Algorithmic music that does not repeat

[ark]

Suppose you want to assemble a piece of music out of a small number of fragments, in such a way that no sequence of one or more fragments is ever repeated. How many such fragments do you need, and how can you do it?

Scientific American answered that question a long time ago. First, note that the number of fragments must be greater than 2. For suppose that you have only two fragments, which we will call A and B. Suppose without loss of generality that the first fragment in your piece of music is fragment A.

Then the second fragment must be B, because otherwise you'd have AA, which is a repeat. For the same reason, the third fragment must be A. But now, the fourth fragment can be neither A nor B, because ABAA repeats A and ABAB repeats AB.

What if there are three distinct fragments? Then the article proved that it *is* possible to produce a piece of music with no repeats. The strategy involved three sequences of fragments, each about a dozen fragments long. These sequences have the property that you can pick any of the sequences and replace each of its fragments by the corresponding sequence without generating a repeat.

In other words, if we name the sequences R, S, and T, we can pick any of R, S, or T, and replace each instance of fragment A by the complete sequence R, each instance of fragment B by the complete sequence S, and each instance of fragment C by the complete sequence T, thereby multiplying the length of the piece of music by the length of the sequences (all the sequences are the same length) without ever generating a repeat.

This process can be repeated indefinitely, thereby showing that with only three fragments, it is possible to make a piece of music that never repeats any nonempty sequence of fragments.

Can anyone give me a pointer to the article?

[apalomba]

Sounds very much like a context free grammar or a lindemier system.
I would be very interested in this article too.

[blue hell]

Around what year was this in Sci.Am. ?

Did some searching based on the presumption Douglas Hofstadter would have been involved, I found nothing though.

[ark]

[blue hell]

[Kassen]

[Kassen]