Talk:Listen to a sequence

Expanding

At the 2012 JMM a number of fans of the OEIS discussed ways to listen to sequences. Ideas and discussion are welcome!

Key and notes

One idea that came out of the discussion was to split off the high bits from the low bits. Right now a base (e.g., 88) is chosen and the least significant digit in that base is taken, giving the note to play. Instead, one could choose a smaller base (e.g., 56) and interpret those as notes in a particular key; the high bits could give the key to play in. This way, if the sequence does not grow too quickly, the key does not change too frequently, leading to (possibly) more melodic sound. Further, this frees up more bits for use in polytonic music, if desired.

Polytonic music

Whichever bits are used for notes (the whole number, if a key is not being used, or the number less the key part otherwise) can be interpreted in a suitable base (e.g., 56); all significant digits are played simultaneously. Alternately, a Zeckendorf-like representation could be used, ensuring that consecutive notes are not played (if this is desirable).

The volume could be modified so that not all notes are of equal loudness, to ensure that large terms do not cause a 'muddy' sound; perhaps the k-th least significant digit should be played at 1/k-th the volume of the least significant digit. (I chose this since the harmonic diverges, so truly huge sequences would become loud; a different asthetic might lead to 2^-k or another. Of course this and other features could be customized by the user, but the choice of defaults is important.)

Expertise

It was suggested that ideally someone with background in music (music theory, etc.) should look this over to give suggestions, since some of the ideas might be misguided.

Coding

To turn these ideas into reality, someone must write the program; this presumably requires familiarity with the MIDI spec. I don't know if it's simple or complex.

Charles R Greathouse IV 03:00, 9 January 2012 (UTC)

I think the only time I have ever used the "listen to a sequence" feature prior to today was either Beethoven's Fifth (A054245) or Für Elise (A123456). I've tried it with both of those now and only for the latter are the results anywhere near worthwhile; since the latter has more consecutive notes of equal duration it does better in this treatment. And this reminds me of the Recaman's sequence video on YouTube (on the Favorites playlist of WSUEngineering). I will have to listen to some more sequences before I can really advise on this.

However, for now, I can tell you one thing about the MIDI spec: if you know how to read music and you know how to program devices like printers at the C or assembly level, then the MIDI spec should seem quite simple once you get down to reading it. Alonso del Arte 17:06, 12 January 2012 (UTC)

Well that's encouraging on the MIDI front at least.

I await your feedback on the general issue of listening to sequences. Of course there's no hurry.

Charles R Greathouse IV 01:50, 13 January 2012 (UTC)

Also possibly relevant: http://arxiv.org/abs/1201.2654

Charles R Greathouse IV 05:45, 13 January 2012 (UTC)

Over the past couple of days, I have taken the opportunity to try out the listen feature on various sequences that have caught my interest for reasons apart from this. A lot of what I've heard sounds like it could have been written by an avant-garde composer of the 20th century. Alonso del Arte 18:36, 14 January 2012 (UTC)

My latest idea is to incorporate a Shepard tone into created music, such that a sequence like A000027 can actually sound like it increases forever. I'm not sure how to properly generalize this so that it works for more than just simple sequences and without muddying tones too much. Charles R Greathouse IV 14:47, 13 July 2012 (UTC)