[CAUT] "key coloration"

[Fred Sturm]

On Mar 8, 2009, at 1:13 PM, Dan Reed wrote:

> My vote is, that comparing the P5 to the M3rd, the M3rd  was (and  
> still is), the target interval to adjust......the interval that most  
> dramatically stands out, from beatless.

	Yes, the M3 is the target interval to adjust. But how do you adjust  
it? You can't just do it directly, and come up with a complete,  
balanced temperament. The actual temperament procedure requires using  
5ths.
	You can adjust M3s directly within an octave: CE, EG#, G#C. But that  
doesn't get you 12 notes. You have to use another interval to come up  
with a circular system, where you produce all 12 notes. The 5th  
(together with its inversion, the 4th) is the practical alternate  
interval.
	And you have to keep in mind that whatever you do to "improve" one  
thing, it requires you to make something else worse. That is the basic  
temperament "riddle," and it is insoluble. All one can do is come up  
with a compromise.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu