Re: Diatonic notation system

[Hans Aberg]

On 8 Dec 2008, at 12:28, Graham Breed wrote:

> > Also, I made keyboard map, which I have used in Scala playing in  
> > mainly E31
> > for the last couple of months:
> >   A#  B#  Cx  Dx  Ex
> >  A   B   C#  D#  E#  Fx  Gx  Ax  Bx
> >    Bb  C   D   E   F#  G#  A#  B#
> >      Cb  Db  Eb  F   G   A   B   C'# D'#
> >        Dbb Ebb Fb  Gb  Ab  Bb  C'  D'  E'
> > It will them work in any such generalized diatonic system.
>
> You mean you have a keyboard mapped like this, or you use a virtual
> keyboard in Scala?
>
> Anyway, it'll only work in a system with a single spiral of fifths
> (singly positive or negative in Wilson's terminology).  No good for
> miracle or magic temperaments.

The link <http://x31eq.com/paradigm.html> you gave says:
  Miracle scales can be described as subsets of either 31, 41, or 72  
note equal
  temperament. For example, the 21 note "blackjack" scale looks like  
this:
  1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 /31
  1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 /41
  2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 /72
So the m M-model will work, and also the keyboard layout above, if  
adding more note names. One must give those names in Scala, but the  
vectoring is the same.

There is a practical problem: it is nice to have the octaves level.  
And having a lot m's makes the keyboard span short.

  Hans