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

Nicely done. You could include the proper Sagittal symbols in the PDF, at higher resolution than the forum smilies, if you install the Bravura font. Unfortunately, there isn't yet an easy way to type the symbols, as there is for the forum smiles. But it would be possible to make a Windows keyboard layout that would let us do so. Do you use Microsoft Windows?

I note the potential for confusion of the vertical bar | with the digit 1. Some fonts are worse than others, for this. That's why I use square brackets for bra <...] and ket [...> vectors except when writing an inner product <... | ...>, in which case there will be a space on either side of the vertical bar. An alternative to using square brackets is to always include a space between the vertical bar and any digits.

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

Thanks for those. I'm pleased to see that we do have the reduced value 416/405 for

in George's

JI notation spreadsheet,

the JI notation levels diagram and in footnote 19 on page 24 of

http://sagittal.org/sagittal.pdf.

I see that 576/572 was erroneously given for

in sag_ji4.par. George's spreadsheet gives the 13-limit comma 567:572 for that symbol. So it seems "67" was accidentally transposed to "76" when making sag_ji4.par.

I have now corrected both of those in

http://sagittal.org/sag_ji4.par. Thanks.

My apologies. You are correct that

is not an exact representation of 9:10. That symbol represents a 19-limit ratio, as you say. When untempered they differ by only 0.003 cents. The only exact representations of 9:10 involve a change of nominal, e.g. C:D

or C:E

= C:E