Re: Diatonic notation system

[Hans Aberg]

On 9 Dec 2008, at 13:42, Graham Breed wrote:
> > > > And key signatures make the notes sound different.
> > >
> > > Yes, and it's a classic cause of errors in performance, despite the
> > > key being reinforced by the music.
> >
> > If you don't know how to read them.
>
> Even if you know how to read them you are likely to make mistakes.

Not using key signatures will not solve that problem.

> > > They always, or even generally, write in major keys.  Willaert, in
> > > particular, was writing before major keys were defined.  But let's
> > > assume they'd notate it as just intonation.
> >
> > But the question is how to notate a change a key from C to D.
>
> Write different notes?

Rather which accidentals do you use?

> > No, the first two m M are used generate the staff system and  
> > sharps and
> > flats.
> >
> > Then one add a suitable number of neutrals n_1, ..., n_k to get the
> > intermediate pitches.
> >
> > For example, putting n = M3 - M gives an accidental suitable for Just
> > relative Pythagorean.
>
> Sorry, I was wrong.  You do have more generators.

Only that I give them variable names, and consider the linear algebra  
they generate.

> > > > If it now can produce other than multiple of 12.
> > >
> > > Do you have evidence that it ever didn't work?
> >
> > I attached file, you can try to tweak it into proper E53 if you like.
>
> What does E53 have to with anything?  We were talking about correct
> transposition.

If transposition calls for say a comma below an m, and that m is  
computed not against E53, but E12, I think there might be an error. I  
leave it to you figure out. By contrast, if it is in E53, then I know  
it is right, and I do not have to do that exercise.

> > C to C# is M - m, C to Db is m.
> >
> > C to an E31 above C#, can be described as a double flat. double  
> > sharp, or by
> > adding a neutral second, all having different musical function.
>
> No, not an E31.  An enharmonic diesis.

Since the name diesis has many uses, you will have to elaborate.

> m is not a double flat.
> 2(m-M) would be a double flat.  m is not a double sharp.  2(M-m) would
> be a double sharp.

In E31m these are 4 tonesteps, so the difference with M is one E31  
tonestep.

> Adding a neutral second to what?  m is not a
> neutral second.  m is, in fact, m.  How does abstract m and M
> distinguish it from m?

If you want to have the tonestep between Db and D, that is a neutral  
second, generating a symbol for an intermediate pitch.

> > But i want to find out how you want to notate it: as E53 with  
> > intermediate
> > pitches or a system where the note names have different interval  
> > values.
>
> I'm not writing it.  If I did I'd probably use Pythagorean notation
> with a comma accidental.

So that would then work with the method I gave.

  Hans