Re: Microtonal accidentals

[Hans Aberg]

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 ?
>> 
>> No, since in regular E53, the minor second m = 4, and the major second M = 
>> 9, so sharps and flats alter with M - m = 5 E53 tonesteps.
> 
> But you also have arrow alterations, so you can distinguish more than two 
> types of second.
> 
> You have the diatonic scale of the bare note-names
> C  -9-  D  -9-  E  -4-  F  -9-  G  -9-  A  -9-  B  -4- C
> but the major scale build on the major triads is closer to
> C  -9-  D  -8-  E, -5-  F  -9-  G  -8-  A, -9-  B, -5- C
> (with , lowering one step)
> 
> You might choose seconds from the set m=4 n=5 N=8 M=9 and have alterations
> M - n = N - m = 4  close to a traditional sharp
> M - N = n - m = 1  close to an 81/80 comma
> then the D major scale, for example, looks more simple
> D -9- E -8- F# -5- G -9- A -8- B, -9- C# -5- D
> 
> M-m = 5 steps is another choice for an alteration, but if I write that with a 
> sharp I find it harder to understand because I have learned that a sharp is a 
> tiny bit less than half a whole tone.

It is not possible to do that with current LilyPond; Graham Breed retuned the 
fifth in his regular.ly, so there is still only two generators. What I wrote 
here [1] will do it, though.

When describing Just intonation, I think most will depart from Pythagorean 
tuning and reach Just intonation via syntonic commas 81/80, or in E53, a 
tonestep. 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.


1. https://lists.gnu.org/archive/html/lilypond-devel/2013-11/msg00062.html