'Hierarchical music'

Per Nørgård's compositional universe in the 70s, based on 'The Open Hierarchies'.

by Erling Kullberg

Introduction

Per Nørgård's music from the 70s is basically grounded in his preoccupation with 'the hierarchical principle' as a universal principle for the organisation of phenomena: the basis of all order, whether in society, nature, the universe or art.

In fact, Per Nørgård's interest in hierarchies was shared by many other thinkers in the humanities and the natural sciences at the end of the 60s. This was the period leading up to a major paradigm shift, when holistic philosophy was being formulated as a possible replacement for those reductionist, atomist patterns of thought that had hitherto been dominant.

Arthur Koestler was one of the main figures behind this particular intellectual scene, and his book, Beyond Reductionism, was a great source of inspiration to Per Nørgård. This book presents a wide treatment of the hierarchical principle of organisation as the necessary condition for all life.


Open hierarchy
In this context, the term 'hierarchy' is of course not to be understood in the negative, everyday sense of the term, indicating a rigid social system governed from above (by clerics, as in the Middle Ages), but in the sense of 'open hierarchies' without any absolute top or bottom. What is apparently a 'top' can be hierarchically linked with other 'tops' at the same level, pointing upwards to even higher relative 'tops'. In the same way, the system can be infinitely subdivided in a downward direction.

In an open hierarchy, no level is of higher rank than another; each element is at once a converging point for lower layers and forms part of a context converging at some higher level.

Man could be used as an image to represent an element in such a hierarchy. We are composed of organs, which in turn are composed of tissues, cells, molecules and atoms; upwardly, we are organised in families, communities, nations, and so on.

Nørgård's interest in the hierarchical principle is closely linked to his experiences as a composer. When he was working on the development of the melodic infinity row he quickly became aware of its hierarchical qualities: that it retained the same basic identity, whether one played each single note, every fourth note, every sixteenth, and so on (for a detailed explanation of these qualities see the articles about the infinity row).
The challenging perspectives opened up by this principle were explored by Per Nørgård in a number of works, but as time went on he felt the need to find a system for organising the fields of rhythm and harmony, corresponding to the infinity row in the melodic dimension.
Such a system would have to be:

    • infinite
    • hierarchical in structure

Gradually, Nørgård unearthed his three infinity hierarchies, and at the same time developed theories for how these could be linked together to form a single comprehensive system.
At this point - in the middle of the 70s in the works surrounding the 3rd Symphony - the principles of what has been called 'hierarchical music' were fully developed.


The melodic infinity series

The basis of the melodic infinity series is of course the infinity row, the many special characteristics of which are comprehensively dealt with in the articles specially devoted to this topic.

Here we will only examine a small section of the row.


It goes without saying that the infinity row exemplifies the type of 'open hierarchy' described in the introduction, in which no level is of greater importance than the others. Just as the original row is the same as wavelengths (WL) 4, 16, 64, etc., one can imagine that 4, 16 or 64, etc. notes of the infinity series could be inserted between the 1st and 2nd notes of the row - at a 'faster' level.

The perception of these features of the melodic infinity series - features that make it suitable as an abstract symbol of the idea of a relationship or structural identity between large and small elements within the cosmic totality - is magnificently audible in musical form in Voyage into the Golden Screen (1967).
Regardless of the intriguing perspectives artistically expressed in works such as Voyage into the Golden Screen, however, it would hardly be fruitful in the long run to continue to simply map out the physically existing infinity series in work after work .

The work with the infinity series only presents really interesting perspectives when the wavelength idea is developed further, and the complete series does not necessarily have to be present as sounding notes to function as a unifying factor. In other words, wavelengths can be simultaneously present as different yet related musical layers, precisely dimensioned in accordance with the proportions along the wavelengths. Only then does the infinity series emerge as the DNA of hierarchical music, the basic structure determining all development, but not necessarily activated (i.e., visible or audible) to its full extent at all times.

This may be seen in analogy with the biological DNA molecule, where the whole molecule is not active in all cells (other parts of the DNA molecule are active in a big toe cell, for example, than those that are active in a liver cell). Nor is it necessarily active all the time in the individual cell (the pancreas, for example, does not produce insulin all the time).