The 'super sequence' and Helle Nacht
The first attempt to expand the 'transformation crystal ball' led to the so-called 'super sequence'.
In expanding the 'transformation crystal ball' into a 'super sequence', Per Nørgård turned to the constituents of the 'transformation crystal ball': the four clusters of fifths:
These may be said to belong together in pairs in two different ways:
- As clusters of fundamental and focus notes.
Stacks 1 and 4 are both regarded as clusters of fundamental notes, as their notes are situated at planets with a positive polarity.
In the case of clusters 2 and 3, their notes are situated at planets with negative polarity, and they are regarded as clusters of focus notes.
- As C and F sharp major clusters.
The first two clusters represent the C major notes, with the exception of D. The last two represent the F sharp major notes, though with the exception of G sharp.
In his extension of the 'super sequence', Per Nørgård makes a division of the four clusters into two fundamental note clusters and two focus note clusters. The extension takes place by letting the fundamental note clusters (clusters 1 and 4) constantly repeat themselves a second higher, while the focus notes (clusters 2 and 3) repeat themselves a minor second lower each time. After twelve repetitions the four clusters (with a suitable octave transposition along the way) will have arrived back at their starting point. The beginning of the sequence can be seen here:
However, when composing the last movement of Helle Nacht, Per Nørgård needed a scale even longer than the twelve times twelve notes mentioned above. He achieved this by tripling each of the four rows using the principles of the infinity series.
This means that each of the three-note groups in the four clusters is extended to nine by inserting extra notes. Then the four rows are woven together again, and the four nine-note groups, as they have now become, then move in pairs chromatically up and chromatically down respectively. All in all, this means that the 'super sequence' consists of no less than 432 notes! The score sample below shows the 12 basic notes of the 'super sequence' expanded to 36 notes:
