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Bifrost

🔗Gene Ward Smith <gwsmith@svpal.org>

6/15/2003 6:18:58 PM

This has six meantone fifths, leading to three pure thirds, on each
side of the chain of meantones we put two pure 3/2's, so we have four
pure fifths in total; we then round out with two sharp fifths of
size sqrt(2048/2025 sqrt(5)), of size 706.355 cents. This leads to
three sharp major thirds which are within a cent of being pure
14/11's, being of size 426.619 cents; and two more sharp thirds of
size 406.843 at E and Ab.

! bifrost.scl
! [45/64*5^(1/4), 1/2*5^(1/2), 16/45*5^(3/4), 5/4, 2/5*5^(3/4),
15/16*5^(1/4), 5^(1/4),
! 1/2*10^(1/2), 1/2*5^(3/4), 8/15*5^(3/4), 5/4*5^(1/4), 2]
!
Six meantone fifths, four pure fifths, two on each side, two fifths of
sqrt(2048/2025 sqrt(5))
12
!
86.802144
193.156856
299.511569
386.313714
503.421572
584.847143
696.578428
793.156857
889.735285
1001.466571
1082.892142
1200.000000

🔗Gene Ward Smith <gwsmith@svpal.org>

6/15/2003 6:44:32 PM

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
This leads to
> three sharp major thirds which are within a cent of being pure
> 14/11's, being of size 426.619 cents; and two more sharp thirds of
> size 406.843 at E and Ab.

416.619 for the 14/11 thirds.