[Bell Historians] Musical scales

[Carl S Zimmerman]

At 23:12 +0000 06/12/08, Andrew Wilby wrote:
>Yes well done, but as Dickon says to complete the picture we need all 24
>major keys.
>
>I don't know from where comes the suggestion that some of them are not
>used.... a the point is that all of them can be.


There are only 12 notes to an octave in the equal-tempered chromatic 
scale.  It is true that each of those has an alternate name (as the 
sharp or flat of something else), so that there are 24 possible note 
names in the same span.  But A-sharp and B-flat are the same note, 
and to argue otherwise indicates a presumption of some other 
temperament.

Therefore, in equal temperament there are only 12 distinct major 
scales.  For one of those scales, both possible names (Gb/F#) are in 
regular use, because neither six flats nor six sharps has any 
practical advantage over the other.  That is why I included 13 scales 
in my tables rather than 12.  The other 11 note names simply are not 
used as the names of major keys; in fact, for 9 of them there is no 
conventional key signature.

The two marginal major keys are Cb (seven flats) and C# (seven 
sharps).  Key signatures do exist for them.  But since *every* note 
of the diatonic scale is either flatted or sharped, they are really 
inconvenient to use in comparison to their tonal equivalents of B 
(five sharps) and Db (five flats) respectively.  I believe that a few 
pieces of music have been written in these marginal keys, though I 
have never encountered one.  I suspect that it was done more because 
a composer wanted to prove that it was possible than because there 
was a distinct musical benefit to be derived from doing so, but I 
wouldn't argue with anyone who expressed a contrary opinion.

In unequal temperament, the story is different, and there may well be 
more than 12 distinct notes to an octave in some temperaments.  I 
have modified my new Webpage to reflect my assumption of equal 
temperament and to touch very lightly on matters of unequal 
temperament.  But I don't consider myself competent to write at 
length on this subject, so I will leave that to others.  (You can 
call me an equal-temperament musician if you want to do so.)  Suffice 
it to say here that present-day customary use of key signatures and 
note names does not convey any information with respect to 
temperament; that information has to be provided in some other way.

CSZ