Xen-Gedankenwelt wrote:Ok, I finished the list of 7-limit ratios (including lower limits) with an exact Olympian representation:
7-limit Olympian set.pdf
However, I noticed that there seem to be two errors in sag_ji4.par:
- 6656/6480 should be reduced to 416/405
- 576/572 doesn't make sense: If reduced, it becomes 144/143, but that doesn't match with the specified accidental / cent range
In addition, and don't seem to be an accurate representation of 9:10. A double-apotome minus is which represents the 19-limit ratio 39/38, so has to be a 19-limit ratio, too. Still, it seems to be a close approximation for 10/9, but not completely accurate.
Xen-Gedankenwelt wrote:Just to make sure that I understand systematic comma names correctly:
25:28 = +-[4 0 -2 1> (not in Olympian set) would be 7:25MS+A, and 1792:2025 = +-[-8 4 2 -1> (contained in Olympian set) would be c7:25MS+A, correct?
Some of the ratios in the Olympian set have a somewhat high absolute value of 3-exponent, and the highest I found is [-43 24 1 1>. Is it guaranteed that there is at most one less complex ratio (in terms of absolute value of 3-exponent), or do I have to check if there are more? In the latter case, would I prepend cc, ccc and so on?
P.S.: Working with those lists is a great way for me to understand and learn Sagittal notation - thanks for your help so far!
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