Johann Philipp Kirnberger's definition of the temperament that is now known as "Kirnberger III"

From a letter to Forkel, first published in 1871 in the Allgemeine Musikalische Zeitung as the third in a series of articles by H. Bellermann.

... Oder wenn man will, lasse man C-e ganz rein, und stimme diese vier Quinten C-G, G-d, D-A, A-e, jede Quinte abwärtsschwebend, so wird jede Quinte niemand übellautend vorkommen.
Or if one desires, leave C-e quite pure, and tune these four fifths C-G, G-d, D-A, A-e, each fifth beating narrow, so each fifth would be found offensive by no one.

...

Oder wenn man von C nach e 80 : 81 in vier Quinten vertheilen will, kann es folgender Art geschehen:
Or if one prefers to split 80:81 into four fifths from C to e, it can happen by the following method: 


	C-G  216 : 323 temperirte Quinte = 2/3 - 1/324
	     216 : 324 reine Quinte
	      -------------------------------------
	G-d  215 1/3 : 322 temperirte Quinte = 2/3 - 1/323
	     215 1/3 : 323 reine Quinte
	      -------------------------------------
	A-e  214 2/3 : 321 temperirte Quinte = 2/3 - 1/322
	     214 2/3 : 322 reine Quinte
	      -------------------------------------
	D-A  214 : 320 temperirte Quinte = 2/3 - 1/321
	     214 : 321 reine Quinte
	      -------------------------------------
[The above is a convoluted way of saying that the fifths are narrow by amounts equal to the ratios 323/324, 322/323, 321/322, and 320/321 respectively, each of which is essentially 1/4 of the syntonic comma. The order of them is curious.]

Auf eine andere Art der Quinten-Excess vertheilt in drei Quinten, wie auch in fünf Quinten:
From another method the Pythagorian Comma splits into 3 fifths, in the same way into 5 fifths: 


	        |      |  oder  |  oder  |
	---------------------------------|
	C-G     |   0  |  0     | -2     |
	Cis-Gis |   0  |  0     |  0     |
	D-A     |  -6  | -5 1/2 | -3 1/2 |
	Dis-B   |   0  |  0     |  0     |
	E-H     |   0  |  0     |  0     |
	F-c     |   0  |  0     |  0     |
	Fis-cis |  -1  | -1     | -1     |
	G-d     |   0  |  0     | -2 1/2 |
	Gis-dis |   0  |  0     |  0     |
	A-e     |  -5  | -5 1/2 | -3     |
	B-f     |   0  |  0     |  0     |
	H-fis   |   0  |  0     |  0     |
	---------------------------------|
	        |  12  | 12     | 12     |
[The numbers in the last column are novel. Nothing in the letter prepares for them nor explains them.]

Gleichschwebende Temperatur: 


C. | Cis |  D  | Dis |  E  |  F  | Fis |  G  | Gis |  A  |  B  |  H  |  c
---------------------------------------------------------------------------
   |  7  |  2  |  9  |  4  | 11  |  6  |  1  |  8  |  3  | 10  |  5  |  0
---------------------------------------------------------------------------
[The numbers are the amount by which each note differs from its pitch in a series of pure fifths starting from C and proceeding sharpwise.]

Abweichung meiner beiden Temperaturen gegen die angezeigte gleichschwebende:
Divergence of both of my temperaments from the equal one shown: 


	     | C |Cis|  D   |Dis| E | F |Fis|  G   |Gis|  A   | B | H | c 
	     |---|---|------|---|---|---|---|------|---|------|---|---|---
	 I.  | 0 |-5 |+2    |-3 |-7 |-1 |-5 |+1    |-4 |-2 1/2|-2 |-6 | 0     i.e., "K II"
	     |---|---|------|---|---|---|---|------|---|------|---|---|---
	II.  | 0 |-5 |-3 1/2|-3 |-7 |-1 |-5 |-1 3/4|-4 |-5 1/4|-2 |-6 | 0     i.e., "K III"
	      ------------------------------------------------------------
[This may be the first time that anyone ever defined a temperament in terms of its deviation from ET. Electronic tuner users: double these numbers. The results are your cents offsets (add a constant if not starting from C).]