[This was originally posted in the Microtonal Music and Theory facebook group in response to Cryptic Ruse's post (I can't type or pronounce the name he goes by now). It is preserved here at the request of Joe Monzo. Thanks Joe.]

Congratulations on finishing the draft. It may well lead to improvements in Sagittal ET notations. I'd be happy to wait for a more polished version, but hopefully these comments based on your original post will help.

The Spartan subset of Sagittal, that consists of 8 pairs of simple symbols, presently notates 47 of the most commonly-used ETs from 5 to 72. Those that require additional symbols are 14, 20, 30, 32, 37, 44, 47, 48, 49, 52, 54, 55, 58, 59, 60, 61, 66, 67, 68, 70, 71. With some notable exceptions, most of these ETs have rarely been used by anyone, except possibly in exercises of the kind: "I'm going to prove I can write something even in this awful ET".

I assume you mean your notation is "ASCII-friendly" in the way that Sagittal is ASCII friendly, and not in the way that HEWM is ASCII-friendly. i.e. I hope you just mean it can be unambiguously represented in ASCII, and you're not proposing to use ASCII symbols on the staff. HEWM's use of + and - is particularly problematic, unless they are heavily modified so that the horizontal strokes become Bosanquet's comma slashes, as in Erv Wilson's version.

I understand your point about those ETs that are inconsistent regarding certain combinations of primes, and so may in some cases have multiple usable mappings.

When standardising Sagittal notations for ETs we deliberately tried to avoid using symbols for sets of primes that were not mutually consistent. So Sagittal already attempts to be agnostic about the mappings of primes which could map in multiple ways. We may well have failed to do so in some cases. We'd be grateful if you could point these out, preferably on the Sagittal forum where they will still be findable in weeks (and years) to come, unlike these ephemeral facebook discussions.

I'm surprised that you include 72-ET in this class of ETs. I would have thought there was no argument about its 11-limit mapping, combined with the fact that 11-limit symbols are quite sufficient to notate it.

It seems to me that when an ET _does_ have a definite best mapping for some small set of low primes, then it is not an advantage, but a disadvantage to fail to indicate it in the notation. Being agnostic in these cases seems to me to just be ignoring the facts. However, even if there is a good reason to ignore such facts, you are free to do so no matter what the notation is. You are always free to ignore the fact that a certain symbol has a certain meaning when notating JI, and simply treat it as the symbol for so many degrees of that ET.

You claim to be "drastically reduc[ing] the number of accidentals that must be learned". Firstly I would say that since only 8 pairs of Sagittals are required to notate 52 ETs, including the most popular by far, reducing from 8 to 6 is hardly "drastically reducing". But it's worse than that.

Since you're not notating JI (or large ETs) you're not actually reducing the number of symbols to be learned at all. You're increasing it. Unless of course you're repurposing Sagittal symbols, which would be fine if it's done in a logically consistent manner, or unless the user of your notation can guarantee they will never in their life need to learn a JI (or large ET) notation.

There is no "ambiguity or uncertainty in using Sagittal to notate ETs ... that support multiple useful mappings within a variety of prime limits". In Sagittal, the ET composer is not required to "determine which mapping to use or what limit the temperament is conceived as tempering". She can simply look up the standard notation for the ET.

Of course Sagittal also ensures that all pitches can be notated in alphabetical order (with enharmonic spellings), and that no more than one accidental symbol (two if you want to keep existing sharps and flats) will ever be necessary to notate a given pitch (however you're free to use more, e.g. in one-symbol-per-prime JI notation).

And of course existing Sagittal ET notations also respect subsets such as 17 and 34, since accidentals are defined based on harmonic relationships rather than ET steps. The ultimate example is the mutual consistency of all the 12n-ET notations. But if you can find subsets we've missed, please let us know.