On Thu, Apr 05, 2007 at 12:34:23PM -0400, Charles Linart wrote:
As others have already pointed out, this isn't true, but I'd like to add
a little to the discussion.
Experimental musicians have occasionally used equal tempered scales
other than the common Western 12 tone scale, the most common that I'm
aware of being the 19 an 22 tone scales. Keyboard instruments have
actually been constructed for the 19 tone scale by splitting each black
key in two (so that, e.g., F# and Gb are two different notes), and
adding a red key between the B and C, and another between the E and F
keys. This allows traditional music notation to be used in this scale.
The 19 tone scale has major thirds that are slightly more in tune than
the 12 tone ET scale, while fourths and fifths are slightly less in tune.
I also read an article years ago about a guy who constructed an electric
guitar with 22 frets per octave for the 22 tone ET scale. The 22 tone
scale has major thirds that are slightly more in tune than either the
12 tone scale or the 19 tone scale, while fourths and fifths are slightly
less in tune.
If you heard music in either of these systems, it would sound no more
alien to you than many other forms of non-Western music. The point is,
it doesn't matter how many notes you divide the octave up into. What
matters is whether there are notes within the system whose frequencies
are at or near to small number ratios to other notes in the system, for
the sake of harmony. These ratios are:
No equal tempered scale will have any of those ratios, exactly, except
for the octave. Just tunings will have some of those ratios, exactly,
buy only in certain keys, because it's impossible to have all fifths or
all thirds perfect, for example.