Thomas Jefferson Tuning Scheme I

[Billbrpt]

In a message dated 98-03-04 03:15:16 EST, you write:

<< The wolf is actuallyG#4 Eb5. It is not tuned as that is the result of
tuning pure fifths. It takes a keyboard to see this.  Jefferson tuned 7 fifths
up to G# and 4 down, to Eb. The twelth fifth then is G#--Eb Which according to
Pythagoras would be flat, very flat.  Indeed the spread sheet shows that fifth
beating at 16.9 cps flat. >>

   It is much more likely that these 5ths were all tempered and that the wolf
5th is actually wide.  This would have been some kind of meantone temperament
but we just don't know exactly what kind.  

   If the 3rds tests revealed pure 3rds, it would have been a 1/4 comma MT.  I
suspect that Jefferson merely listened for a "pleasing" resonance which would
have meant that the 3rds tested would simply have beat slowly.  Considering
the era in which this was done, the kind of music which would have been played
and the kind of instrument, slowly beating 3rds among those which were tested
would most likely have been the goal.  If pure 3rds were desired, the scheme
would have tuned 3rds, not merely tested them.

   Since there was no control over how much tempering was meant to be in the
5ths, we can assume that the amount may have varied somewhat but that,
considering the era, they were in the range of 1/5 to 1/6 comma 5ths.  It is
highly unlikely that Jefferson would have tuned pure 5ths in this scheme.
This would have made the 3rds that were tested beat very rapidly.  This would
have been quite out of character both for his instrument and the music of the
time.  The curious ">>" marking may have been Jefferson's "fudge" interval.
He may have considered the key of E, with 4 #'s as being one which could be
varied or manipulated or he may have been sensitive to how dissonant he would
allow his "wolf" interval to be.  If he "fudged" on this interval, he could
have made the key of E be rather bright and in doing so, mitigated the "wolf"
thereby creating a modified meantone temperament, a very common practice.

Respectfully,

Bill Bremmer RPT
Madison, Wisconsin