I spent a ridiculous amount of time investigating the possibilities for this Fibonacci tuning notation, with a number of spreadsheets. I found the following 37-limit map that gives no error greater than 1.6 cents in any primeרועיסיני wrote: ↑Thu May 25, 2023 8:09 pm The Trojan accidentals are not very good at flag arithmetic, so I wasn't very worried about that, but if it's important to you we may try to fix it! I haven't found a good accidental between and in the graph, but I think I have a solution: use instead of for -68g, and thus becomes free of meaning and can be used as a flag in = +131g. You can also use as a synonym for = +165g, if you like, but I'm not sure I'd advise to do that as is actually about 0.7¢ larger than for the golden fifth size. This proposition makes some problems with the flag arithmetic considerations you made afterwards, but I don't think we should place a lot of weight on them, as they involve double shaft accidentals, which don't have flag arithmetic in Trojan anyway, and which isn't used here. What do you think? Do you have another solution?

⟨0 12 82 44 30 -61 -149 -36 93 -92 191 66].

I applied it to every comma up to the half-apotome that has an Olympian notation.

There is no unaccented symbol corresponding to 131 generators. And there is no accented version of corresponding to 131 generators, which is equivalent to saying that there is no secondary comma for that corresponds to 131 generators. Therefore there is nothing to be gained by not using for -68g.

And it is preferable to use rather than for -68g because notates simpler ratios (ratios of 7 rather than 25).

I have only two suggestions for notating 131g. My preference is for . This is not valid according to any Olympian comma for that symbol, but only becomes valid when we define as -233g by fiat, simply because it is such a useful thing to do for this notation and it does at least give a size that is similar to its untempered size.

Another possibility is to use the fact that the 11/17-small-diesis corresponds to 131g with the above mapping, and its symbol is which falls between and in untempered size order. The accent could be dropped, which is equivalent to saying we could use with a secondary comma definition of 11/17S.

The final spreadsheet is attached.