A001511 (formerly <no subject>)

[Antti Karttunen]

Marc LeBrun wrote:

> >= Jaap Spies
> >>=Henry Gould
> >> Can anyone interpret the sequece below?
> >> 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 
> 1 3 1 2
> >> . . . . .
> > Sounds like music! ;-)
>
> As I told NJAS, usually such things aren't very musical (more "for the 
> eye only" as Bach put it). 

Often not, but sometimes are!
I would look/listen to sequences with interesting, _almost_ periodic 
patterns, but not as
predictable (and boring?) as in A001511. Compare these:

**http://www.research.att.com/projects/OEIS?Anum=A054245
%S A054245 5,5,5,3,4,4,4,2,5,5,5,3,6,6,6,5,10,10,10,8,5,5,5,2,6,6,6,5,11,11,11,9,

http://www.research.att.com/projects/OEIS?Anum=A084452
%S A084452 4,4,4,0,5,5,5,0,0,6,3,5,0,5,0,6,6,0,6,0,0,7,3,0,6,6,0,0,7,0,6,6,0,0,0,
%T A084452 7,7,7,0,...

The first one is actually quite nice, when played with the proper 
instruments...
(maybe we could search sequences with the shortest Hamiltonian or some other
kind of "distance" to A054245 ?)

The other one could be listened with the aid of such program as
JuggleMaster which is available at: http://www.juggling.org/programs/ibm-pc/
which plays different tones for the throws of different heights.
I have used that program to play, not that one, but a few finite
siteswap-patterns created just for the nice rhytmical/musical effects 
they make.


This also reminds me Campanological "compositions"
http://www.research.att.com/~njas/sequences/Sindx_Be.html#bell_ringing
some of which you can listen to at
http://www.eccentrix.com/members/johnketteringham/
(click the letters), and also by following the links given at:
http://www.ringing.info/index.html#recordings

and of Laurent Dorey's ideas of using periodic sequences
to "modulate" the plot of a story. See his message forwarded by Neil
to this group, around February 2003.


So, maybe this search doesn't tell much about the _mathematics_
of the sequences, but instead it might tell something about
_what kind of sequences (of tones) people find pleasing_,
which itself is a serious field of musicology/cognitive science.
Try googling with the keywords "Yale" and "melodic sequences".


Terveisin,

Antti


>
>
> But THIS sequence, in particular, sounds like "Towers of Hanoi" by 
> Andrew Schloss in the following!
>
> The Digital Domain. Elektra/Asylum Records 9 60303-2, 1983. Works by 
> Jaffe (Finale to ``Silicon Valley Breakdown''), McNabb (``Love in the 
> Asylum''), Schloss (``Towers of Hanoi''), Mattox (``Shaman''), Rush, 
> Moorer (``Lions are Growing''), and others.
>