Talk:847/845

As (125/121)/(175/169)?

What's important about this? What's the point of introducing intervals with 5³ and 5² when the comma only contains one instance of 5? —FloraC (talk) 16:43, 6 May 2026 (UTC)

It's important because tempering out 847/845 equates two of the simplest very small intervals in the 5.7.11.13 subgroup. That alone is enough justification. You are considering one thing (out of many) that can make a description of a comma useful, and taking its absence to mean that the description is useless. Consider the page for 243/242; only two of the many equivalent expressions there don't use any other factors at all (2187/2048/(33/32)² is a particularly "bad" example) yet it would be hard to argue that they aren't useful or worth including. Squib (talk) 22:20, 6 May 2026 (UTC)

I did some number crunching; turns out that 125/121 and 175/169 are actually the simplest two intervals (by factor count) smaller than 100 cents, and they differ by 847/845. The next two (aside from 847/845 itself) ALSO differ by 847/845. Squib (talk) 00:20, 7 May 2026 (UTC)

125/121 and 175/169 are quartertone-sized yet they should be treated as commas by default? I don't see why. And considering them in the 5.7.11.13 subgroup should imply this subgroup is of some significance in the first place, which is yet to be proven. The rastma is described in terms of significant intervals that belong to significant subgroups. It's the plain opposite with what we have here. Given the current state I think it's at best a trivia for the curious and at worst actively unhelpful cuz users are unlikely to be familiar with those intervals. The best way to get to 847/845 is already shown: (7/5)/(13/11)², and no alternatives can be as clear as that. —FloraC (talk) 08:51, 7 May 2026 (UTC)

The 5.7.11.13 subgroup is interesting mostly because it lacks primes 2 and 3, but also because of its structure. 847/845 is by far the smallest comma of any reasonable complexity, and it's extremely natural to temper it out, which makes it very important in this subgroup. I'm not treating 125/121 and 175/169 like commas, but they're right next to each other and it's relevant that they're separated by 847/845. It's not simpler than (7/5)/(13/11)², but it's still an important result of tempering it out in its subgroup. Squib (talk) 02:26, 20 May 2026 (UTC)