@FloraC, I just realised (while updating the Xenharmonikon article, and thanks to a
facebook post by Nicholas Denton Protsack) that 130edo and 137edo do
not use every Spartan accidental as I claimed earlier. Sorry. They do not use
because it is the same number of steps as
. Although they do match the list you gave, which only goes up to 6 steps.
To fully match Spartan, we need an EDO with 13 steps to the sharp, not 12 as in 130edo and 137edo. Although 135edo, 142edo and 149edo all have 13 steps to the sharp, and reasonably accurate fifths, the honour of using all of Spartan belongs to
142edo alone. 135edo has the best fifths of the three, but it tempers the 5-comma and 7-comma to the same number of steps (3 steps), and 149edo has a gap between the steps for the 5 and 7 commas (2 and 4 steps).
Only 142edo has all the Spartans as consecutive steps:
1\:
2\:
3\:
4\:
5\:
6\:
7\:
8\:
9\:
or
10\:
or
11\:
or
12\:
or
13\:
or
Of course you don't
need to use
in 142edo (or any tuning), since you could use
instead, just as you could use
instead of
.
However, 130edo is a far better model for a low-precision JI notation than is 142edo, because 130edo is 15-limit consistent while 142edo is only 9-limit consistent.