Who says E.T. is the best way to solve octave divisions?

[A440A at aol.com]

Julia writes
 << Why is equal temperament the only way to solve the dividing of 
octaves? <<

Greetings, 

     It isn't.  It is just a limit since there is nothing left to compromise. 
 It is the most often used temperament because it is the only one of its kind 
and everybody has grown up trusting it.  

>>I know that the beautifully mathematical solution on paper sounds and 
works fine, but what if there a way we could be missing out on something, 
such as 
better sounding music? <<

      What is being missed is the increased emotional engagement created by 
actual key color in 18th and 19th century keyboard music. 
      However, I don't know about "better", since that really depends on how 
much the listener is getting out of the experience.  What some just love, 
others detest.    What is fairly clear is that the equal temperament is not as 
complex as the well-temperament, so there is less information being passed.  That 
information would have been registered at the subliminal level.   Some prefer 
it that way.  Others bemoan the loss. 
         So, the idea is that if the composer WANTED a certain transition 
chord to really speak out in contrast, a wide third might be more effective than 
a small one, and if that composer wanted to resolve a progression on a calm, 
harmonious chord, it was really nice to have a near pure third to land on.  It 
makes musical sense.   If that info wasn't installed by the composer, it is a 
moot question.  Very few listeners can detect a "bent" temperament from the 
audience if the maximum third is 18 cents or less.   
     That "beautifully mathematical solution" is what some seek, and  to 
them, everything else represents an unacceptable compromise. Others are repulsed 
by that solution and must have pure thirds, even if it means restrictive 
tunings.  Still others go by using whatever tuning is best suited (ITHO) for its 
intended use.  

    It helps to remember that the state of temperament has AWAYS been in a 
state of flux.  It has now been sitting still for at least 100 years.  What does 
this mean?  
       Over the last 600 years, the evolution of temperament shows a 
consistant pattern of periodically changing.  Of interest is that the period has 
steadily been shortening.  Thus, we see the use of Pythagorean from say 400  
(Boethius) to 1,200 , Meantone from 1,200 to 1700, Well-tempered from 1700 to 1900, 
ET from 1900 to 2000.   These figures can be moved around a lot without 
departing from the basic progression evinced here:   800, 500, 200, 100 year 
intervals.  Where do we go from here?   
    Do we go where the keyboard world has never gone and embrace a 
multi-temperament awareness?   That would be new. Something similar happened in the 13th 
century, but nothing like what is possible today.  We have the benefit of 
being able to see a historical trajectory that very few before us had.   It seems 
logical to make use of it.  
     Or do we go, at all?  That is a question everyone will answer for 
themselves. Do we allow the status quo to define this life-experience for us, or do 
we look for ways to expand the horizons and perhaps be part of the  change 
that is constantly going on?   
     
>>Havent we manipulated string lengths and diameters to 
force E.T. to sound well?  >>

        I don't think the tension differences between ET and WT create 
variances large enough to matter.   Given that wires increase by .001" per size, the 
inherent compromises forced by this gradation are larger than the change of a 
few cents up and down among the notes, (I think and observe that). 
    ET is convenient, easy to find, and easily measured.  Those three things 
are, at present, enough to insure its continued use.  However, there are a 
growing number of pianists aware of its limitations.  I expect that to continue.  
Regards, 


Ed Foote RPT 
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html
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