6 ms·

Talking to myself, some research here. https://www.medieval.org/emfaq/harmony/pyth5.html https://www.medieval.org/emfaq/harmony/pyth5.html >>>Around 1300, the

Talking to myself, some research here. https://www.medieval.org/emfaq/harmony/pyth5.html 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-renaissance-theory-practice/theoretical-background/ 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://en.wikipedia.org/wiki/Gioseffo_Zarlino https://journals.sagepub.com/doi/10.1177/000313131706700215?int.sj-abstract.similar-articles.7= 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.

throwaway91827 6d ago
Just wanted to say, thank you for the detailed response, I suppose my comment looks a bit glib in comparison. I appreciate this perspective- I knew about some basic elements of tuning and acoustics, but it's fascinating that there's this much structure that you can study in it, I understand the interest. 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?

throwaway91827 6d ago

Just wanted to say, thank you for the detailed response, I suppose my comment looks a bit glib in comparison. I appreciate this perspective- I knew about some basic elements of tuning and acoustics, but it's fascinating that there's this much structure that you can study in it, I understand the interest. 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?