This is the frequency table for the historical Bach tuning. Reconstructed by scientific methods. Usable for 24 Keys. "Das Wohltemperirte Clavier" was composed for this temperament. A detailed description of how to lay this temperament is to be found in: Practical Introduction to Historical Tunings. by Herbert Anton Kellner. (My version is in German). (Einfuehrung in die Praxis historischer Stimmungen.) (Der Piano und Fluegelbau, by Herbert Junghans, ISBN 3-923639-60-0) (C 1984 Verlag Bochinsky, Frankfurt) Bach centr. A Difference Bach centr. Bach centr. from equal equal equal C normal A in cents C 523.2511306 523.2511306 525.7047253 +8.099 B 493.8833013 491.3261646 493.6300588 -0.888 Bb 466.1637615 465.1121161 467.2930891 +4.189 A 440.0000000 437.9464105 440.0000000 0.000 G# 415.3046976 413.4329921 415.3716348 +0.279 G 391.9954360 391.4007084 393.2360388 +5.470 F# 369.9944227 367.4959930 369.2192310 -3.631 F 349.2282314 348.8340871 350.4698169 +6.144 E 329.6275569 327.5507764 329.0867059 -2.843 D# 311.1269837 310.0747441 311.5287261 +2.234 D 293.6647679 292.7723017 294.1451503 +2.830 C# 277.1826310 275.6219947 276.9144232 -1.676 C 261.6255653 261.6255653 262.8523626 +8.099 A Comparison of some piano temperaments: Sources: KORG Multi temperament tuner MT 1200 Owner's Manual. Bach numbers by Wabnig. Key is C maj where appropriate Cent Values: Temperament C . D . E F . G . A . B -------------------------------------------------------------- Equal 0 0 0 0 0 0 0 0 0 0 0 0 Just maj +16 -14 +20 +31 +2 +14 -16 +18 -12 0 +33 +4 Just min +16 +49 +20 +32 +2 +14 +47 +18 +30 0 +34 +4 Mean +10 -14 +3 +20 -3 +14 -10 +7 -17 0 +17 -7 Pythagoras -6 +8 -2 -12 +2 -8 +6 -4 +10 0 -10 +4 Werckmeister 3 +12 +2 +4 +6 +2 +10 0 +8 +4 0 +8 +4 Kirnberger 3 +10 +1 +3 +4 -3 +8 +1 +7 +2 0 +6 -2 Vallotti&Young +6 0 +2 +4 -2 +8 -2 +4 +2 0 +6 -4 Bach +8 -2 +3 +2 -3 +6 -4 +6 0 0 +4 -1 Bach is absolutely up-to-date. Can you see? Yours, Helmut Wabnig wabi@net4you.co.at
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