1-dim Penrose tiling = "musical sequence"? Why?

  • #1
nomadreid
Gold Member
1,481
150
In several places (e.g., page 12 of http://www.cs.williams.edu/~bailey/06le.pdf), I have come across the aperiodic intervals in a one-dimensional Penrose tiling as "musical sequences". I do not see the connection between aperiodicity and music.
The history of a fruitless but amusing search:
(a) The best I could find is that the timbre of a hoarse voice, such as whispering, uses aperiodicity vibrations of the vocal chords, (but that doesn't help.)
(b) Amusingly enough, when I used included the key words "Amman bars", which can be used to generate the 1-d aperiodic tilings, Google gives me primarily sites about pubs in the capital of Jordan.
(c) Martin Gardner (https://www.maa.org/sites/default/files/pdf/pubs/focus/Gardner_PenroseTilings1-1977.pdf) says that Conway invented the name "musical sequence" in this context, but Gardner just labels them "Fibonacci sequences". Then, a search for Conway and Fibonacci Sequences turns up the fact that there is a classical music ensemble called "Fibonacci Sequences" which gave a concert in Conway Hall in London.
So, does anyone know why the name "musical sequence" is appropriate here?
 

Answers and Replies

  • #3
nomadreid
Gold Member
1,481
150
Thanks, Asymptotic. They do define what is meant by musical sequence "The spacing between bars is either long or short. In these musical sequences a short cannot follow a short and a long cannot follow two longs." and "In musical sequences a long interval can follow another long interval but a short interval must follow two long intervals, and a short interval must be followed by a long one." However, I still do not see what this has to do with music.
 
  • #4
779
526
I'm thinking the analogy is to song forms. For example, AAA is common in traditional folk (think "House of the Rising Sun") where the same figure is repeated ad infinitum, AABA is perhaps the most prevalent (here is a good run down on AABA), while other forms include AABB, ABAB, and so on, sometimes interspersed with C, D, or more discrete sections.
 
  • Like
Likes nomadreid
  • #5
nomadreid
Gold Member
1,481
150
Thanks, Asymptotic. That is as good a guess as I suppose is possible without a definitive answer from Conway (John Horton) himself. He's 80 now, and trying to get an answer from him would probably not be a Good Thing. Unfortunately, as I do not have access to a decent academic library (for access, for example, to the three books of Conway's that Gardner cites) and the Internet comes up with nothing (unless I wanted to order all those books), I will have to assume that Conway's love of music made him stretch an analogy a bit far. Or maybe this is what music looks like for the "creatures" from Conway's Game of Life.
 

Related Threads on 1-dim Penrose tiling = "musical sequence"? Why?

Replies
2
Views
3K
  • Last Post
Replies
23
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
11
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
3K
Replies
3
Views
2K
Replies
7
Views
2K
Replies
4
Views
2K
Replies
13
Views
4K
Top