One of the things I'm struggling with here, in regard to revising some of the standard notations to use 3-limit fractional comma notations, is how and where to make the transition from the JI-based notations (primes greater than 3 allowed, fractional commas not allowed) to the apotome-fraction notations.

The further transition from apotome-fractions to limma-fractions seems obvious enough: Only use limma fraction symbols for EDOs where the apotome is zero or negative (6, 11, 9, 16, 23, 7, 14, 21, 28, 35).

Ideally such a transition (JI to fractional-3) would somehow be gradual and seamless. It's difficult to imagine how that could happen, but it could be that the maximum prime allowed could be stepped down gradually. In any case it's worth keeping the idea of a smooth transition in the back of our minds in case something occurs to us.

But whether the change is gradual or abrupt, it's not totally clear to me what property of the EDO should determine the JI-ness or otherwise of its notation. Our first pass at this was that it would be determined by the size of the EDO -- large EDOs have JI Notations, small EDOs have fractional-3-limit notations. But that doesn't work because I think 22-edo and 29-edo should definitely keep their existing 5-limit notation, while 42-edo and 47-edo don't deserve anything above the 3-limit.

People may of course choose to use a fractional 3-limit notation for 22 and 29 -- they both divide the apotome into 3 parts -- but this would not be their standard notation.

So my current suggestion is to base it on the error in the fifth. Error greater than 10 cents gets a fractional-3-limit notation. The 10 cent cutoff seems somewhat arbitrary. Reducing it to 9 cents would add 26 and 52 on the narrow side and 27, 54 and 59 on the wide side, as EDOs requiring fractional-3-limit notations. With a 10 cent cutoff, 47-edo has the greatest number of steps to the apotome (7 steps). With a 9 cent cutoff, 59-edo has 9 steps to the apotome, requiring more fractional-apotome symbols. One might argue that 26-edo is a meantone and so deserves a JI-based notation, however, like 12 and 19, it only has 1 step to the apotome, so its standard notation is the same whether JI-based or fractional-apotome.

I toyed briefly with the idea of making the notation fractional-3-limit whenever the EDO was not 1,3,9-consistent, i.e. whenever 2 fifths are not the best approximation to 4:9. But that occurs whenever the error in the fifth is more than 1/4 of a step, and so it does not have any upper limit in ET numbers, and therefore no upper limit on the number of steps per apotome requiring symbols. So I currently prefer a fifth-error cutoff, and 10 cents seems right to me.