[CAUT] three M3s

[Fred Sturm]

On Mar 8, 2009, at 3:22 PM, Dan Reed wrote:

> Three contiguous Mj3rd can be used to balance the octave..is there a  
> better way aurally to set two precise markers inside the octave?

	I was fascinated to discover recently that this method goes all the  
way back to Rome in the 1640s, as the procedure used by Atanasio  
Kircher to produce ET (there was a small group of ET advocates in Rome  
at that time). This is attested by Galeazzo Sabbatini in a manuscript  
from around 1650, examined by Patricio Barbieri and reported in an  
article published in 1986. Sabbatini himself used a method involving  
three M3s (dividing each into its "component" four 5ths), but in order  
to create 1/4 comma mean tone. His M3s were GB, EbG, and EG# (which  
obviously don't, together, form an octave). He commented on the  
similarity of his method to that of Kircher in producing ET, saying  
that Kircher divided the octave into three equal M3s in his method  
(then proceeding to divide each M3 into its "component" four 5ths).
	It's amazing how little has changed, and how many things are  
constantly rediscovered. The method was again "discovered," this time  
in Germany, around 1750 by Marpurg and Sorge. And by Montal in the  
1830s. And popularized by John Travis in the mid 20th century. And I  
agree, it is a good one.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu