Series

Score

Sound

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Infinity series workbench

X
Folding
0
0
0
Wavelength
1
1
1
First note
C4
C4
C4
Scale
Repeat
X
Note value
Clef
Meter
Bars
4
X
Volume
3
3
3
Instrument
Tempo
112 BPM
Accent
2   3   4   5   6   7  
X

The Infinity Series

This section draws heavily from the website about Per Nørgård, www.pernoergaard.dk. Great site with lots of reading on Per Nørgård and his work.

Per Nørgård discovered the infinity series in 1959, and throughout the years it has had a tremendous influence on his compositions.

The infinity series is a series of numbers - and thus the use of it in musical composition has to be called a serial technique, but Nørgård never falls into the trap of uncritical, mechanical composition. The infinity series is used to create a melodic line, but not at the same time to control rhythmical and dynamic aspects, such as prescribed by Central European serialism.

Nørgård has said that he did not invent the infinity series, but discovered it. In this way he gained insight into a view of the world which was well ahead of his time. This might seem a pompous statement, but in fact the infinity series exhibits a number of fascinating characteristics which one would not hesitate today to describe as fractal. In 1959 there was no real corpus of scientific knowledge concerning this phenomenon, nor a scientific language to describe it. This did not appear on the scene until the general spread of the Chaos Theory around 1980.

The series looks like this: 0, 1, -1, 2, 1, 0, -2, 3, -1, 2, 0, 1, 2, -1, -3, 4, 1, 0, -2, 3, 0, 1, -1, 2, -2, 3, 1, 0, 3, -2, -4, 5, -1, 2, 0, 1, 2, -1, -3, 4, 0, 1, -1, 2, 1, 0, -2, 3, 2, -1, -3, 4, -1, 2, 0, 1, -3, 4, 2, -1, 4, -3, -5, 6, 1, 0, -2, 3, 0, 1, -1, 2, -2, 3, 1, 0, 3, -2, -4, 5, 0, 1, -1, 2, 1,

To use it in a musical context requires counting the numbers from a base-tone. From C4, the fist notes will be: C4, C#4, B3, D4, etc.

That is, if projected on the cromatic scale. On a harmonic scale, like the Major, it will be: C4, D4, B4, E4, etc.

The parameters of the app

  • Folding Folding is a modulus operation on the numbers of the series. If folding is set to 4, no nubers will come outside the range -4 to 4. The number -7 will become -7 % 4 = -3 (some may argue that -7 % 4 = 1, but... not in this case).
    When folding is applied, there will be repeated notes - this will never happen in the original series.
  • Wavelength takes every wavelength number of the series. In wavelength 2, the series will be 0, -1, 1, -2, -1 etc.
  • First note is the first note, the fundamental note of the series.
  • Repeat defines how pereated notes are treated be the software. Play, default, meaning that all notes are sounded, while Pause meaning that only the first note is heard.
No animals were harmed in the making of this app.