2 ms·

That's interesting. I would leave to see that analysis across a lot of performances. I know that barbershop folks often say to "aim high" or "sit on top of" you

That's interesting. I would leave to see that analysis across a lot of performances. I know that barbershop folks often say to "aim high" or "sit on top of" your major thirds, but I always thought that's simply because it sounds really bad to be even slightly flat. What's the theory behind why string quartets aim slightly sharper than 5:4? Is it something to do with inharmonicity or acoustics? Could it also have something to do with avoiding going flat? Is it possible that listeners are so accustomed to equal tempered thirds that a 5:4 third actually sounds flat?

kmill 5y ago
I can't say I fully understand it, but having compared major triads with different intonations, I can only say I myself find slightly sharper thirds to sound nicer in chords. Here's one thing I've used: http://tmp.esoteri.casa/interval-test.html http://tmp.esoteri.casa/interval-test.html (5-limit is "just intonation", Pythagorean uses 81 : 64 for the major third, 1/6-comma meantone is 55-EDO, and 12-EDO is standard equal temperament.) One thing I like is that the slight dissonance takes the edge off the ringing. I find that to be a rather strong flavor. The book I mentioned offered suggestions why sharper major thirds are used, but I don't remember there being anything convincing other than observations about how harmony works. Maybe your thought that going too flat sours the third makes sense: if it's sharp, you have a little more freedom to adjust your intonation without accidentally going flat. Plus, thirds are fairly forgiving anyway since they're corresponding with the fifth harmonic, which over two octaves higher. It's worth mentioning that the Pythagorean major third is about 1.266 : 1, which is quite sharp, yet it's still just intonation since it's from going up by 3 : 2 fifths.

2 ms·

That's interesting. I would leave to see that analysis across a lot of performances. I know that barbershop folks often say to "aim high" or "sit on top of" you

by tshaddox 5y ago

kmill 5y ago
I can't say I fully understand it, but having compared major triads with different intonations, I can only say I myself find slightly sharper thirds to sound nicer in chords. Here's one thing I've used: http://tmp.esoteri.casa/interval-test.html http://tmp.esoteri.casa/interval-test.html (5-limit is "just intonation", Pythagorean uses 81 : 64 for the major third, 1/6-comma meantone is 55-EDO, and 12-EDO is standard equal temperament.) One thing I like is that the slight dissonance takes the edge off the ringing. I find that to be a rather strong flavor. The book I mentioned offered suggestions why sharper major thirds are used, but I don't remember there being anything convincing other than observations about how harmony works. Maybe your thought that going too flat sours the third makes sense: if it's sharp, you have a little more freedom to adjust your intonation without accidentally going flat. Plus, thirds are fairly forgiving anyway since they're corresponding with the fifth harmonic, which over two octaves higher. It's worth mentioning that the Pythagorean major third is about 1.266 : 1, which is quite sharp, yet it's still just intonation since it's from going up by 3 : 2 fifths.