>>>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.<<<
>>>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<<<
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.
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.