Construction by the projection of intervals


By Jørgen Mortensen

We first meet the infinity series in the form it took in connection with Voyage into the Golden Screen and Symphony No. 2. Here, the infinity series is developed on the basis of a chromatic scale - but it could just as well be a diatonic scale or something quite different.

The starting point is the two notes G and A flat. These are the kernel of the whole structure and each is at the same time the root of its own 'half layer' - that is, every other note from the first and every other note from the second.

 

The interval between the two notes, an ascending semitone step (+1), is projected twice: first inverted in the 'upper' system (moving from G to F sharp), then non-inverted in the 'lower' system (moving from A flat to A). This, in turn, produces two new notes: F sharp and A:

 

The next interval we read off is A flat-F sharp, two semitones down (-2). This interval is to be extruded in a corresponding manner: inverted in the 'upper' system and non-inverted in the 'lower' system. This produces the notes A flat and G, respectively:
When the next interval, F sharp-A (+3), is extruded, we get the notes F and B flat - and so the process continues. The first 128 notes look like this:

If we had developed the infinity series within a diatonic scale, the smallest unit would have been steps in the scale - which can be both semitone and whole tone steps. Starting with the notes G and A, the first 64 notes look like this: