"Reverse Well"?, NOT!

[Billbrpt]

In a message dated 98-03-16 00:01:12 EST, you write:

<< Billbrpt wrote:
  I would never let my C major 3rd beat faster than the BE or DbF 3rd's which
are consecutive to it.  The same goes for my FA and GB 3rds.  If I were trying
to tune an ET, and couldn't get it entirely equal, I wouldn't allow the
results of my inherent errors to be a RW.  I'd rather make it sound like a
very mild Victorian (VT) or Quasi- Equal (QE) like the Marpurgs.>>
 
<< Bill, 
 The light is beginning to come on, here. To put it in my own words, I would
say that the white key thirds should beat a little slower than the rest. I
have tuned that way, when I tuned aurally, on spinets and consoles which
refused to accept my best attempts at ET. Realizing that I no longer do that
since using RCT, I will do some experimenting. On a poorly scaled piano, it
makes sense to put the noisier intervals in the keys distant from C major and
make the easy keys more friendly.
  Tom>>

You don't have to alter the program very much if you don't want to.  You are
correct in the above.  The black key and black & white key 5ths will be a
little purer and the white key 5ths a little more tempered.  Make them satisfy
your idea of what is tolerable but still incorporate these variations.  You
can make changes to the program as little as 1¢ or 2¢ in order slow down a 3rd
or speed it up.

Here would be a suggestion:

F: +2¢   F#: -2¢  G: +2¢  G#: +1¢  A: no change  A#: +1¢  B: -2¢

C: +2¢  C#: -1¢  D: no change  D#: +1¢  E: -2¢

These should be easy for you to plug in.  You can make larger changes and you
can make 1/2¢ changes (or any small amount) too.  Generally, varying one note
of a 3rd by 1¢ will produce a barely perceptible beat rate change.  Therefore,
varying two notes in the opposite direction by 1¢ will make a more noticeable
change, by 2¢ in one direction and by 1¢ in the other, another level, by 2¢ in
both directions even more and so on.  

Remember that if you widen a 5th from an ET program by 2¢, it is pure.  You
don't want it any wider.  Narrowing a 5th by 1¢ will hardly be noticeable.  By
2¢ will probably be your threshold of tolerence for what sounds like an
acceptable 5th.  When played in the context of a triad, this slight "wow" in
the 5th virtually disappears.  This is why a tempered 5th becomes acceptable
in a musical context.

Historically this would have still been called "equal" but today it cannot be
thought of that way.  Still, this is where I think some of the confusion lies.
Just what is meant by "equal"?   As a CTE, I most certainly have my definition
of "equal" but others' may be far looser.  Still, there is quite a leap from a
true ET, a Victorian and 1/4 comma Meantone.  There are all kinds of in
between possibilities.

Good luck with your blind test and please let the List know what the results
are.

Bill Bremmer RPT
Madison, Wisconsin
 
 -- 
 Thomas A. Cole RPT
 Santa Cruz, CA
 
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