![]() |
||||
|
||||
If one can expand the 'transformation crystal ball' from 12 to 36 notes using the infinity series, there is no reason why one should not expand the 36 to 108 and 324, and so on ad infinitum. Strictly speaking, there is no need to work out all the rising and falling sequences that compose the 'super sequence'. Whether Per Nørgård's thinking ran along these lines we do not know, but the 'super sequence' was only used as the basis for his compositional technique in connection with Helle Nacht. After that, the so-called 'tone lakes' took over - at least, when the technique had been thoroughly worked out. One reason to expand the 'transformation crystal ball' was a certain fascination with the tonal commuting between two keys. So one may hope to find this movement back and forth, or something like it, when the 'transformation crystal ball' is unravelled using the infinity series. As it turned out, the manner in which the 'transformation crystal ball' was lengthened using the infinity series meant that the two tonal planes disappeared. In the Fifth Symphony the rows were lengthened in another way, but nor did this procedure lead to the desired result. He we see the the 'false' tone lake, 'the 36', which was used in the Fifth Symphony: |
||||
See moreover the analysis of Symphony No. 5. It was only in the works that came after the Fifth Symphony that Per Nørgård found a way to lengthen the rows that produced the desired result, and which may therefore be regarded as a consistent procedure for expanding the rows. Compare the above with the 'genuine' tone lake, 'the 36'. |
||||