Thanks Juhani. For other readers:
There is an explanation of Johnston's system, up to prime 13, starting on page 6 of this article by Marc Sabat.
However, he appears to be in error when he writes, "In Johnston’s notation, septimal intervals above a note are indicated by adding a small 7 accidental. An inverted 7 simply means that the septimal interval was generated downward." He later contradicts this by writing, "The 7 sign alters a 9/5 interval (the 5-Limit minor seventh) downward by approximately a quarter-tone to produce the septimal minor seventh 7/4." This agrees with the SMuFL document linked below.
Johnston's symbols, to 13, can be seen, starting on page 113 of the SMuFL document, here
(Sagittal starts on page 119)
In other words, if you interpret Johnston's 7-comma symbol as a kind of half-arrow you will get entirely the wrong idea about the direction of its pitch alteration.
The following post explains why SMuFL does not include Johnston's symbols beyond prime 13, and what they would look like, namely small versions of the numerals themselves (presumably for the harmonic), and their 180-degree rotation (presumably for the sub-harmonic).
We can represent Ben Johnston's accidentals in plain text as:
Determining the most direct Sagittal equivalents is complicated by the fact that the chain of fifths that includes C natural is
So we do not simply want the Sagittal symbols for those commas listed above. All but the 11-comma include factors of 5 whose job is, in effect, to cancel out + and - signs. In the following, I assume that we want to choose Sagittals that preserve Johnston's choice of nominal (and hence staff position) plus sharp or flat, for each prime harmonic of C, although an alternative is just to use whatever is most natural in Sagittal.
So how would those prime harmonics be notated in Johnston's notation? Using the above commas I get the following. Can you confirm this Juhani? (or anyone else) I'm not confident of those above 13. In particular, the requirement for a + sign in notating the 23rd harmonic seems strange.
The direct Sagittal equivalents are:
That seems like a perfectly reasonable prime set to me. Compared to the set I gave earlier, it favours smaller commas at the expense of nominals-plus-sharps-or-flats that are slightly more distant from C on the chain of fifths. It differs from it only for primes 13, 17 and 31. A minor consideration is that it uses
for 13 instead of
and this is more prone to confusion with the 7-limit combination
. But then such a misreading wouldn't matter very much since the two differ by less than half a cent.