Yeah.Dave Keenan wrote: ↑Mon Jun 15, 2020 10:21 am Therefore, we only need to ensure that our comma size categories are no wider than 23.46 cents (upper bound minus lower bound) to ensure that any "complex"-named comma must differ from its base comma by at least 41 in its 3-exponent. Our widest comma size category is the specific "comma" category, which ranges approximately from 11.73 cents to 33.38 cents, a width of approximately 21.65 cents, which is indeed less than the above-mentioned 23.46 cents.
Category HalfSizeMonzo Cents -------- ------------- ----- schismina [ - 84 53 > 1.807523 - close to 5s schisma [ 401 -253 > 2.692391 - between 91s and 19:4375s kleisma [ -336 212 > 7.230092 - 3.74E+50:3.76E+50 = 106edo-kleisma exactly comma [ 46 - 29 > 21.65249 - close to 5C and slightly less than 12edo-comma S-diesis [ - 19 12 > 11.73001 - close to 11:35k M-diesis [ - 19 12 > 11.73001 L-diesis [ - 19 12 > 11.73001 Ssemitone [ - 19 12 > 11.73001 limma [ 46 - 29 > 21.65249 Lsemitone [ 65 - 41 > 9.922482 - between 7:11k and 275k apotome [ -168 106 > 3.615046 - 1.93E+25:1.94E+25 = 53edo-schisma exactlyNote that, while 29edo has a slightly better fifth than 12edo in terms of absolute error, its comma is actually larger (the 29edo-S-diesis of 43.30497¢) than the 12edo comma (of 23.46001¢), so we don't have to worry about it being too big.
Unless the commas are non-directionally named, in which case we get a similar issue to the one with the two 253-commas, with, for example, [336 2 -146> (1.1E+109:1.3E+109 = 202.1078¢) and [-342 2 146> (9.0E+102:1.0E+103 = 205.7122¢) both being 5^146MS+A's with the same 3-exponent and not just the same absolute value of the 3-exponent. Again, these examples probably don't have any musical relevance, but still...