Meantone & kleisma

Here are two meantone scales where the kleisma is made away. I haven't
seen them before, so they are probably of theoretical interest only.
The kleisma is 15625/15552 or about 8.1 cents and the difference
between five fifths and six major thirds plus an octave.
The first is almost indistinguishable from 1/5-comma meantone.

1: 16384/15625 82.11775
2: 194.891 cents 194.8910
3: 307.664 cents 307.6641
4: 389.782 cents 389.7821
5: 502.555 cents 502.5552
6: 584.672 cents 584.6723
7: 697.445 cents 697.4453
8: 779.563 cents 779.5633
9: 892.336 cents 892.3364
10: 1005.109 cents 1005.109
11: 1087.227 cents 1087.227
12: 2/1 1200.000

1: 16384/15625 82.11775
2: 207.153 cents 207.1530
3: 289.271 cents 289.2711
4: 371.388 cents 371.3881
5: 496.424 cents 496.4242
6: 578.541 cents 578.5413
7: 703.576 cents 703.5762
8: 785.694 cents 785.6943
9: 910.729 cents 910.7294
10: 992.847 cents 992.8474
11: 1074.965 cents 1074.965
12: 2/1 1200.000

The first is also close to 74 and 117-tET and the second to 29-tET.
Equal temperaments wherein the kleisma disappears are 15, 19, 23, 30,
34, 38, 49, 53 and more.

Manuel Op de Coul coul@ezh.nl

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