Another version of 12-tET

To celebrate the 1200th digest, I will present another version of
12-tET:
0: 1/1 0.000000
1: 1662005/1568693 100.0340
2: 1760309/1568693 199.5188
3: 1865285/1568693 299.7998
4: 1975877/1568693 399.5162
5: 2093975/1568693 500.0176
6: 10223/7229 599.9410
7: 2349463/1568693 699.3218
8: 355633/224099 799.5039
9: 2636887/1568693 899.1276
10: 399193/224099 999.5407
11: 2960239/1568693 1099.381
12: 2/1 1200.000

Before you think that I went crazy, I didn't invent this. I just
calculated the ratios for the sake of it. This tuning was used in pianos
by the English "Best Factory Tuners" in 1840.
The idea becomes clear by showing the beat frequencies of 3/2 for the
octave above middle C:

0: 0.000: -1.1930
1: 100.034: -1.1930
2: 199.519: -1.1930
3: 299.800: -1.1930
4: 399.516: -1.1930
5: 500.017: -1.1930
6: 599.941: -1.1930
7: 699.322: -1.1930
8: 799.504: -1.1930
9: 899.127: -1.1930
10: 999.540: -1.1930
11: 1099.381: -1.1930
12: 1200.000: -2.3859

Now someone can persuade his piano tuner to set this tuning and let us
know if it's an improvement.

Reference:
Jorgensen, Owen Henry. _Tuning. Containing: The perfection of
eighteenth-century temperament, The lost art of nineteenth-century
temperament
and The science of equal temperament. Complete with instructions for aural
and
electronic tuning_. Michigan State University Press, East Lansing, 1991.

Manuel Op de Coul coul@ezh.nl


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