On Wed, 23 Nov 1994, Kent Crispin wrote:
> You can define a measure of "goodness" of a tempered scale in numeric terms
> by calculating the theoretical differences in frequency between the scale
> and perfect intervals (this is sort of a distance function in a vector
> space, if that helps).  She then did a computer study to analyze equal
> temperament scales with different numbers of notes -- the twelve tone
> equal tempered scale is actually an amazingly good fit -- much better than
> an 11 note or 13 note scale.  That is, a twelve-tone scale comes "pretty
> close" to many perfect intervals.  There are other scales with many more
> notes with better fits, though, and she composed a piece in a tuning with
> something over 200 notes per octave, if I remember correctly.  A very
> interesting piece...
 
 
Did anybody hear the interesting piece on All Things Considered about a
month ago about a composer at Urbana-Champaign who received a NEH grant
to write compositions using equal temperament scales from, I believe, 8
to 24 notes per octave?  Some of the pieces were very good, including a
sort of Christmas carol for (synthesized) brass in 17 n.p.o, I think,
which was more perfect than 12.  Some of the other pieces were deeply
painful to listen to.  An interesting exercise, all in all.
 
 
 
________________________________________________
Robert P. Forbes <[log in to unmask]>
Department of History
Yale University
New Haven, CT  06520  (203)432-0714