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Schedule for tuning various temperaments using an electronic tuner with meter


Dr. Bradley Lehman of University of Michigan sent us these three temperaments recently -- thank you, Brad. He's done extensive research on historic temperaments; he discovered, or perhaps deduced is the correct word, the Bach (Lehman) Wohltemperirte temperament, full story here http://www.larips.com/ (it is fascinating). His website is a treasure trove of temperaments discussion, theory and practice of tuning temperaments and includes text and video of his 2008 lecture/demonstration at James Madison U -- well worth reading whether you want to get into the weeds or just want to know how he figured it out.

Temperaments by cents deviation from equal temperament.
Temperament C C# D Eb E F F# G G# A Bb B More information
1/4 Meantone 10 -14 3 20 -3 14 -10 7 -17 17 -7  
1/5 Meantone 7 -10 2 14 -3 9 -7 5 -12 0 12 -5  
1/6 Meantone 5 -6 2 10 -1 7 -5 3 -8 0 8 -3  
Bach (Barnes) 6 0 2 4 -2 8 -2 4 2 0 6 0  
Bach (Kellner) 8 -1.5 2.5 2.5 -2.5 6 -3.5 5.5 0.5 0 4 -1  
Bach (Lehman) 5.9 3.9 2 3.9 -2 7.8 2 3.9 3.9 0 3.9 0 http://www-personal.umich.edu/~bpl/larips/math.html
Bruder (P. Vier) 3 -2 5 0 -6 2 -3.5 4.5 -1 0 1 -5  
Buxtehude/Böhm (Lehman) 7.3 -0.5 2.4 1.5 -2.4 5.4 -.05 4.9 1.5 0 1.5 -0.5 http://www-personal.umich.edu/~bpl/larips/practical.html#17c_germanic
French 1/5 7 -5 2 1 -3 9 -5 5 -3 0 5 -5  
"Handel" 4 -3 0 1 0 3 -3 2 -1 0 2 -1  
Kirnberger III 10.5 0.5 3.5 4.5 -3.5 8.5 0.5 7 2.5 0 6.5 -1.5  
Lambert 1774 4 -2 1.5 2 -1.5 6 -4 3 -0.5 0 3.5 -3  
Mersenne I 10 -14 3 9 -4 13 -11 7 -17 0 11 -7  
Mersenne II 10 -14 3 -2 -4 13 -11 7 -17 0 6 -7  
Neidhard 1724 6 2 2 4 0 4 2 2 2 0 4 2  
Neidhard 1729 6 2 2 4 0 6 2 4 2 0 6 2  
Pythagorean -6 8 -2 -12 2 -8 6 -4 9.5 0 -10 4  
Rameau 1/6 comma (Lehman 2008)
(one of four versions)
4.9 -2.9 1.6 3.6 -1.6 6.5 -3.1 3.3 1.6 0 8.1 -3.3 http://www-personal.umich.edu/~bpl/larips/practical.html#rameau_ordinaire
Table of all its values:
http://www-personal.umich.edu/~bpl/larips/00Rameau1726_16SC_Bb.jpg
"Rameau" I 10 -3 3 8 -4 13 -5 7 -1 0 17 -7  
"Rameau" II 11.5 -4 4 0 -4 15.5 -6 8 -2 0 8 -8  
Schlick (H. Vogel) 8 -6.5 2.5 2.5 -3 11 -8 5.5 -4.6 0 9 -5.5  
Silbermann 6 -8 2 12 -2 8 -6 4 -9.5 0 10 -4  
Silbermann (P. Vier) 6 -4 2 0 -2 8 -6 4 -2 0 6 -4  
"Telemann" 5 -8 1 0 -2 7 -6 3 1 0 9 -4  
Valotti 6 0 2 4 -2 8 -2 4 2 0 6 -4  
Werkmeister III 12 2 4 6 2 9.5 0 8 4 0 7.5 4  
Young 6 -4 2 0 -2 4 -6 4 -2 0 2 -4  

 

If you have data of this type for other temperaments, we would be happy to post it here. Please contact us.


Note: This chart assumes A = 0 (that is, tuning is done starting from A as a convenience for giving other members of an ensemble their pitch). To convert to a "C = 0" tuning subtract the value of C from every note in the line, eg.:
                   C   C#    D   Eb    E    F   F#   G   Ab  A  Bb   B

Werkmeister III   12    2    4    6    2   10    0   8   4   0   8   4
less: value of C -12  -12  -12  -12  -12  -12  -12 -12 -12 -12 -12 -12
                   _______________________________________________________

Werkmeister III(C) 0  -10   -8   -6  -10   -2  -12  -4  -8 -12  -4  -8
The using this process to "zero out" the starting note will allow you to take your pitch from any instrument or tuning fork.

C+L+A+V+I+E+R+S B+A+R+O+Q+U+E+S

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last updated October 6, 2010