From: Hans Aberg (firstname.lastname@example.org)
Date: Tue May 19 2009 - 13:42:49 CDT
On 18 May 2009, at 13:11, Thomas LAMBERT wrote:
> I'm currently writing a web application for music theory, and in
> this app (and in general in music) i would like to promote the use
> of the dozenal (duodecimal) system, because it will make additions
> of intervals very easier (among other advantages).
> For quite some time i've been roaming in unicode pages to find 2
> perfects characters to complete the decimal numbers with no luck.
> Cause A and B reprensente notes in music, so i decided not to use
> them to avoid confusion.
> I was wondering if you had any advice for me ?
In computing, one typically extends the digits 0,...,9, with letters
A, ..., upper/lower-case as you please. In music, for describing E12
(12 tone equal temperament), you might use lowercase Greek letters,
One might note that E12 is just one possible temperament, even in
Western music only restricted to certain fixed pitch instruments, some
mainstream popular music, or so. An orchestra is more likely switching
between adaptive Just intonation and Pythagorean tunings as needs
arise - somebody said that even a Schoenberg piece for violin was in
actuality played more like in the Pythagorean tuning, rather than
In the Renaissance, various meantone tunings were in use, particularly
the quarter-comma meantone that sets the major second to sqrt(5/4),
which is well approximated by E31. And E12 is just the first n-ET
approximation of the pure fifth rational interval 3/2, the next better
ones are E41 and E53, and the last is used in one Turkish music
I have just written a file for ChucK <chuck.cs.princeton.edu/>. by
which these can be played on a computer keyboard (posted on its users
mailing list) - the layout is such that the playing patterns do not
depend on the tuning system.
So extending E12 by something other than the obvious letter extensions
might not be worth the effort.
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