Thomas Jefferson Tuning Scheme I

[Jim Coleman, Sr.]

Hi Richard:

I think you may be on to something in your analysis. I hope some of the
Meantone or modified Meantone people will pick up on this and further 
elucidate. I can remember struggling through these same procedures as a
kid before I was finally taught ET and the use of graduating 3rds. Going
back as far as Jefferson, every musician pretty much tuned his own 
instrument. My guess is that ET has created the market for all of us as
piano technicians. Tuning just became too complicated for the average 
musician when the Well Temperaments and Equal Temperaments came into vogue.
We owe our livelihood to this change.

Jim Coleman, Sr.

On Wed, 4 Mar 1998, Richard Moody wrote:

> 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
> 
>