<HTML>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> </HTML>