Ash9903b4 wrote: ↑Sun Mar 15, 2020 11:39 am
I’ve been trying to represent 494EDO in Sagittal, but I don’t know how to make it work. I’ve read somewhere on this forum that the Promethean level was specifically designed for 494, but there are some inconsistencies I can’t figure out.
Hi Ash. Welcome to the forum. You're certainly on the bleeding edge in wanting to notate 494-edo. It isn't quite correct to say that Promethean was designed
for 494-edo. It's more that 494-edo (really 47-eda [equal division of the apotome {chromatic semitone}]) was used to help decide where to close Promethean, i.e. where to stop generating what might otherwise have been an almost endless series of arrow-like symbols involving every possible combination of flags, many of which would have been very close in size to one another.
But that certainly does suggest that we ought to be able to make a notation for 494-edo using only Promethean symbols. However I could not find, in searching through emails, anywhere that George or I proposed such a notation, let alone agreed on it. Good on you for having a go.
For other readers, Promethean can be seen here:
http://sagittal.org/SagittalJI.gif, where you'll notice that it actually notates 52 ratios to the apotome, because you can count 26 symbols to the half-apotome (56.8c). So there are 5 symbols (3 single-shaft) in Promethean that are outside any 47-eda set.
First of all, the Athenian subset works perfectly, with consistent flag arithmetic and everything, and with symbols spaced by either 2 or 3 degrees of 494:
2,
4,
6,
9,
11,
14,
16,
18,
20,
22,
25,
27
I can confirm that the above are all correct, based on the primary comma role for every symbol.
But once extended to Promethean, there are a few problems.
(99/98) maps to 7 degrees, which doesn’t have an exact half, and
(513/512) maps to 1 degree, which is inconsistent with
and
. Do I need to start using schisma accents here, or is Promethean enough?
I did find email from George that mentioned that
and
were additional to 47-eda, but are required to complete the Olympian level. Fortunately, we don't need to use
for 7 degrees because we have
, the 23-comma (736/729), for 7 degrees. Also, both
and
map to 16 degrees, so if one of them breaks the flag arithmetic, we can ditch that one.
The other thing to be aware of is that while 494-edo is 17-odd-limit consistent (and possibly {1, 3, 5, 7, 9, 11, 13, 15, 17, 23}-consistent), it is not 19-odd-limit consistent, so you have two choices for how to map prime 19, which relates to the mapping of
and other symbols containing that flag (left scroll or rai).