Equal Temperament, history of, judgement of

[Billbrpt@AOL.COM]

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In a message dated 2/27/02 8:00:10 AM Central Standard Time, 
remoody@midstatesd.net (Richard Moody)
 writes:


> 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)
> 
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> 

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