[seqfan] Re: Need help reverse engineering sequence from Per Noergard
jean-paul allouche
jean-paul.allouche at imj-prg.fr
Sun Dec 30 23:13:01 CET 2018
Nice questions and nice answer!
About the fractal-like property, I guess
it is somehow between the lines in the
paper by Jeff Shallit, where several sequences
linked to the infinity sequence are proved to be
2-regular: see https://www.fq.math.ca/Papers1/43-3/paper43-3-9.pdf
best wishes
jean-paul
Le 30/12/2018 à 23:02, Neil Sloane a écrit :
> Jon, that is very helpful!! when I've digested it I propose to take the
> liberty of adding an edited version as a text file to A004718. I'll let
> you know when.
>
> I'll also add a comment about the fractal-like property of the infinity
> sequence (based on taking every 16-th term), which was new to me.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
>
> On Sun, Dec 30, 2018 at 4:35 PM Jon Wild <wild at music.mcgill.ca> wrote:
>
>> 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.
>>
>> Best,
>>
>> 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/
>>
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
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