4:5 Ratio of Contiguous 3rds

[Billbrpt@AOL.COM]

---------------------- multipart/alternative attachment
List,

Recently, I read again of someone's contention and insistence that there is 
no such thing as the 4:5 Ratio of Contiguous 3rds in ET.  Unfortunately, 
these statements undermine the most important advancements in aural tuning to 
take place since William Braide White's instructions for tuning Reverse Well 
written about 100 years ago.

I heard about the 4:5 test for contiguous 3rds some 20 years ago from PTG.  
In 1986, I studied with Bill Garlick RPT at Steinway who told me that it was 
his idea and that Dr. Sanderson had confirmed it.  At the time, he said that 
the ratio was not a theoretically exact 4:5 relationship but that for all 
practical purposes, it could be considered that.  That was then and is now 
good enough for me.

Now, the reality:  This is a very small but important distinction which is 
perceived and made when trying to perfect an aurally tuned ET.  In testing 
the contiguous 3rds, one listens for the lower one to be only *slighty* 
slower than the upper one.  Virtually any error in temperament equality, as 
little as one cent will cause this relationship to be incorrect.  Are the 2 
intervals beating exactly the same?  It's wrong.  Is the bottom one obviously 
much slower than the upper one?  It's wrong.  Is the lower one faster than 
the upper one?  It's wrong.  Each of the above conditions can exist when 
there is only a very small error, the kind which may not be easily perceived 
when only listening to 4ths & 5ths or even playing chromatic 3rds listening 
for "smoothness".

If the contiguous 3rds test does not prove correct, there will always be a 
4th too pure, a 5th too tempered, etc., which will correspond to the improper 
relationship found in the contiguous 3rds.  Therefore, the contiguous 3rds 
test is the most valuable and useful tool there could ever be for aural 
tuning of ET.  It does not matter one iota what all those irrational numbers 
are that say it is not exactly a ratio of 4:5.  The FACT is that it a a 
relationship of "a *little* slower" to "a *little* faster".  It is far easier 
to know when the relationship is incorrect than to decide that it is 
perfectly correct.

William Braide White's instructions did not provide this diagnostic tool.  
Therefore many people who have followed them of the decades probably made the 
error that John Travis identified as the "tendency to err towards the just 
5th" and create habitually as a consequence, Reverse Well, all the while 
*believing* it to be ET.

Bill Bremmer RPT
Madison, Wisconsin
 <A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A> 

---------------------- multipart/alternative attachment
An HTML attachment was scrubbed...
URL: https://www.moypiano.com/ptg/pianotech.php/attachments/b1/39/54/d2/attachment.htm

---------------------- multipart/alternative attachment--