Symphony No. 2

Analysis

Tempo layers

The four shields represent the slowest of the melodic layers derived from the basic infinity series. There are 1,024 notes (=128 bars) between each attack, and the tempo is described as 'wavelength 1,024'. The attacks take place on the fourth beat of bars 154, 282, 410 and 538. Each of the shields plays a two-note sound, and the top tones of the motif as a whole are the first four notes of the infinity series (transposed), while the base tones are the (transposed) inversion of these notes.

The next slowest layer is represented by the 16 phases, wavelength 256. Here, from phases 2-16 (phase one contains all the introduction and the quarter-tone version of the infinity series), we have the first 15 notes of the infinity series, transposed.

Relationship to the structure of the series

Such a formal division is logically derived from the structure of the infinity series. One consequence of the principle according to which it is generated is precisely this, that it constantly reproduces itself at a tempo four times slower. Notes 1, 5, 9 and 13 are thus identical with notes 1, 2, 3, 4. They are also identical with notes 1, 17, 33, 49, etc., or notes 1, 257, 513, 769, etc., or notes 1, 1,025, 2,049, 3,073, and so on.

The initial notes of the phases and shields - the lowest level of detail

When attacking the phases and shields Per Nørgård makes use of the fact that the series does not simply reproduce itself on different wavelengths from the first note onwards. Every new note produced by the infinity series can be the beginning of a new - transposed - infinity series (see The 'open hierarchies' of the infinity series).


Because new notes arise on note 256 and note 1,024, Nørgård is able to present us with a new 'note 1' far into the series.

Within the phase

Since this is a work for a large orchestra, even larger numbers of simultaneous tempi can be used in the symphony than in 'Voyage...'.

As an example of how many layers can be experienced, there follows a list of the melody lines which begin in phase 2, and which in most cases, with small variations in the instrumentation, continue until phase 8 (bars 250-251).

The list shows what instruments are playing on what wavelength from bar 59, as well as the precise note in the infinity series from which they start. If the series does not start with note 1, (tr) is appended in the case of all notes relating to transposed series, and a precise starting note number for series that start from uneven notes after note 1:

Wavelength 1, flutes, note 257.
Wavelength 2 (tr), clarinets, note 274.
Wavelength 4 (tr), oboe, note 276.
Wavelength 4, horn, note 273.
Wavelength 8 (tr) harp, note 256.
Wavelength 16 (7), bassoon, note 263.
Wavelength 32 (3) 2nd. violins, note 259.
Wavelength 64 (tr), trumpet, note 256.
Wavelength 256, rest of strings, note 257
Wavelength 256 (tr), organ.

The fact that this mêlée of melody lines does not become a cacophony is due not only to the to the innate characteristics of the infinity series. It is to a large degree the accomplishment of a composer who tirelessly listens with a finely-tuned ear down to the level of each nanosecond and insists that the music should appear to have been created at that very moment, even though the whole piece, from individual notes to the overall form seems to be determined in advance.


For further information, see Lars Bisgaard: Per Nørgårds 2. Symfoni - en rejsebeskrivelse I og II. (Per Nørgård's 2nd. Symphony - a Travelogue I and II)