Re: Diatonic notation system

[Hans Aberg]

On 10 Dec 2008, at 12:47, Graham Breed wrote:

> > Perhaps you mean the between a sharp and a flattened M, like  
> > between F# and
> > Gb, which may be positive or negative. Since I do not impose any such
> > relations, those are not confused.
>
> Yes, that's the one.  If you only record pitches with M and m they
> will be confused because m=m.  The diesis above C# (let's call it C#^)
> will come out the same as Db.  If I asked for C#^ maybe you'll give me
> Db.

This is because you do not know how to work out the diatonic values.  
C to C# is M - m, and C to Db is m, so C# - Db = M - 2m, the same as  
the definition of a comma in Pythagorean tuning.

One can see this by computing the scale degree d, which are unchanged  
by accidentals. So d(C#) = d(C), and d(Db) = d(D), so d(C# - Db) = 0  
- 1 = -1. Since this is nonzero, commas are nit confused.

In fact, it is the other way around, for example E12 confuses scale  
degrees, because F# = Gb. This is however not a problem, as the  
Western notation system is diatonic, forcing one to write one of  
them. Then one can confuse them if called for.

  Hans