Christoffel words

Here's a presentation on the mathematical equivalent of MOS scales:

http://www-irma.u-strasbg.fr/~kassel/ChristoffelNJ0407.pdf

So, they're old, and they're known to relate to continued fractions.

The Fibonacci sequence makes a special guest appearance!

Graham

A great find. The author is apparently unaware of the music
connection, citing biology and such but not music theory.
I like the graphic method. I bet Erv would appreciate that.

-Carl

At 07:02 PM 4/21/2009, you wrote:
>Here's a presentation on the mathematical equivalent of MOS
>scales:
>
>http://www-irma.u-strasbg.fr/~kassel/ChristoffelNJ0407.pdf
>
>So, they're old, and they're known to relate to continued
>fractions.
>
>The Fibonacci sequence makes a special guest appearance!
>
>
> Graham

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
I agree. This is exactly the type of math I am looking for.
I was daunted at first by the 123 pages, but actually, it's kind
of a Powerpoint style piece, and doesn't take too long to get through.

I especially liked the diagram of the staircases going in four
directions, what a great visualization of Christoffel words.
It's a very generous and straight-to-the-point contribution overall.

- Paul

>
> A great find. The author is apparently unaware of the music
> connection, citing biology and such but not music theory.
> I like the graphic method. I bet Erv would appreciate that.
>
> -Carl
>
> At 07:02 PM 4/21/2009, you wrote:
> >Here's a presentation on the mathematical equivalent of MOS
> >scales:
> >
> >http://www-irma.u-strasbg.fr/~kassel/ChristoffelNJ0407.pdf
> >
> >So, they're old, and they're known to relate to continued
> >fractions.
> >
> >The Fibonacci sequence makes a special guest appearance!
> >
> >
> > Graham
>