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.]). Later he became interested in the Swiss artist Adolf Wölfli, who inspired many of Nørgård's works (Anon [n.d.]), including the 4th 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).
Nørgård is also a prolific writer. He has written many articles dealing with music not only from a technical but also a philosophical viewpoint.
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, comparable to fractal geometry. Mathematically, the infinity series is an integer sequence. The first few terms of its simplest form are 0, 1, −1, 2, 1, 0, −2, 3, … (sequence A004718 in 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.
Selected list of works 
- Symphony No. 1 Sinfonia austera (1953–55)
- Symphony No. 2 (1970)
- Symphony No. 3 (1972–75)
- Symphony No. 4 (1981)
- Symphony No. 5 (1990)
- Symphony No. 6 At the End of the Day (1998–99)
- Symphony No. 7 (2006)
- Symphony No. 8 (2011)
- Concerto for Accordion Recall (1968)
- Cello Concerto No. 1 Between (1985)
- Cello Concerto No. 2 Momentum (2009)
- Harp Concerto No. 1 King, Queen and Ace (1988)
- Harp Concerto No. 2 through thorns... (2003)
- Piano Concerto Concerto in due tempi (1994–95)
- Percussion concerto No. 1 For a Change (1983)
- Percussion concerto No. 2 Bach to the Future (1997)
- Viola Concerto No. 1 Remembering Child (1986)
- Violin Concerto No. 1 Helle Nacht (1986–87)
- Violin Concerto No. 2 Borderlines (2002)
- Labyrinten (The Labyrinth) (1963)
- Gilgamesh (1972)
- Siddharta (1974–79)
- Der Göttliche Tivoli (The Divine Circus) (1983)
- Orfeus: Den uendelige sang (Orpheus: The Endless Song) (1988)
- Nuit des Hommes (1996)
Selected other works 
- Trio No. 1 (1955) Op. 15
- Konstellationer (Constellations) (1958)
- Piano Sonata No. 2 Op. 20
- Voyage into the Golden Screen (1968)
- Libra (1973)
- Turn (1973)
- Nova genitura (1975)
- Wie ein Kind (Like a Child) (1979–80)
- Drømmesange (Dream Songs) (1981)
- I Ching (1982)
- Najader (The Naiads) (1986)
- Solo Intimo Op. 8 for Solo "Cello" (1953)
- Nordic Council Music Prize (1974) for his opera Gilgamesh
- Léonie Sonning Music Prize (1996; Denmark)
- Anon. [n.d.] "Adolf Wölffli: Wölfli's influence". (Archived copy from 23 October 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.
- 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.
- Mortensen, Jørgen. [n.d.] "Uendelighedsrækken" (The Infinity Series), English version. (Archived copy, accessed 14 May 2010. Formerly on the composer's website, taken off line in November 2007.)
- Nørgård, Per. 1975. "Inside a Symphony". Translated by L. K. Christensen. Numus-West 2, no. 2:4–16.
- 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
- Jørgen Mortensen The 'open hierarchies' of the infinity series