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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.
| 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 | 0 | 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.
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 -8The using this process to "zero out" the starting note will allow you to take your pitch from any instrument or tuning fork.
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| © 2004-2011 Claviers Baroques | last updated
October 6, 2010
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