Talk:13/10

Seemingly arbitrary "fact"

"Because 13/10 is an interseptimal interval, stacking it four times will result in a good approximation of a septimal interval." Where does this come from? Stacking 15/13 four times sort of gives an approximation to 7/4, but it is over 22 cents sharp, so not really. From (13/10)^4 being close to 10/7, we know that (15/13)^4 is close to 567/320, but that interval is quite complex. It seems even more arbitrary when we consider that 13/10, 15/13, and their octave complements aren't the only interseptimal intervals; for example, (22/19)^4 is close to 9/5, but not to any simple septimal interval. A less arbitrary fact would be two septimal intervals stacking near a pythagorean interval (e.g. 4/3, 27/16, or 256/243), but I don't think that general fact is worth including on this page either. However, it may be worth including that (13/10)^2 is sharp of 27/16 by just 676/675.--Overthink (talk) 03:34, 19 October 2025 (UTC)