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

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Discussion Overview

The discussion revolves around the concept of "musical sequences" in the context of one-dimensional Penrose tiling, exploring the connections between aperiodicity in tiling and musical structures. Participants examine historical references, definitions, and analogies related to the term without reaching a consensus on its appropriateness.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the connection between aperiodicity in Penrose tiling and music, noting a lack of clarity in existing references.
  • Another participant provides links to resources that discuss aperiodic tiling and its relation to musical sequences, suggesting these may clarify the term's usage.
  • A participant shares a definition of musical sequences, highlighting specific rules about interval arrangements, but expresses confusion about its musical relevance.
  • One participant proposes that the analogy may relate to common song forms, suggesting parallels between musical structures and tiling patterns.
  • Another participant speculates that Conway's choice of the term may stem from a personal affinity for music, while acknowledging the difficulty in obtaining definitive answers from Conway himself.
  • A later reply mentions that Conway's naming conventions, including "musical sequence," may be intended for amusement, referencing a source that discusses this in detail.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the appropriateness of the term "musical sequence" in relation to Penrose tiling. Multiple interpretations and analogies are presented, but the discussion remains unresolved regarding the connection to music.

Contextual Notes

Some participants express limitations in accessing academic resources that could provide further clarity on the topic, which may affect the depth of the discussion.

Who May Find This Useful

Readers interested in the intersections of mathematics, art, and music, particularly those exploring aperiodic tiling and its conceptual implications.

nomadreid
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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?
 
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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.
 
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.
 
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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.
 
They're well described in Grünbaum and Shephard's book Tilings and Patterns (chapter 10, section about Ammann bars in Penrose tilings). They say Conway chose this name, like he chose the names of the vertex configurations like Jack, Queen and King... so I guess it's basically about fun and games :)