Re: Diatonic notation system

[Hans Aberg]

On 9 Dec 2008, at 02:29, 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.
>
> So the layout you gave won't work because it doesn't have enough note
> names.  You need to add note names and move the existing ones around,
> making it a different layout, and implying a different notation.

Right, but the underlying vectoring in terms of m and M is the same -  
the problems appear by defining it in terms of notation system, a  
limitation of Scala, and easier to understand for those just working  
with the traditional diatonic system.

> > There is a practical problem: it is nice to have the octaves  
> > level. And
> > having a lot m's makes the keyboard span short.
>
> That's why I prefer square keys for miracle.

The layout is alto optimized for fingering. There is a mirror reverse  
version for E31 here
  http://www.huygens-fokker.org/instrumenten/fokkerorgel.html
but then I think it will be difficult when passing the thumb under  
the hand. Similarly, for chords, they should match the natural  
curving of the hand.

In addition, ideally, the key board should be rotated, so that the  
octaves are level.

I think the buttons of the Roland virtual accordions would be ideal.

  Hans