[seqfan] Musical information about a sequence

[Veikko Pohjola]

Dear seqfans,

Applying floor(tan(n)) repeatedly, a limiting sequence results composed of 0’s and 1’s only. The proportion of 1’s is somewhat over 12% and they distribute interestingly forming a repeating pattern. Converting the sequence of distances between the positions of 1’s into music (say piano) turns it to fascinating music manifesting a steady beat with a theme and delicate variations. Counting the number of beats in a sequence of known length permits to assess the number of individual sounds (terms) within each measure to about 42.

I am wondering whether such a steady beat could be inherited from the periodic nature of the mother function (tan) and if so, should the length of the pattern thus be predicted. And in general, are this sort of musical findings regarded to belong to recreational domain and not at all to hard mathematics, not even when some useful mathematical information could be obtained by listening.

Best regards,
Veikko Pohjola