[seqfan] Re: Need help reverse engineering sequence from Per Noergard

Jon Wild wild at music.mcgill.ca
Sun Dec 30 22:35:28 CET 2018

Dear Neil,

The musical notation in that image is just the composer's "infinity 
sequence" read into an array 16 pitches wide, 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, 

The notated tune on the staff that starts at the centre of the spiral and 
proceeds outwards contains the infinity sequence (each entry of the 
sequence gives the interval measured from the starting note, G). The 
"spokes" of the spiral present the vertical columns of the array above. It 
looks as if the vertical spoke that is aimed downwards in the image you 
linked, and which contains the leftmost column of the array here, 
reproduces the infinity sequence itself. (Does this hold? It doesn't 
appear in the notes to A004718.)

Overlaid on that spiral are the various coloured lines that appear to be 
constructed in fairly ad hoc ways:

The five yellow lines start from the first member of the series. One of 
them hits every 15th element, one hits every 17th element, one every 20th 
element, and the two others might be every 65th and 78th element but they 
hit so few notes it's hard to extrapolate from what we see.

There are blue and green lines emanating from the 4th and 5th pitches that 
hit every 15 notes. And so on, with many other colour connections that 
seem to have just been drawn onto the diagram in a way that pleased the 
composer or that were suggestive to him for some unknown reason.

Then as to the question of how the actual musical work was composed, given 
this "pre-compositional" design: that can only be figured out from an 
intensive study of the score and/or the composer's sketches, or else by 
asking him. I'm pretty sure, knowing some of his other works, that it will 
have been done far from mechanically, and with many note choices made for 
reasons other than mathematical.

The excerpt you posted at https://www.youtube.com/watch?v=wc8GvMkjGBc 
involves microtones, which don't appear anywhere on the image, so I 
imagine portions of the work are not derived from that image at all.

The other excerpt at https://www.youtube.com/watch?v=ELIA88kHJr4 starts on 
F# and follows the sequence "0 1 -1 -2 2 -4", which is obviously 
spiral-like in a way, but doesn't appear exactly like that near the 
beginning of the sequence. The flutes come in with E-D-F#-G# or "0 -2 2 
4", another spiral-like design. All that to say: I'm not sure the music is 
composed according to this design at all, but if it is, it's done so in a 
very obscure and personal way.


Jon Wild

On Sun, 30 Dec 2018, Neil Sloane wrote:

> Dear Seq Fans, If you look on YouTube for a musical work by the famous
> Danish composer Per Nørgård called "Iris" or maybe "voyage into the golden
> screen", you see something that looks like a sequence written around a
> spiral.
> One of these links may work, depending on what country you are in:
> Per Nørgård [Noergaard], <a href="
> https://www.youtube.com/watch?v=wc8GvMkjGBc">Voyage into the golden
> screen</a>, on YouTube.
> https://www.youtube.com/watch?v=ELIA88kHJr4
> Could someone convert this to a sequence for the OEIS?
> (The infinity sequence is another work of his, for which the sequence is
> A004718)
> The test for success would be that when you click the listen button on the
> OEIS entry,  you hear something that is an approximation to the musical
> work.
> --
> Seqfan Mailing list - http://list.seqfan.eu/

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