on Meantone

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<< diatonic scale created by tuning pure fifths.   In such a scale, the
do-re and re-mi intervals, both whole tones, are not equal, the do-re whole 
tone
is larger than the re-mi whole tone.  This, of course, creates a problem if 
you
want to modulate (which is why we temper in the first place) and in the mean 
tone
system of tempering the goal was to create one "mean tone" which is neither a
major whole tone or a minor whole tone but a "mean tone" or an average between
the two. >>

Greetings, 
     I would like to add that we temper for reasons other than modulation!  
Getting to what was the intention for the meantone tunings development, I 
would submit that it was the arrival of the strung keyboards, ca 1400, that 
caused the move.  
     As you mentioned, a pure fifths, Pythagorean octave would create unequal 
size semitones, etc. and it would also have some very harsh thirds.  This was 
not a problem before 1200, since the thirds were not used in composition, 
being regarded as discords, (which they were in the tunings of the era).  As 
keyboards developed more than eight keys per octave, there were new problems 
to deal with in tuning.   
     With the documented 14th century use of pure thirds in the harmony of 
English choirs, (Walter of Odington), and the arrival of strung keyboards,  a 
system for producing the maximum number of pure thirds developed.  This is 
what Pietro Aaron documented in 1523. The C-E third was tuned pure, and the 
fifths between were all tempered by 1/4 of the syntonic comma. (the syn comma 
is the difference between a ditone, which is the pythagorean third and a Just 
major third).  
  Mersenne mentions that tuners would use pure thirds in their tuning 
meantone, so the central location of say, D between C and E,  was a 
resultant, rather than a goal.  
Regards, 
Ed Foote  RPT