Re: Microtonal accidentals

[Keith OHara]

On Fri, 08 Nov 2013 01:30:02 -0800, Hans Aberg <address@hidden> wrote:

> On 8 Nov 2013, at 01:47, Keith OHara <address@hidden> wrote:
>
> > On Thu, 07 Nov 2013 13:26:04 -0800, Hans Aberg <address@hidden> wrote:
> > > On 7 Nov 2013, at 21:47, Keith OHara <address@hidden> wrote:
> > > > Hans, I am late, but can I persuade you to try this with sharp and flat
> > > > representing 4 tone-steps rather than 5 ?
> It is not possible to do that with current LilyPond;
> Graham Breed retuned the fifth in his regular.ly, so ....

Well, neither LilyPond nor Graham will object if we adjust the naming convention
(as attached and at http://k-ohara.oco.net/Lilypond/).

With 53 steps, there is an interval very close to how a violinist would play D 
F# in traditional notation.  If you choose the sharp to represent 4/53 of an 
octave, then 53-step notation also shows this interval as D F#.

Then the glyph to show the fifth B F#' would get an arrow indicating that it is 
larger by a comma; the M-m=5 alteration would use the symbol sharp.uparrow.  I 
find this convention uses fewer arrows to represent real music.

> In JI C major, the D minor triad is out of tune. If trying to pivot sequence of 
> triads C F Dm G C the pitch will slip with a syntonic comma. So the pitch must 
> be adapted somehow.

We are led to a different frequency for the D depending on whether we go 
through F (two fifths down and major third up) or through G (two fifths up).  
Using 53 steps per octave lets us see that, with a nice scaffold of 
equally-spaced named pitches that might ease understanding.

53EDO_2_16.ly
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