Historical Temperaments

[Robert Scott]

It has been interesting reading this latest explosion of interest
in historical temperaments.  Here are few observations and a question.

Comments have been made about the method of tuning an HT as
it relates to the tonal center.  Bill Bremmer may be right when he says:

>   All of the HT's that have been a part of this recent discussion are created
>with C as the tonal center.

And it may be that the historical methods of arriving at the historical
temperaments started with C.  But as Bill also points out, these two facts
need not be related.  The method can be independent of the outcome. (As an
analogy, if you have a Master combination lock with combination numbers
A, B, and C, you can open the lock by starting to the left instead of the
right using combination numbers A-9, B+4, C.)   So if A-440 is an
absolute requirement, then alternate aural methods can be found starting
with A.

But I wonder if A-440 is that relevant to HTs.  Suppose you have an HT
that is defined in terms of cents offset from equal temperament.
Further suppose that for this particular HT, the offset for A from equal
temperament is fairly large.  Then what good does it do to force A to be
440 if in so doing the rest of the temperament is forced to be quite far
from their equal temperament counterparts?  Here is a more uniform 
criterion. Tune an HT so that the average offset from an A-440 equal-
tempered scale is zero.  Doesn't this make more sense than insisting
on strict adhearance to A-440 in this case?  It comes closer to the goal
of keeping the same average tension on the strings, and is thus kinder
to the instrument.  And it also comes closer to the goal of minimizing
differences between the piano and fixed-tuned instruments.

It has also been pointed out on this list that some of the HTs are 
not well-defined in terms of today's measuring methods.  The temperaments
are defined by the methods used to achieve them rather than by their
outcome.  This makes it more difficult to duplicate them today.
This is especially true with regard to the differences between
modern piano inharmonicity and historical piano inharmonicity.  Perhaps
those of you in the historical rebuilding business can comment more
accurately, but didn't those old pianos use thinner wire and lower tensions
than modern scales?  And so we would expect much lower inharmonicities
from historical instruments.  The inharmonicities affect beat rates.
We cannot expect HT tuning methods that rely on specific beat rates to 
give the same results when applied to a modern piano.  So following the
old instructions to the letter may not produce the best adaptation of an
HT to a modern instrument.

Here is a proposal that would work for users of VTDs.  Find an authentic
historical instrument appropriate the the HT in question.  Tune it aurally
according to the historical instructions.  Then measure the fundamental for
each note in a temperament octave, which will give offsets in cents from
equal temperament for the temperament octave.  Now to tune a modern instrument
in the HT, use that set of 12 offsets to modify a good equal tempered tuning
curve that has been customized to a modern piano.

This bring me to my question.  I would like to collect a library of historical
temperaments for users of my TuneLab program.  Some users have already sent me
a few historical temperament files, and I thank them.  But is there one
source I can go to that lists all (or most) historical temperaments in terms
of offsets from equal temperament?  I have not looked at Jorgensen's book
yet, but I will buy it if someone can tell that it contains such a list.

Bob Scott
Ann Arbor, Michigan
Detroit-Windsor Chapter, PTG