ramblin'

[Jim]

Hi Richard:

One little thing caught my eye in your last reply where you said that
a pure 4th and a pure 5th could be tuned within a pure octave. Well, for
one pair that is true, but you can't have both continuing in a 
temperament.
As you spread the octave in order to fit in the pure 5ths, the 4ths
actually get faster. Now I'm learning that they will always be faster than
the stretch octaves. Sometimes more than twice the speed of the octave.

I hope this clue helps those who are actually trying to set a scale with
pure 5ths. Doing it with the SAT was so easy, that almost all the pianos
I tune now are tuned this way. But doing it aurally is quite another 
matter.  I am working out a foolproof method now for doing it aurally.
It should be on the list in just the next few days.  I would like to
actually do it a few more times before I publish.

Jim Coleman, Sr.