Variants of the tripartite infinity series

By Jørgen Mortensen

Other series can arise either from another initial note or by using another reduplicating mechanism with regard to non-inversion/inversion. In Iris, for example, there are 8 concurrent sequences for the second violins in bar 10. Each of these has its own three-note interval.

One of the sequences (which in itself is but one part) looks like this:
Here, the initial three-note group is E, C sharp, D. It is projected as inverted - non-inverted - inverted, rather than inverted - non-inverted - non-inverted, as before. The first interval, a descending minor third, is projected from E to G, from C sharp to B flat, from D to F. The next interval, an ascending minor second, is projected from G to F sharp, from B flat to B and from F to E. The next note is C sharp. In Iris, two of the notes (B flat and B) are freely transposed an octave up.

It may be seen that the third note in every three-note group is a major second below the first note in the group. Since they do not immediately follow each other, the result will not be monotonous. It may also be seen that within these first 10 notes no notes are repeated, and nor will this subsequently be the case.

In tripartite series outside the 'tone lakes' Nørgård has never used initial figures that would involve the repetition of notes. In a letter to the present author, Nørgård wrote that:

    this is partly due to the analogy with the basic two-note series, in which notes are never repeated, partly - and more especially - because such a repetition of notes would disturb the tonal progression. Various freely-composed note values already appear in the third love song (“Wie soll ich....”) from 1963, and in addition 'expressive' repetitions of the same note. It would therefore be 'structurally unclear' if 'built-in' repetitions of series were to be added to this.
    (Letter of 12.9.1992 to Jørgen Mortensen).

It should be noted that Nørgård allows the repetition of notes in the 'tone lakes', though here they never come to play a dominating role.
Series from Iris