Temperament Charts,

[A440A@AOL.COM]

Greetings, 
David writes: 
<<  I am curious what Bill Bremmers EBVT looks like. >>

     Well, plot them out.   (I use metric, so that a cent can easily be 
represented by mm or cm,  depending on what size chart you want.)  
    Any temperament which is described by offsets from ET can be easily 
plotted, just subtract or add the differnces to or from 13.7, (or 14 if you 
like to round things off).  There are equal beating combinations in the 
Coleman tunings also, they are not unique to any one tuning.   
   Fifth's charts can also be instructive, just observe the differences inre 
the  -1.9 cents or so that you would expect an ET fifth to begin with.  I 
haven't used the fifths for my lectures, since the thirds are so much in 
control of apparent consonance and dissonance.  Also,  the degree of 
complexity that is useful when introducing the subject to newcomers is much 
less than what is possible, ie.  consider Chopin's use of such extreme key 
signatures.  When you "parse" a passage of his, you find that he often j
uxtaposes a melodic line of pure fifths over a very highly tempered harmony. 
This combination creates a harmonic "space" in the music that is obscured in 
ET.  It is recognizing this harmonic texture that is a learned skill, but it 
is easily learned, just listen with open ears and mind.  
     The converse is also interesting, in that in the simpler keys the more 
purely tuned harmony provides a very "lush" background that is behind the 
expressive line formed by the more highly tempered fifths in a melody.  
Temperament resources also make possible "shock value" if the composer cares 
to modulate in such a way as to take advantage of contrasts.  (Beethoven 
sorta lead the way in this technique, I think).  
 
    The highly tempered thirds can often be seen to have been ameliorated by 
separation, such as 10ths and 17ths instead of thirds.  This sort of 
separation cuts the beating in half or farther, and it is common to hear the 
beating brought down to speeds that approximate vocal vibrato, ( around 7 
bps).    
    The effect of temperaments is a deep subject, and I really believe that 
as more of us investigate the changes wrought by them, we will continue to 
find more and more examples of very sophisticated usage.  This was the gist 
of an earlier thread on the composers treatment, that the 'colors'  were seen 
as a feature, not as bugs. 
   It is a wonderful time to be a tuner.  As Kent mentioned earlier, for the 
first time in history, we have the ability to compare them all.  All tuners 
before us, I think, basically tuned what was the temperament of the times, 
which changed so slowly that one lifetime was scarcely long enough to 
experience more than one stage.  I encourage any tech to broaden their view, 
the piano has been treated to a wide variety of intonation, and the music 
that accompanied these stages reflects something of them.  
Regards, 
Ed Foote RPT