Re: Issue 1278: Arrow notation for quarter-tones. (issue3789044)

[Keith OHara]

On Thu, 17 Feb 2011 21:58:28 -0800, <address@hidden> wrote:
> On 2011/02/18 05:43:36, Keith wrote:
> > The extra complication, for which the care was given, makes the system
> > more difficult to learn, understand, use, and repair.
>
> Unfortunately, I believe that the extra complication is necessary.  The
> commit message didn't clarify the background or our previous discussions
> on the topic, but it boils down to composers wanting to distinguish
> between cis+1/4 and cisis-1/4

I read the emails, and understand wanting cisih distinct from cisiseh.
The current representation can store them as distinct pitches :
   -isih = 1/2 + 1/5  = 7/10
   -isiseh = 1/2 + 1/2 - 1/5 = 8/10
This would be consistent with notations (extended Helmholtz-Ellis) that use 
natural-up to represent a pitch somewhat flatter than sharp-down.

The only request I saw for cisiseh and cisih to be in some sense the 'same 
pitch', was for transpositions.  The request 
(http://lists.gnu.org/archive/html/lilypond-user/2009-04/msg00649.html) is for :
    \transpose c cih { cisih } == cisis
and analogously
    \transpose c cis { cisis } == dis

Neither the current representation, nor the patch's, makes the identities above 
happen.  Either would need (later) a different flavor of \transpose that 
'normalizes' (and maybe rounds) its output, to serve the equal-temperament 
users, while the current \transpose serves the just-intonation camp.

> NB: most requests were for *arbitrary* tunings, such as 31-tone or IIRC
> even 78-tone.

There current system has no trouble representing 66 pitches in an octave in 
makam.ly.

In the end, I'm a physicist, and pitch is a scalar, so a one-dimensional 
real-valued representation seems wisest to me.