürten: Stockhausen-Verlag.
• Toop, Richard. 1986. 'Stockhausen and the Kontarskys: A Vision, an Interval, and a Mantra'. The Music Review 47, no. 3 (August): 194–99.
• Toop, Richard. 2005. Six Lectures from the Stockhausen Courses Kürten 2002. Kürten: Stockhausen-Verlag. Lecture 3: 'Mantra', pp. 75–98. ISBN3-00-016185-6.
• Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN978-0-521-68200-8 (pbk).

External links[edit]

• Armstrong, Newton. n.d. 'Stockhausen's Mantra (1970): A Technical Guide'. City University Staff Personal Pages (accessed 25 July 2016).
• Lecture by Karlheinz Stockhausen on Mantra at the Imperial College, London, 1973. Part 1, Part 2, Part 3