Temperament nomenclature

[A440A@aol.com]

Jason writes:

<< This kind of tuning
produced a distinctive "key color" that was also used consciously by
composers in the 18th-19th centuries. Over time, from Bach's era to the
early 20th century (when the math for tuning Equal Temperament was first
solidified and a reliable ET bearing plan was first developed), the
differences between the sweetest third and the harshest third were gradually
reduced, but the key color remained >>

Greetings, 
     I think the math for ET was worked out long, long before the 20th 
century.  I don't have my hands on the research right now, but I seem to remember a 
Chinese or Japanese description of ET from centuries before. 
I agree with the idea of a reliable bearing plan for ET being a late arrival 
in the history of our instrument.  However, I don't think the lack of a 
reliable bearing plan was holding the use of ET back, we tend to invent things to 
suit our purposes when we need them.  I think what delayed the use of real ET 
was a combination of how the skillset of tuning was passed along, what the 
market wanted, and the rising influence of standardization in culture and 
manufacturing.  A particular tuning that may impart increased beauty to one era's 
compositions doesn't find a ready home in the culture of mass production.   
    We see a variety of tuners in 1885 that varied from ET.  What is 
important is that the departures were not random.  They all varied in the same 
direction, just to lesser or greater extents.  There was some acknowledged departure 
from making it all exactly equal, and everyone seemed to be doing it in a 
similar way.  I think I can see why.  These were working guys, and extra effort is 
to be avoided.  It is certainly easier to stack the dissonance in ascending 
piles than it is to divvy it up in 12 exactly equal amounts.  How well one 
could do this might determine how much they could charge for their work, and  I 
can imagine some of those tuners were proud of their particular temperament, and 
might guard it carefully.  
   I don't think the clinically strict ET we test with today was particularly 
attractive to the composers or listeners of the classical era, since 
everything was about tonality, and the use of keys was following some general 
organization.  It seems that most composers resembled their peers in their choice of 
keys, i.e., if we compare the prevalence of a key's usage to the width of its 
tonic third, we find a direct correlation in almost all the keyboard composers. 
 Across the board, the smaller the third, the more often the key was 
employed.  The graph of Beethoven's piano pieces mimics the same shape as the graph of 
a generic well temperament.  Same with Haydn.  And Mozart, though the 
temperament his music matches is more of a meantone, (Mozart really avoided the four 
most remote keys). 
     Schubert's music also shows these tendencies.  What is interesting is 
that as we move past Chopin,(who is quite hard to categorize inre temperament 
influences, but that is a different story), we find, increasingly, more 
democratic use of the keys.  At the same time, the science of tuning was fast taking 
hold and the norm in temperament equality was probably higher than it had ever 
been previously.  By the time we get into the 20th century, pretty much all 
the keys are in use, as we would expect in a temperament era of equality.  This 
long term correlation between how the keys were used and plausible styles of 
tuning is easily shown.    
   I personally don't think the correlation is coincidence.  Given the state 
of keyboard tuning, (if we accept that a tuner in 1790 would probably be 
well-tempering) and the rules of sonata form, It makes sense that keys would be 
chosen for where in the circle of fifths they were.  This choice of tonic 
influences where the modulation takes you in terms of consonance or dissoance.  In 
the key of C, no matter where you modulate, there is going to be a lowering of 
the tempering as you return to your home key, this will increase the feeling of 
resolution when you finally come back to the consonance of home.  If the 
composer wanted something more energetic, beginning in a higher key like E might 
brighten things up. It certainly has a busier third.  What about the  extreme? 
        In the WT frame of mind, it is a real challenge to begin in F# and 
have anywhere to go to build more tension, and then try to come back to F#,(the 
most highly tempered key in many WT's), with a sense of resolution.  Could 
that explain why there is virtually NO use of F# as a home key in the piano music 
between 1700 and 1900? Beethoven wrote exactly one sonata in F#, and it is 
something of an anomaly.  Many others never touched it.  
     In the WT era of say, 1720 to 1890,  F#, with B close behind, are among 
the least used and most highly tempered keys. Everybody composed more in C 
than any other key.  No musicologist I, but  I would be interested in other 
explanations why the composers chose the keys that they did.  Anybody?   
Ed Foote RPT 
http://www.uk-piano.org/edfoote/index.html
www.uk-piano.org/edfoote/well_tempered_piano.html