"diluted" temperaments (long)

[Billbrpt@AOL.COM]

In a message dated 4/17/00 1:33:45 PM Central Daylight Time, 
drwoodwind@hotmail.com (Ron Koval) writes:

<< Even one cent can make a difference, if placed in the right location.
  >>
This is great work you have done, Ron.  I also have a temperament that I use 
very occasionally when the usual EBVT still seems too strong for the 
customer.  I called it the "1-0 Temperament" because every note was either a 
+1, -1 or a 0 deviation (although I think there are one or two .5 cent 
deviations in there too).  Surprizingly, this still gives the Cycle of 5ths 
based colors that are the entire basis for doing this kind of work.  The 
temperament falls into the Quasi ET range but it still satisfies the Rules 
for Well-Tempered Tuning.

I might mention that I once did a "numbers" type study to see if I could 
produce a Well-Tempered Tuning that would still "pass" the PTG RPT Tuning 
Exam.  To my surprise, not only could I but I could produce an 18th Century 
type that would barely "pass" with a score of 80, a 19th Century type which 
would "pass" at a score of 90 (and which is considered outstanding in itself 
and qualifies the Examinee to train as an Examiner if all scores end up that 
high) and finally, a very mild Quasi-ET type that
still met the rules of Well-Tempered Tuning but which would "pass" the Exam 
at a perfect score of 100. 

The last one had it's greatest deviation at .9 cents.  Now the difference 
between .9 and 1 cent might not be audible in itself but as you noted, the 
cumulative effect of a series of .9 cent deviations surely can be heard.  And 
yes, this does mean at least theoretically anyway that someone could pass the 
PTG RPT Tuning Exam with a perfect score of 100 and not have the temperament 
be ET at all.  I do not suggest trying it, though, not at all, DON'T!

When I set out to construct a Victorian Temperament along the pattern of the 
18th Century Modified Meantone Temperament that I liked so much but which was 
too strong for most people to accept, I did essentially the same thing as you 
have done.  I tried to keep my deviations within 4 cents of 0 with most being 
in the one to 3 cent range.

With my A3 at 0, and my D4 usually falling at 0 or 1 cent at the most, there 
are no notes which vary from ET more than a cycle or two at most.  Therefore, 
the EBVT can play compatibly with other fixed pitched instruments or with 
MIDI programs such as the Orchestra Soft which are presumed to be based on 
ET.  Keeping my deviations constrained keeps my temperament within the range 
of tolerance that most people have for the way the piano should sound.

If it is presumed that many, (especially aural) attempts at tuning the piano 
have errors, then it follows that there will be wider and narrower 3rds than 
the usual 14 cents of ET.  22 cents probably does go too far for most 
sensitive listeners but holding the widest to 18 or 19 cents can make the 
temperament palatable.  This is also the range in which Jim Coleman's Coleman 
11 lies.  Remember too that a 3rd which is either pure or very slowly beating 
may sound "flat" to the contemporary ear.  It makes a lot of sense to use a 
mild type temperament when tuning the piano for a general use situation or 
for introducing the customer to the world of Cycle of 5ths based harmony.

My very last resort before tuning a true ET which I did last sometime in the 
Summer of 1989, would be the Marpurg-Neidhart Quasi Equal Temperament 
(usually called just "Marpurg") where you get 3rds and 6ths identical to ET 
but 9 pure 4ths & 5ths with 3  1/6 Comma 4ths & 5ths.  For many technicians 
who are afraid to use even a Victorian Temperament, this is as far as they 
will go.  I have heard of many Concert Tuners using this instead of ET.  For 
those who like the sound of pure 5ths, it is a very good choice and it does 
not produce the rather strained, bursting at the seams sound of the ET with 
Pure 5ths.

Bill Bremmer RPT
Madison, Wisconsin