רועיסיני wrote: ↑Mon Jun 12, 2023 1:53 am
It's just a different equivalent way of looking at things, that may be more intuitive to some people. It means that things you neglect may aggregate into something large and bite you if you're not careful.
Ah. OK.
It does not seem like so, at least not for the eight I wrote explicitly. Of course, they all are some number of tinas (the number of degrees they are mapped to in 8539edo) and any default tina number value can be expressed as a sum or a difference of the Promethean schisminas because every 23-limit interval can, but the intervals themselves don't seem to be the same.
OK. Thanks. I see that the primary-commas for 1 to 9 tinas, with the 5-schisma, cannot form a basis for all of the Promethean schisminas because prime 23 doesn't occur among the accents' commas and
uses a 23-limit flag <
> while its primary comma is only 19-limit.
I suppose you meant
and not
there...
Yes, I did. Sorry. Edit note added above. As you would know,
is only valid as 2 degrees of 216edo (which would give correct flag arithmetic), not 3 degrees as we have it.
Anyway, I gave 216 here only as a possible counter argument that someone could make, like "Trojan is not really focused on JI because it's just assigning symbols to capture zones to make the flags look nice, there are even Trojan notations that cannot be justified by any val so the fact that 60's is not justified by the patient val is not that important".
There is a good deal of truth in that. Anyone who uses the Trojan notation for anything other than 12n-edos ≤ 144edo probably doesn't care very much about JI. Anyone is welcome to use a more JI-based (or accented Trojan) notation for the larger 12n-edos.
We only aim to give (at least) one standard notation for each EDO that we think anyone might want to use, so that people who don't want to get into the math can obtain something immediately "off the shelf".
Of course I don't blame you or anyone for any seemingly bad choice that was made in the design of the Trojan system, especially for large EDOs. I understand the need of a consistent 12R notation and of course when you also try to fit a JI-based system where symbols are made from a small number of components to this task some compromises have to be made. I agree that Trojan is a very good JI based system for 12n ≤ 144 edos, and to a lesser extent also up to 192 and even 204edo.
Thanks.