Infinity series
The infinity series (Danish: Uendelighedsrækken) is a musical composition method developed by the Danish composer Per Nørgård first for serializing melody, subsequently augmented with approaches to harmony, and rhythm.
Norgard discovered the melodic infinity series in 1959 and it provided 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) and Symphony No. 2 (1970) that it appeared overtly. 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.
Melodic infinity series
The melodic infinity series (∞ M), the infinity series proper, is based on a series of interlocked intervals.
Two-tone version
In the simplest infinity series, two pitches are given. The interval between pitch 1 and pitch 2 is protected in its original version at pitch 3, while the inversion is projected at pitch 4.
As Nørgård briefly summarized:
- Every interval appearing on the time axis is successively projected from an odd-numbered tone in original version to the position of the next odd-numbered tone, and from an even-numbered tone in inversion to the position of the next even-numbered tone.
Rhythmic infinity series
The rhythmic infinity series is based on the golden section.
Harmonic infinity series
The harmonic infinity series has its basis in the natural overtone and undertone series.