Per Nørgård

Nørgård was born in Gentofte, Denmark. He studied with Vagn Holmboe at the Royal Danish Academy of Music in Copenhagen, and subsequently with Nadia Boulanger in Paris. To begin with, he was strongly influenced by the Nordic styles of Jean Sibelius, Carl Nielsen and Vagn Holmboe. In the 1960s, Nørgård began exploring the modernist techniques of central Europe, eventually developing a serial compositional system based on the "infinity series" (Nørgård 1975), which he used in his Voyage into the Golden Screen, the Second and Third Symphonies, I Ching, and other works of the late 1960s and 70s (Mortensen & n.d.(a)). Later he became interested in the Swiss artist Adolf Wölfli, who inspired many of Nørgård's works (Anon. n.d.), including the Fourth Symphony, the opera Det Guddommelige Tivoli and Papalagi for solo guitar.

Nørgård has composed works in all major genres: six operas, two ballets, eight symphonies and other pieces for orchestra, several concertos, choral and vocal works, a very large number of chamber works (among them ten string quartets) and several solo instrumental works. These include a number of works for the guitar, mostly written for the Danish guitarist Erling Møldrup: In Memory Of... (1978), Papalagi (1981), a series of suites called Tales from a Hand (1985–2001), Early Morn (1997–98) and Rondino Amorino (1999). One of his most important works for percussion solo is I Ching (1982) for the Danish percussionist Gert Mortensen. He has also composed music for several films, including The Red Cloak (1966), Babette's Feast (1987), and Hamlet, Prince of Denmark (1993).

His eighth symphony was premiered on 19 September 2012 in the Helsinki Music Centre, Finland, by the Helsinki Philharmonic Orchestra conducted by John Storgårds. Heikki Valska from the Finnish radio described the symphony as "very bright and lyrical" and "approachable". It was well received by the audience at the premiere (Anon. 2012). It was later recorded by the Vienna Philharmonic Orchestra conducted by Sakari Oramo.

Nørgård is also a prolific writer. He has written many articles dealing with music not only from a technical but also a philosophical viewpoint.

with numbers=scale steps and 0=A

Nørgård's music often features the use of the infinity series (Danish Uendelighedsrækken) for serializing melody, harmony, and rhythm in musical composition. The method takes its name from the endlessly self-similar nature of the resulting musical material (Mortensen & n.d.(b)), comparable to fractal geometry. Mathematically, the infinity series is an integer sequence. "Invented in an attempt to unify in a perfect way repetition and variation," (Sloane) the first few terms of its simplest form are 0, 1, −1, 2, 1, 0, −2, 3, … (sequence A004718 in the OEIS).

Nørgård discovered the melodic infinity series in 1959 and it proved an inspiration for many of his works during the 1960s. However, it was not until his Voyage into the Golden Screen for small ensemble (1968)—which has been identified as the first "properly instrumental piece of spectral composition" (Anderson 2000, 14)—and Symphony No. 2 (1970) that it provided the structure for an entire work (Nørgård 1975, 9). The harmonic and rhythmic infinity series were developed in the early 1970s and the three series were first integrated in Nørgård's Symphony No. 3.

• Nordic Council Music Prize (1974) for his opera Gilgamesh
• Léonie Sonning Music Prize (1996; Denmark)
• Wihuri Sibelius Prize (2006)
• Marie-Josée Kravis Prize for New Music (2014) (Kozinn 2014)
• Ernst von Siemens Music Prize (2016)

• Anon. n.d. "Adolf Wölffli: Wölfli's influence" at the Wayback Machine (archived October 23, 2007). (from the composer's former website. Accessed 14 May 2010)
• Anon. 2012. "Ny symfoni af Per Nørgård uropført i Helsinki". DR (broadcaster). 20 September 2012. Archived from the original on 24 September 2012.
• Anderson, Julian. 2000. "A Provisional History of Spectral Music." Contemporary Music Review 19, no. 2 ("Spectral Music History and Techniques", edited by Joshua Fineberg): 7–22.
• Kozinn, Allan. 2014. "Danish Composer Wins $200,000 Prize from Philharmonic". The New York Times (11 June): ArtsBeat (accessed 17 December 2014).
• Mortensen, Jørgen. n.d.(a) "Uendelighedsrækken" at the Wayback Machine (archived October 10, 2007) (The Infinity Series), English version. (accessed 14 May 2010. Formerly on the composer's website, taken off line in November 2007.)
• Mortensen, Jørgen. n.d.(b) "The 'Open Hierarchies' of the Infinity Series". Subsection of Mortensen n.d.(a).
• Nørgård, Per. 1975. "Inside a Symphony". Translated by L. K. Christensen. Numus-West 2, no. 2:4–16.
• Sloane, N. J. A. (ed.). "Sequence A004718 (Infinity sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

• The infinity series – composer's website
• Plain language description of infinity series generation. (Accessed 15 May 2011)
• Mathematical proofs of the results on the composer's website – and the connection with other self-similar "sloth canon" number sequences
• Per Nørgård on IMDb
• Per Nørgård kompositioner @ www.kb.dk (Danish)