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Published online by Cambridge University Press: 23 November 2009
PN: We talked about fractals in connexion with theinfinity row–this way of letting music grow in whatyou could call open hierarchic layers. It's not adirector and a slave; it's an interdependent way ofproducing music. If you choose a scale — forinstance, the chromatic scale — it contains itselfan infinite number of times; my Second Symphony isbased on realizing this characteristic. But ifinstead of letting it move in this expansive way,where you get wider and wider waves, you thenconstruct it in the opposite way, you get a figurewhere it never gets out of itself. But it createsstill a fractal rhythmic figure, which was veryinspiring for me in all my percussion music from the1970s. I discovered that feature in the beginning ofthe 70s when I composed the Third Symphony. I foundthe infinity row at the end of the 50s, but it wasnot until I had composed the Third Symphony and someworks before it that I realized it contained itsdark side, which is just as rhythmic and just ashierarchic. In my Third Symphony it comes out likean inevitable development. If you imagine the placein the beginning where it gets up to a very hightrill, it comes in lower at half-tempo, and thenagain more slowly further down. It contains itself,like a Russian doll or a Chinese box.
1 Cf. Anderson, Martin, ‘The Many Patterns of Per Norgard’, Tempi 202, 10 1997, pp. 3–7CrossRefGoogle Scholar.
2 Composed in 1970 and revised in 1971, the Second Symphony is recorded (with the Sinfonia austere, No. 1) by Leif Segerstam and the Danish National Radio Symphony Orchestra on Chandos CHAN 9450.
3 The choral Third Symphony dates from 1972–75; it, too, is recorded by Segerstam and the Danish National Radio Symphony Orchestra on Chandos, with the Concerto in due tempi for piano and orchestra (CHAN 9491).
4 Axel Thue (1863–1922) and Marston Morse (1892–1977). Thue discovered the principle — a binary fractal sequence — that mathematicians now call the Thue-Morse (or Morse-Thue) sequence in 1906, and it was then rediscovered independently by Morse in 1917.
5 The 1968 orchestral work by Norgård in which he first used the infinity row as the basis of an entire musical structure.
6 In 1979 Norgård discovered the art of the schizophrenic Swiss painter Adolf Wolfli (1864–1930) in an exhibition at the Louisiana Museum of Modern Art, just north of Copenhagen. It triggered a radical re-evaluation of his music.
7 Recorded with the Sixth Symphony by Thomas Dausgaard and the Danish National Symphony Orchestra on Chandos CHAN 9904. (See p.27 of this issue–Ed.)
8 Terrains vogues was premièred by Davis, Andrew Sir and the BBC Symphony Orchestra in the Barbican on 1 04 2001Google Scholar.
9 1990, rev. 1991; recorded by Segerstam and the DNRSO, with the Fourth Symphony, on Chandos CHAN 9533.
10 Borderlines was a joint commission from the Cheltenham Festival, Sealand Symphony Orchestra and the Ostrobothnian Chamber Orchestra.
11 This is the choral song Du skal plante el trae (You shall plant a tree), composed in 1967.
12 Holmboe's pianist-photographer wife, née Graf.
13 On 29 March 1997.
14 TheThree Pieces, op. 59, of 1928.