“They weren’t yet using the “equal temperament” system ...”
Very interesting. Thanks!
Have you realized how “lucky” the 12-tone octave is where each successive halftone is the 12th root of two from its neighbor.
That irrational ratio produces intervals very, very close to the ‘perfect’ intervals.
I don’t know if it’s “luck”; I think it all comes down to the fundamentals of harmonics. Like, you could divide the octave into any number of intervals, equal or otherwise, but then your notes won’t necessarily line up with any of the notes on the harmonic sequence beyond the octave. The 12-tone division that we use just happens to have most of the important notes of that harmonic sequence represented closely by one of the 12 tones. And for the couple of notes of the sequence that don’t match up, we invented “blues” to add those extra notes back in :)
And that’s why the songs performed by a four-part a capella quartet operating within Bach’s Riemneschneider rules can be so beautiful, because the coupling of the human’s ear with one’s infinitely tunable voice can do exactly what a well-tempered piano can never do, and that is sounding out a perfectly tuned major/minor seventh chord!