Thank you Graham.
I don't understand very much what is written within the page you sent me. But 
from the "quick start" I have understood the basic and was able to implement 
this code:
http://lsr.di.unimi.it/LSR/Snippet?id=786
It works. Unfortunately I can only re-name the existing standard notation.What 
about adding arrow-"ed" accidentals to the already existing ones?
I can read on the "accidental" paragraph of the web-page you have provided:
"Whether or not you want new accidentals, you need a new associative array for 
microtonal tunings."

But really I don't understand where to look about to learn how to create new 
accidentals (instead of just replacing existing ones).
Luca

> Subject: Re: Microtonal notation - arrows up and down
> To: lilypond-user@gnu.org
> From: gbr...@gmail.com
> Date: Wed, 9 Dec 2015 21:18:16 +0000
> 
> > Date: Wed, 9 Dec 2015 01:05:11 +0100
> > From: Luca Danieli<mr.luce...@hotmail.it>
> 
> > Hello everybody,
> > I found out very few about arrows down and up for microtonal 
> > notation.Neither a quick research on the mailing-list has shown many 
> > results.
> > I found the best example of it in the following page but I hoped to find 
> > some more information on how to set up arrows down and up.
> > http://lsr.di.unimi.it/LSR/Search?q=microtonal
> > Can someone lead me to the right tutorial, if there is any?
> 
> http://x31eq.com/lilypond
> 
> You have to decide what they mean.  Then, set new note names, define the 
> accidentals, and set a base scale, if you need it.  Probably the default 
> or a regular retuning of it will do.
> 
> 
>                Graham
> 
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