Commissioned by Applause Music, and written for the Ros|car-duo.
This work is divided in two parts. The first, Preambulum, is an introduction. Then the second and main movement starts. This part features a continous stream of 16ths that is derived from the infinity series. In a way, this piece is inspired by Per Nørgård’s idea to use this string of integers.
About the infinity series:
Mathematicly, that serie is an integer sequence, where each next value is determined by a previous one. It is constructed in such a manner, that in subsets the series contains itself and its inversions.
I like the idea of a self-referential series of notes, and wanted to explore that in this work.
The infinity-series is constructed in the following manner:
The first number of the series is 0:
a(0) = 0
Each odd number is the previous even number with the addition of 1:
a(2n+1) = a(2n)+1
Each even number is the negative of that number / 2:
a(2n) = -a(n)
I have fit the integers on a hexachordal scale: C (0), Db (1), E (2), F (3), G# (4), A (6).
And a value like -1, becomes the A an octave lower, etc. The use of the hexachordal scale results in an harmonic sound that is different from the application of Nørgård.
This row could go on indefinitely. The second section spells out over 500 notes of the series.
This sequence of integers, translated to notes has a few interesting properties. One of the main one is a interesting mix of variation and repetition. Another property is that of self-reference.
Because each even number of the string is the negative or inverse of that number’s halve value, each 4th note of the series, (the negative of the negative) contains the row itself. This can be seen in the fact that tenor part in the harp from [D] (and the violin in [E]) play in continuous parallel with the corresponding note in the stream of 16th notes. The same applies to a larger extent to the bass-line in the low register of the harp.
Aprox. duration: under 5 min.
Score availble on request.