How to choose Temperament? was Another Recital in 1/7 Comma

[Billbrpt@AOL.COM]

In a message dated 4/13/00 2:45:50 PM Central Daylight Time, A440A@AOL.COM  
writes:

<< << Greetings, 
      I must disagree.  
  A pure M3 is 386 cents wide.  Three of these span a distance of 1158 cents. 
 
  An octave is 1200 cents wide.     The difference between three Just 
  contiguous thirds and an octave is a diesis, and it is approx. 41 cents.  
    A syntonic comma is the difference between four just fifths and two Just 
  octaves. See Jorgensen, "Tuning", pg 777
  Regards, 
  Ed Foote RPT
   >> >>

Ugh!  Ya got me.  I should know better.  41 cents is the size of the Ab-C 3rd 
in 1/4 Comma Meantone, the diesis itself.  It does bring up a question I have 
always had.  Do you know the answer?  Why are all of the Meantones named by 
the fraction of the Syntonic Comma that all of the 5ths are tempered by?  I 
know this to be a fact and that is why tuning a chain of 5ths by that 
fraction (with an adjustment for inharmonicity) works.  But the aural tuning 
instructions always concentrate on 3rds and only involve 4ths and 5ths when 
you run out of 3rds to tune.

In other words, the Meantones are all about how the 3rds sound but the name 
of the temperament is always the fraction of the Syntonic Comma that the 5ths 
are tempered by.  Why is that so? And why was the Syntonic Comma chosen as a 
value rather than anything else?

In a message dated 4/13/00 2:47:32 PM Central Daylight Time, 
drose@dlcwest.com (Don) writes:

<< At 08:20 AM 4/13/00 EDT, you wrote:
 >Generally, the earlier the period, the more unequal.  The more unequal, the 
 >purer the sound from the simple keys, 0-3 sharps or flats and the more 
 >vibrant or harsh, the remote keys, 4-6 sharps or flats.
 
 I used to think this too until I started looking at graphs of various
 *tempermants* (mannering might be a better term). I know you are one of the
 HT experts--please enlighten me, if what I am saying is *wrong*. 
 Regards,
 Don Rose,  >>

As the message and answer above indicate, I am not an expert on Historical 
Temperaments and don't claim to be.  I am merely a practitioner of what I 
know by association with my colleagues, from lectures and demonstrations, 
reading and personal experience.  There may be HT's or ancient tunings that 
have characteristics other than the Cycle of 5ths harmonies that I often 
speak about but I have never practiced or worked with them.

All of the Meantones, Modified Meantones, Well-Temperaments, Victorian 
Temperaments and Quasi-Equal Temperaments I know and work with have the same 
basic characteristics that I wrote about.  And as I said, generally the 
earlier, the more unequal, the later, the closer the gravitation towards ET 
they get.  The Romieu 1/7 Comma is one exception and so are the Marpurg Quasi 
Equal Temperaments.

My belief is that these kinds of temperaments formed the basis and reason to 
write any particular music in a particular key. Those reasons have survived a 
century of ET and therefore, HT's work with most any kind of music, even all 
of the kinds of music that are popular today.  If you have a temperament that 
produces something else, then it is likely to make the music sound wrong, 
having a kind of off or out of focus sound.  I really don't know which graphs 
you have seen or which temperaments they illustrate.  Do you have any of the 
names of these arrangements which you have found questionable?  That might 
help.

Regards,

Bill Bremmer RPT
Madison, Wisconsin