A case for modern "HT's"

[Ron Koval]

In response to my posting yesterday on a new introductory temperament, I got 
this back:

<snip>
Absolutely *superb* use of the gray matter!  Now, can you define it as an 
aural tuning temperament sequence?
<snip>

Thank you very much!
The short answer is: no

The long answer is: maybe, but I don't think I want to.

The recent attempts at calulating the "numbers" for the EBVT has forced me 
to rethink what we know about HT's.  We owe a great debt to Owen Jorgensen 
for his studies into the historical record.  However, I feel that 
considering our failure with translating what one technician has developed 
into reliable numbers, it would be advisable to consider the places for 
errors to creep into the process.

First, a tech must come up with a plan.  Next there must be a written record 
to pass along.  Here is the first opportunity for errors.  What makes 
perfect sense to the author can be less than clear to the reader.  How pure, 
or how equal beating, or how accurate in beats?  Even testing a temperament 
on a piano is problematic.  So, if a technician follows a written record, 
then measures a tuning, there are tuning errors to consider, as well as the 
measurement process. (what partial, how repeatable, etc...)  Historical 
temperaments have academic value, but I think that modern temperaments may 
provide more accurate results.

In "larger" temperaments, small errors have little effect on the overall 
implementation of the bearings.  As the temperaments get closer to equal, a 
half-cent error here and there makes the margin for error larger than the 
offsets produced.  I have always been distrustfull of published numbers for 
historical temperaments listed to the hundreth of a cent, it just seems 
impossible to really know what was practiced to that degree of precision.

So, to take any temperament offsets, and translate to a bearing plan is to 
invite mistakes into the process.  If someone else wants to crunch the 
number, come up with a plan, and check it out, I'd welcome the effort.  I 
think that in this case, technology has driven the interest in optimizing 
temperaments.  Those that choose to tune without ETD's will not be able to 
take advantage of the new research into these tunings.

There are a few of us creating temperament with the aid of spreadsheets to 
predict beat rates, and interval widths.  This allows "tweaking" of offsets, 
to create the maximum equal beating effects, or whatever the author is 
trying to accomplish.  These have been tested in the field, and will produce 
consistant results when placed onto an accurate tuning calculation. (There's 
the BIG if, folks) I've done most of my work in the "quasi-equal" level, so 
my two are listed first.  I'm sure they are all listed in the archives, but 
if there is interest,I could come up with the numbers.  These are listed in 
order of "strength".  The first one as an equal substitute, the next for a 
little more variation without getting too rough in the remote keys, and the 
last couple to be used as a client looks for more color.

EBKM - max offset 1.5 cents, thirds from 11.5-15.5 cents from pure
EBK  - max offset 3 cents , thirds from 9.2-16.9
Wendell well 2002 - 4.88 cents max, thirds from ~8-18
Bailey well  - 6.2 max , thirds from ~6 - 21 cents from pure

Paul Bailey also has a "heavy duty" meantone that he has worked on for  
specific clients.

looking forward to your responses

Ron Koval
Chicagoland



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