<HTML>In a message dated 2/27/02 8:00:10 AM Central Standard Time, remoody@midstatesd.net (Richard Moody) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Even a causual reading of Braid White, both in "Tuning and Allied Arts" (1946) and "Theory and practice of Piano Construction" (1906) reveal more than just an understanding the theoritical rates to acheive ET.  In "Theory and Practice....  he states, "If we could secure an absolute standardization of pitch { ie A440 and not A442}  it would be possible to construct tables that would show the exact number of beats that ought to occur between ann the equally tempered sounds within the whole compass." (p126).   Now this table was published at least as early as the 5th edition (1945) of "Tuning and Allied Arts".     He goes on to say, "In default of such a method, {beat table} it is necessary to resort to a variety of tests and to prove the correctness of the tempering of each interval...." (p 126).   He describes 3rds and 6ths as examples.    Regarding "Tuning...."  5th edition ET can be tuned correctly from the informantion he gives there.   I don't now how far back the editions carry the beat tables, but  with beat tables there is no more accurate way to tune ET unless you want to argue that a tuning machine is better.    Braid White, I suppose, did not explain the 4:5 ratio of contiguous ET 3rds because it does not exist. The ratio is actually 1.25992105, Which is sharp of the ratio of 5/4 by 13.686 cents.  (1.25992105/1.25) </BLOCKQUOTE> A-440 is accepted as Standard Pitch but since when did everyone tune every piano to it every time?  You can say the same about ET.  Show me a single piano that was ever tuned so that all of the beat rates exactly matched what Braide White wrote.  If you could (and you can't), I'll tune a piano right next to it that sounds a hell of a lot better, in ET, not to mention EBVT.   The last statement made here must be some kind of misunderstanding.  Contiguous 3rds in ET will beat at a ratio of 4:5.  It is the single most important diagnostic tool when trying to sort out errors when tuning ET.  Not understanding this concept will inevitably lead to uneven progressions of 3rds & 6ths.  Very often these days, that unevenness is the exact opposite form of a Well Tempered Tuning, hence the term, "Reverse Well". 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>