Formula composition
Encyclopedia
Formula composition is a serially
-derived technique encountered principally in the music of Karlheinz Stockhausen
, involving the projection, expansion, and Ausmultiplikation
of either a single melody
-formula, or a two- or three-voice contrapuntal construction (sometimes stated at the outset).
In contrast to serial music, where the structuring features are more or less abstract and remain largely inaccessible to the listener's ear, in formula composition the musical specifications of pitch
, dynamics
, duration, timbre
, and tempo
are always directly evident in the sound, through the use of a concisely articulated melodic tone succession, the formula, which defines the large-scale form as well as all the internal musical details of the composition (Blumröder 1982, 184–85).
of 1951, the technique made its first appearance in Mantra
in 1970, and became the central focus of Stockhausen's music up to 2003. Stockhausen's mammoth opera
cycle Licht
is based on a three-strand "super-formula".
Hermann Conen (1991, 57) identifies two kinds of formula composition in Stockhausen’s works prior to Licht:
Works of the first type include Mantra (1970), Inori
(1973–74), Jubiläum
(1977), and In Freundschaft
(1977); works of the second type comprise Alphabet für Liège
(1972), the “Laub und Regen” duet from Herbstmusik (1974), Musik im Bauch
(1975), Harlekin (1975), Der kleine Harlekin (1975), and Sirius
(1975–77). Other works from the 1970s, such as Sternklang (1971), Trans
(1971), Ylem (1972), the first three parts of Herbstmusik, Atmen gibt das Leben
(1974/76–77), Tierkreis
(1974–75), and Amour
(1976) do not employ formula technique, according to Conen, though the composer includes Atmen gibt das Leben amongst the works composed using "formula complexes" (Stockhausen 1989a).
describes his composition Rituel, in memoriam Bruno Maderna
(1975) as a "ceremony of memory", based on "numerous repetitions of the same formulas", and it has been seen as an analogue to Stockhausen's formula compositions—especially to Inori, because of the shared ritual character of the two compositions (Blumröder 1982, 183–84).
York Höller
, who studied with Stockhausen in 1971–72, uses a similar method, which he names Klanggestalt (literally, "sound-shape"), and at least one writer has used the expression "formula composition" to describe it (Stenzl 1991, 12–15). Finbar O'Súilleabháin, however, while accepting there are parallels between the techniques in Höller's opera The Master and Margarita (1984–85) and Stockhausen's Licht
cycle (1977–2003), concludes that Höller's conception is "perfectly distinct" (O'Súilleabháin 1992).
Serialism
In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...
-derived technique encountered principally in the music of Karlheinz Stockhausen
Karlheinz Stockhausen
Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. Another critic calls him "one of the great visionaries of 20th-century music"...
, involving the projection, expansion, and Ausmultiplikation
Ausmultiplikation
Ausmultiplikation is a German term used by the composer Karlheinz Stockhausen to describe a technique in which a long note is replaced by shorter, "melodic configurations internally animated around central tones", resembling the ornamental technique of divisions in Renaissance music...
of either a single melody
Melody
A melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity...
-formula, or a two- or three-voice contrapuntal construction (sometimes stated at the outset).
In contrast to serial music, where the structuring features are more or less abstract and remain largely inaccessible to the listener's ear, in formula composition the musical specifications of pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
, dynamics
Dynamics (music)
In music, dynamics normally refers to the volume of a sound or note, but can also refer to every aspect of the execution of a given piece, either stylistic or functional . The term is also applied to the written or printed musical notation used to indicate dynamics...
, duration, timbre
Timbre
In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...
, and tempo
Tempo
In musical terminology, tempo is the speed or pace of a given piece. Tempo is a crucial element of any musical composition, as it can affect the mood and difficulty of a piece.-Measuring tempo:...
are always directly evident in the sound, through the use of a concisely articulated melodic tone succession, the formula, which defines the large-scale form as well as all the internal musical details of the composition (Blumröder 1982, 184–85).
Stockhausen's music
Though foreshadowed in Stockhausen's once-withdrawn FormelFormel
Formel is a composition for chamber orchestra by Karlheinz Stockhausen, written while he was still a student in 1951. It is given the number ⅙ in his catalog of works, indicating that it is amongst the pieces preceding the composition he recognised as his first mature work, Nr...
of 1951, the technique made its first appearance in Mantra
Mantra (Stockhausen)
Mantra is a composition by the German composer Karlheinz Stockhausen. It was composed in 1970 and premiered in autumn of the same year in Donaueschingen...
in 1970, and became the central focus of Stockhausen's music up to 2003. Stockhausen's mammoth opera
Opera
Opera is an art form in which singers and musicians perform a dramatic work combining text and musical score, usually in a theatrical setting. Opera incorporates many of the elements of spoken theatre, such as acting, scenery, and costumes and sometimes includes dance...
cycle Licht
Licht
Licht , subtitled "The Seven Days of the Week," is a cycle of seven operas composed by Karlheinz Stockhausen between 1977 and 2003. In total, the cycle contains over 29 hours of music.-Origin:...
is based on a three-strand "super-formula".
Hermann Conen (1991, 57) identifies two kinds of formula composition in Stockhausen’s works prior to Licht:
formula compositions in which the form results from projection of the formula, . . . [and] works in which melodies in themselves possess many internal characteristics of formulas, but where the formal idea itself does not originate from the formula(s) used in their realisation
Works of the first type include Mantra (1970), Inori
Inori
Inori: Adorations for One or Two Soloists with Orchestra is a composition by Karlheinz Stockhausen, written in 1973–74 ....
(1973–74), Jubiläum
Jubiläum
Jubiläum is an orchestral composition by Karlheinz Stockhausen, work-number 45 in the composer’s catalogue of works.-History:Jubiläum is a relatively short work of about 15 minutes duration, written in 1977 on commission for the 125th-anniversary celebration of the Hannover Opera House, and has...
(1977), and In Freundschaft
In Freundschaft
In Freundschaft is a composition by Karlheinz Stockhausen, number 46 in his catalogue of works, which is playable on a wide variety of solo instruments.-History:...
(1977); works of the second type comprise Alphabet für Liège
Alphabet für Liège
Alphabet für Liège, for soloists and duos, is a composition by Karlheinz Stockhausen, and is Work Number 36 in the composer's catalog of works. A performance of it lasts four hours....
(1972), the “Laub und Regen” duet from Herbstmusik (1974), Musik im Bauch
Musik im Bauch
Musik im Bauch is a piece of scenic music for six percussionists and music boxes composed by Karlheinz Stockhausen in 1975, and is Number 41 in his catalog of works. The world premiere was presented on 28 March 1975 by the Royan Festival. The performance was given by Les Percussions de Strasbourg...
(1975), Harlekin (1975), Der kleine Harlekin (1975), and Sirius
Sirius (Stockhausen)
Sirius: eight-channel electronic music and trumpet, soprano, bass clarinet, and bass is a music-theatre composition by Karlheinz Stockhausen.-History:...
(1975–77). Other works from the 1970s, such as Sternklang (1971), Trans
Trans (Stockhausen)
Trans is a composition for orchestra and tape by the German composer Karlheinz Stockhausen, written in 1971. It is Number 35 in the composer's catalog of works....
(1971), Ylem (1972), the first three parts of Herbstmusik, Atmen gibt das Leben
Atmen gibt das Leben
Atmen gibt das Leben , is a choral opera with orchestra by Karlheinz Stockhausen, written in 1974 and expanded in 1976–77. It is Number 39 in the catalogue of the composer's works, and lasts about 50 minutes in performance.-History:...
(1974/76–77), Tierkreis
Tierkreis (Stockhausen)
Tierkreis is a musical composition by the German composer Karlheinz Stockhausen. The title is the German word for Zodiac, and the composition consists of twelve melodies, each representing one sign of the zodiac.-History:...
(1974–75), and Amour
Amour (Stockhausen)
Amour is a cycle of five pieces for clarinet by Karlheinz Stockhausen, composed in 1974–76. The composer thought of each piece as a gift for a close friend...
(1976) do not employ formula technique, according to Conen, though the composer includes Atmen gibt das Leben amongst the works composed using "formula complexes" (Stockhausen 1989a).
Other composers
Pierre BoulezPierre Boulez
Pierre Boulez is a French composer of contemporary classical music, a pianist, and a conductor.-Early years:Boulez was born in Montbrison, Loire, France. As a child he began piano lessons and demonstrated aptitude in both music and mathematics...
describes his composition Rituel, in memoriam Bruno Maderna
Rituel in Memoriam Bruno Maderna
Rituel in memoriam Bruno Maderna is a composition for large chamber ensemble in eight groups by the French composer Pierre Boulez. It was first performed in London, 2 April 1975, by the BBC Symphony Orchestra conducted by Boulez....
(1975) as a "ceremony of memory", based on "numerous repetitions of the same formulas", and it has been seen as an analogue to Stockhausen's formula compositions—especially to Inori, because of the shared ritual character of the two compositions (Blumröder 1982, 183–84).
York Höller
York Höller
York Höller is a German composer and Professor of composition at the Hochschule für Musik Köln.-Biography:Between 1963 and 1970 Höller studied at the Cologne Musikhochschule: composition with Joachim Blume and Bernd Alois Zimmermann, piano with Else Schmitz-Gohrand Alfons Kontarsky, and orchestral...
, who studied with Stockhausen in 1971–72, uses a similar method, which he names Klanggestalt (literally, "sound-shape"), and at least one writer has used the expression "formula composition" to describe it (Stenzl 1991, 12–15). Finbar O'Súilleabháin, however, while accepting there are parallels between the techniques in Höller's opera The Master and Margarita (1984–85) and Stockhausen's Licht
Licht
Licht , subtitled "The Seven Days of the Week," is a cycle of seven operas composed by Karlheinz Stockhausen between 1977 and 2003. In total, the cycle contains over 29 hours of music.-Origin:...
cycle (1977–2003), concludes that Höller's conception is "perfectly distinct" (O'Súilleabháin 1992).
Sources
- 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.
- Blumröder, Christoph von. 1982. "Formel-Komposition—Minimal Music—Neue Einfachheit: Musikalische Konzeptionen der siebziger Jahre." In Neuland Jahrbuch 2 (1981/82), edited by Herbert Henck, 183–205. Bergisch Gladbach: Neuland Verlag.
- 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. ISBN 3795718902
- Hufschmidt, Wolfgang. 1981. "Musik aus Zahlen: Prinzipien der musikalischen Formgestaltung in der seriellen Kompositionspraxis." In Reflexionen über Musik heute, edited by Wilfried Gruhn, 24–57. Mainz: B. Schott’s Söhne.
- Kohl, Jerome. 1983–84."The Evolution of Macro- and Micro-Time Relations in Stockhausen's Recent Music." Perspectives of New Music 22:147–85.
- Kohl, Jerome. 1990. "Into the Middleground: Formula Syntax in Stockhausen’s Licht." Perspectives of New Music 28, no. 2 (Summer): 262–91.
- Kohl, Jerome. 1993. "Time and Light." Contemporary Music Review 7, no. 2:203–19.
- Kohl, Jerome. 2004. "Der Aspekt der Harmonik in Licht." In Internationales Stockhausen-Symposion 2000: LICHT. Musikwissenschaftliches Institut der Universität zu Köln, 19. bis 22. Oktober 2000. Tagungsbericht. Edited by Imke Misch and Christoph von Blumröder, 116–32. Münster, Berlin, London: LIT-Verlag. ISBN 3825879445
- O'Súilleabháin, Finbar. 1992. [Letter to the Editor]. Tempo New Series, no. 181 (June): 68.
- Petazzi, Paolo. 1993. "Karlheinz Stockhausen: dalle tecniche seriali alla 'Formelkomposition'". In Due serate monografiche dedicata a Karlheinz Stockhausen, edited by Mauro Conti and Alberto Paloscia, 17–27. 56° Maggio Musicale Fiorentino 1993: 21 and 23 June. Florence:Teatro Communale di Firenze.
- Stenzl, Jürg. 1991. "York Höller's The Master and Margarita: A German Opera." Translated by Sue Rose. Tempo New Series, no. 179 (December): 8–15.
- Stockhausen, Karlheinz. 1989a. "Multiformale Komposition". In his Texte zur Musik 5, 667. Cologne: DuMont Buchverlag. ISBN 3-7701-2249-6
- Stockhausen, Karlheinz. 1989b. "Die Kunst, zu hören". In his Texte zur Musik 5, 669–700. Cologne: DuMont Buchverlag. ISBN 3-7701-2249-6
- Stockhausen, Karlheinz. 1989c. "Musikalische Metamorphose". In his Texte zur Musik 5, 701–36. Cologne: DuMont Buchverlag. ISBN 3-7701-2249-6