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.

Iannis Xenakis: Composer, Architect, Visionary

Iannis Xenakis: Composer, Architect, Visionary
The Drawing Center
35 Wooster Street, New York
Through April 8

Though best-known as a composer, Xenakis trained as a civil engineer in Greece and travelled to Paris in 1947, where he ended up working in the studio of Le Corbusier. His most famous building design was the Philips Pavilion for the 1958 World’s Fair in Brussels. In this work, Xenakis was able to fully explore the mathematics of hyperbolic paraboloids, and how music could be applied to built form.

-Excerpt from The Architects Newspaper

But what’s the link?

It’s been just about a week since our first session (Architecture in Combination with Music), and despite an extremely  interesting presentation by Mani Mani (www.fishtnk.com) on his Tunable Sound Cloud, I still have questions on what it means to combine architecture and music. Granted this is a rather old debate, but judging from the number of projects that use some aspect of music or sound to drive the design, it seems to still be an active one. So here it goes.

Firstly, what is the role of music in design? Is it purely to produce data that can be fed into a geometry producing script? Can any of the emotional content of the music be revealed in the design? Should it be? And secondly, are there any practical advantages to having music as a design driver?

I’d say the most solid connection between music and architecture comes from the world of acoustics. The idea is that acoustically driven forms will enhance the performance (or at least try to), and conversely, every aspect of a given geometry can be valued in terms of how much it contributes to that performance. Unfortunately, this is a very idealized state and any acoustician will tell you that it’s just not that simple. It also completely ignores the content of the music.

Maybe there’s a kind of organizational principle hidden inside the rhythmic structure of fugues? Who knows….?