Question regarding Well Temp. Tuning

[Billbrpt@AOL.COM]

In a message dated 8/16/00 7:59:27 AM Central Daylight Time, 
remoody@midstatesd.net (Richard Moody) writes:

<<  Without historical evidece we will always be wondering what they used.
 Theorists (of temperaments) could wirte until they were blue in the face but
 that doesn mean anyone of that time followed them. (snip)  Another problem 
of ET was that it did not have a name nor a scheme.  Everyone knew if you 
tune with barely perceptible flat 5ths  wouldn't get a wolf. This then is ET 
but by our standards perhaps a "quasi" ET because the 3rds which were not 
checked might not be as smooth as ours. But could this procedure have been 
called "well tempering"?  >>

Some interesting points are brought up here.  In some respects the view of 
"Meantone" vs. ET is the same now as it always has been.  The 1/4 Syntonic 
Comma Meantone has noticeably tempered 5ths and a "Wolf" that is very 
noticeable at more than 40 cents wide and very dissonant.  Any amount of 
reduction in the tempering of the 5ths would reduce the width and dissonance 
of the "Wolf" and tend to even out the 3rds.

>From what I have read, the Well-Temperaments (WT) (where there is a series of 
pure 5ths which eliminates the "Wolf" were sometimes, if not often called 
"equal" because all keys were considered to be useful.  But, in the example 
given above, simply tempering the 5ths a little less, does not produce a WT 
but instead a milder form of Meantone.  However, the very slight "Wolf" which 
is the result might not have been considered offensive and may have even been 
found useful and appealing.  This is the feature of the 1/7 Syntonic Comma 
Meantone (by Jean-Baptiste Romieu in 1758).

There are also the Modified Meantones, where the "Wolf" interval is divided 
between two or more 5ths and thus mitigated to the point of usefulness.  All 
of the WT's, milder Meantones and Modified Meantones may have been used as 
the "ET" of the time, temperaments which had all 24 major and minor keys 
musically accessible and useful.  Unfortunately, we do not know exactly which 
kind of temperament may have been used by which composer but having said 
that, it might be said that "any one would do".

If tuning a harpsichord or fortepiano for an event of 17th or 18th Century 
music, it makes sense to choose one of the classic temperaments that is 
historically documented to have come from that period.  Using a true ET under 
such circumstances would really be altering the way the music would have and 
should sound.  Surely, it might be "enjoyed by all" but the point is that the 
very least appropriate temperament has been chosen and the audience has not 
been given a choice and is largely ignorant of what the difference might even 
be.  In short, the choice of ET in this circumstance does both the music and 
the audience and injustice.

When tuning a modern piano for a concert, however, there is likely to be 
music from different periods, perhaps spanning from the 17th to the 20th 
Centuries.  The conventional wisdom is that only ET would be appropriate 
because it would serve anything and everything.  I have long contended that 
the choice of ET goes further than it has to in satisfying the requirement to 
be able to play in all keys and to serve all varieties of music.

Instead, I believe it is more important to consider what kind of effect the 
temperament and octave arrangement might have on the way it makes the piano 
itself sound, regardless of the music to be played.  If there is but one kind 
or period of music to be played, the choice of temperament might be made much 
the same way as it should be for a harpsichord or fortepiano but also bearing 
in mind that it is a modern instrument and the more unequal the temperament, 
the more extreme the sounds will be that come from the piano.

Today, the "one or the other" view of "Meantone" vs. ET gives people the idea 
that there is only one choice, ET and anything else is not a matter of 
consideration.  Many tuners will do as described above, "... if you tune with 
barely perceptible flat 5ths ..." (and ignore the precision of the 3rds) you 
will not really get ET.  But, the effects of this haphazard way of tempering 
are ignored and thus a wide variety of effects in tempering, whether they are 
beneficial or not, are accepted by tuners, musicians and listeners alike.

I remember the Jefferson Tuning being published on this List a couple of 
years ago.  I recognized it as a Meantone type pattern but it did not 
identify the amount of tempering of the 5ths.

Bill Bremmer RPT
Madison, Wisconsin