Musical Sequences

Does anyone know why they’re called that? The name is so suggestive and the theory is so nice, that I can’t help but hope there’s some underlying connection, but so far, I can’t find one.

To explain, a musical sequence is an infinite list of two symbols, usually L and S (denoting “long” and “short”). In addition, this list has the property that no section of it can be copied in a regular way so as to create the full list. Another way to say the same thing is musical sequences are non-periodic. They can be generated by repeatedly sending S to L, and L to LS. So, for instance:

LS
LSLL
LSLLSLSL
LSLLSLSLLSLLSL

The incredible thing is that they seem to pop up everywhere in the world of non-periodic and aperiodic patterns (Grunbaum and Sheppard). In fact, once 3d versions of aperiodic tilings were discovered, sure enough, 3d versions of musical sequences were also found. I also haven’t found a good explanation as to why this is the case, but it seems that musical sequences create a kind of underlying organization for less organized, aperiodic, patterns.

 

Their role as organizers is actually what is so useful to design. Frequently, the design intent requires a facade or plan layout to be “random”. The problem is, true randomness is a pretty ugly and unwieldly thing, so more often than not, a pattern that gives the appearance of randomness is used instead. In fact, if such a pattern were to be guided by musical sequences, all sorts of pragmatic issues, like whether or not the nodes of the glazing have any relation to the nodes of the structure that holds it up, get resolved. My personal favorite 3d aperiodic tiling, developed by L. Danzer, is currently on display in a Cecil Balmond exhibition.

The point is, here is a very nice mathematical principle that will improve the constructability of certain kinds of projects while maintaining a certain aesthetic and seems to imply some connection with music. It would be perfect, except that the connection to music is still a mystery to me.