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.