The construction of 'tone lakes'

By Jørgen Mortensen

'Tone lakes' are combinations of the tripartite infinity rows in which the basic unit is the fifth interval. There are four layers in each 'tone lake', four independent rows. The smallest 'tone lake' consists of 12 notes, the next of thrice as many (36), the next of thrice as many again....

The simplest 'tone lake' with only 12 notes is composed of 4 separate rows each containing 3 notes.

These 4 separate rows are:

    The row from G with the first interval downwards (G\)
    The row from E flat with the first upwards (Eb/)
    The row from A with the first interval upwards (A/)
    The row from C sharp with the first interval downwards (C#\)

To illustrate the background for the choice of starting notes it should be pointed out that the G/- and A\- rows together provide six notes which are found in the following cluster of fifths, in which the middle note, D, is left out:

    F C G (D) A E B

This cluster of fifths, formed by the notes of C major, attracted the attention of Nørgård at an earlier stage, both with regard to its astrological and mythological aspects - more details in the section on the Background of the 'tone lakes'.

In a similar manner, the Eb/- and C#\ rows are to be found in the following cluster of fifths around Ab:

    Cb Gb Db (Ab) Eb Bb F

The four rows of 3 notes each are interlinked with each other in four ways:

    non-inverted and progressive
    non-inverted and retrograde (or crab)
    inverted and progressive
    inverted and retrograde (or crab)

The result is the 12 notes:
The 36 notes look like this:
For a more detailed description see Jørgen Mortensen: Per Nørgårds Tonesøer (Per Nørgård's Tone Lakes), VM 1992.