Thomas Jefferson Tuning Scheme I

[Richard Moody]

There was some mention of the tuning scheme of Thomas Jefferson a
while ago, so here it is, courtesy Susan Kline, who mailed me a copy
of  an article by Jack Greenfield titled "Thomas Jefferson, Keyboard
Technician."  PTJ, April, 1981. 

The source for this is given as: Helen Cripe, "Thomas Jefferson and
Music" UVa, 1974. 

	Another source mentioned in the article is the 
 UVa Library to the Manuscripts Department, 
Monticello Music Volume 1, #3177-a, Box no F63155 folder heading
Tuning, Harpsichord. Knowing Jefferson's proclivity for writing every
thing down, there is probably another ton of information of interest
to tuners. 
 

This was written by Jefferson on the back of a page in a volume of 
minuets. 

G3--G4,  G4--D4,  D4--A4,  A4--A3,  A3--E4,  E4--E5,  E4--B4,

		Test G4 - B4

B4-- 3,  B3--F#4,  F#4--F#3,  F#4--C#5,  C#5--C#4,  C#4<<G#4
G#4 -- G#3. 
		Test: G#4 -- E4. 

G4--C4,  C4--C5,  F4--G5[*], F4--F5,  F5--Bb4,  Bb4--Bb3,  
Bb4--Eb4,  Eb4--Eb5, 
		Test: Eb4 -- G4.

F#4--F#5,  G4--G5,  G4--G5, G#4--G#5,  F3--F4. 


The first question arises at F4 - G5 (marked [*](mine ).  This is I
believe a mistake in copying Jefferson's hand writing. The PTJ
article mentions there was bleed through in the MS, so this could be
a place where it happened. 
 	First of all, F4 has not been tuned. Second, later on the
 G5 is shown to be tuned to G4. Third, this would be the first and 
only scheme (to my knowledge) where a ninth is used as a tuning 
interval.  It makes more sense if it read F4 - C5.  But if the
continuity is to be kept,  it seems that the last note is the one 
being tuned, it then should read C5 -F4, as it is preceeded by C4 -
C5, and followed by F4 - F5. 
	The next problem is where  G3 is located. So far, I have been
successful using Middle C as C4. That would make the G below  (Middle
C)--- G3, and the G above--- G4, while B below MC would be B3 making
D above  D4.    
	
	Now we come to the tests.  They are all thirds.  But what are we
testing for?  If we group them by twos, two are contiguous, Eb - G, G
- B; and two are successive, Eb- G, and E - G#.  There are two
possiblities; the thirds are beating, or they are pure.  Jefferson
being the meticulous scholar he was would/should have noted if the
beat rates were different, or what they were.  So perhaps the beat
rates are the same, or zero,  in which case a note to that effect
would be superfluous, especially if they are pure. Rather daunting 
to second guess one of the great intellects of the Enlightenemnt.   
 
There is the curious  <<   between  C#4 and G#4. This it turns out is
not a jumble from hand written notes, nor juxtaposition of symbols. 
I believe this to be the indication of the  wolf interval.   (What a
cute smiley for a howl :))  Here though C#4--G# is NOT the wolf, but
the fifth before the wolf.  Or another way to look at it is that it
is
the last fifth tuned up. (Going through the circle of fifths) 
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.
  
	I have constructed a possible temperament from a spread sheet 
to follow in another post.  Also the cents from ET.   It is
interesting to note that some of the thirds appear to be wildly
beating, in the twenties to 30's.  However it turns out these rates
are equal to divisions by 2 of the fundamental.  For instance if a
third is beating at 20 cps, it turns out the frequency of the root is
320.   I am guessing the ear would hear this rate as part of the
musical envelope, ie another harmonic and perceive such a third to be
pure. !! The rest of the thirds beat less than 3 per second.  
I wonder if there is a name for these  harmonics?  "Beat Frequency
Harmonics" perhaps? 

Richard Moody
3-1-98