Other ancient tuning systems are based on three limit tuning:
https://en.wikipedia.org/wiki/Shi%27er_l%C3%BC
https://en.wikipedia.org/wiki/Pythagorean_tuning
Whether the human ear naturally prefers 5/4 (5-limit) over 81/64 (Pythagorean) for the major third, and 6/5 over 32/27 for the minor third, is still something I don’t have solid research on.
As it turns out, the modern western scale is more closely aligned with Pythagorean tuning than with five-limit tuning. In particular, the Pythagorean thirds are closer to modern 12-tone equal tempered thirds than they are to five limit thirds.
https://www.medieval.org/emfaq/harmony/pyth5.html
>>>Around 1300, the English theorist Walter Odington proposes that major and minor thirds (81:64, 32:27) have ratios close to 5:4 and 6:5 respectively, and that singers lean toward these simpler ratios. His observation may reflect the style of much English polyphony of the period, where thirds often have a pervasive role in the texture and may even serve as closing sonorities.<<<
https://casfaculty.case.edu/ross-duffin/just-intonation-in-r...
>>>Beginning with Ramos de Pareja in 1482,Fn11 the simple ratios of Just intonation began to be cited by theorists and used in their divisions of the monochord. [...] an octave is 2:1, a fifth is 3:2, a fourth is 4:3, a pure major third is 5:4, a pure minor third is 6:5. These “six-limit” ratios—the senarius, or senario, as Zarlino calls them—are the basic harmonic intervals. Zarlino attributed almost mystical significance to the senario<<<
https://en.wikipedia.org/wiki/Gioseffo_Zarlino
https://journals.sagepub.com/doi/10.1177/000313131706700215?...
This article is paywalled, but to summarize, it makes the case that the 5:4 and 6:5 ratios are ratios musicians naturally drift towards in polyphonic contexts.
It reminds me a bit of regular polygons or simple geometry like circles- and it makes sense the Greeks would be interested in both- things that are pleasant and can combine and tile well because of their symmetric and regular properties.
I think my "pushback" was more just at the phrasing of "why" something sounds "good"- I do think when we listen to music, we bring our past and our culture into it, and whether a chord sounds "sad" or "happy" depends on a lot more than just the harmonic structure- I wonder about this concept of "tension" you bring up, I can't tell if you mean something emotional or more mechanical. Is that like something you understand just by crunching the numbers on the ratios?