Re: do these notes exist?

[Hans Aberg]

On 24 Mar 2008, at 19:11, Michael David Crawford wrote:

> I learned a scale with double-sharps just the other day.  Let me  
> see... Key of A# Minor.  From Scales and Arpeggios for Keyboard by  
> Palmer, Manus and Lethco, page 52:
>
> A# Harmonic Minor:
>
>    A# B# C# D# E F# G## A#
>
> A# Melodic Minor, Ascending:
>
>    A# B# C# D# E F## G## A#
>
> Now, F## is G natural, and G## is A natural.  But my understanding  
> for the odd double-sharp and double-flat notation is that  
> convention calls for every letter - ABCDEFG - to be present in  
> every key, with enough sharps or flats added to make the intervals  
> right.

It is not merely a convention (except in 12-ET, see below) - it  
becomes that way in a temperament other than 12-ET.

Write the pitches in the circle of fifths:
  Fbb Cbb Gbb Dbb Abb Ebb Bbb
  Fb  Cb  Gb  Db  Ab  Eb  Bb
  F   C   G   D   A   E   B
  F#  C#  G#  D#  A#  E#  B#
  Fx  Cx  Gx  Dx  Ax  Ex  Bx
here written the on several rows: left/down.

Then transposition in fifths moves set of pitches left/down. So, for  
example A harmonic minor consists of the pitches A B C D E F G#. To  
transpose A A #, just move the whole set down one step.

> Without that convention, the harmonic minor would be:
>
>   A# C C# D# E F# A A#
>
> So you see, C and A would occur twice, but with different  
> accidentals. That would probably be confusing in an actual score if  
> it was notated that way.

In dedicated 12-ET music, it odes not matter how one writes it. But  
in often, instruments are expect to adjust towards a temperament  
where it matter, in Western music, Just intonation. So in such case,  
enharmonic equivalence is not formally applicable.

Also, the notational system does not derive from 12-ET, so if one  
does not adhere to what is a convention in this temperament then, one  
may have to throw in some extra temporary accidentals.

  Hans Åberg