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But I was talking about barbershop quartets and the specific sound they are generally going for based on my experience with and impression of that genre. I don'

But I was talking about barbershop quartets and the specific sound they are generally going for based on my experience with and impression of that genre. I don't know much about string quartet music so I wouldn't wager a guess about what they do. My impression of barbershop harmony is that they're not particularly concerned with how the melodies are tuned. I don't think there's much deliberate intention there, other than that you obviously don't want frequencies to drift too much throughout a song because you want to be in the right ranges for each vocalist. Barbershop harmony seems much more concerned about the "vertical" tuning and my hypothesis is that they do tend to hit very close to the low integer ratios. Can you think of a reason they wouldn't intend to do that? The harmonies tend to be pretty close (unlike a piano) and I would guess that the human voice is less inharmonic than piano strings (although bowed string instruments are very harmonic, right?).

kmill 5y ago
I brought up string quartets because I know about tuning them, and, like barbershop quartets, it's 4-part harmony with extremely harmonic instruments. Bowing a string causes a phenomenon called "mode locking," where the normally somewhat inharmonic strings are forced to be harmonic (my understanding is the human voice also exhibits mode locking). You often do microadjustments to get chords to sound good vertically and horizontally. I pulled up a random barbershop recording and looked at a spectrogram for the final chord, since the final chord is supposed to ring as much as possible, and there are only vertical considerations, so you'd presume they'd tune it as justly as possible, right? Here's what I found: They tuned their perfect fifth justly as 3 : 2 almost perfectly. That's not unexpected, even equal temperament gets perfect fifths close to right (though a little flat). They tuned their major third between 1.253 : 1 and 1.258 : 1. A just major third is 1.25 : 1, an equal tempered major third is about 1.26 : 1, and the 55-EDO system mentioned in the book I referenced in my first comment would give a major third of about 1.255 : 1. Like I expected, they tuned their major third sharp with respect to just intonation, but still flat with respect to equal temperament.
- tshaddox 5y ago
  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.

kmill 5y ago

I brought up string quartets because I know about tuning them, and, like barbershop quartets, it's 4-part harmony with extremely harmonic instruments. Bowing a string causes a phenomenon called "mode locking," where the normally somewhat inharmonic strings are forced to be harmonic (my understanding is the human voice also exhibits mode locking). You often do microadjustments to get chords to sound good vertically and horizontally. I pulled up a random barbershop recording and looked at a spectrogram for the final chord, since the final chord is supposed to ring as much as possible, and there are only vertical considerations, so you'd presume they'd tune it as justly as possible, right? Here's what I found: They tuned their perfect fifth justly as 3 : 2 almost perfectly. That's not unexpected, even equal temperament gets perfect fifths close to right (though a little flat). They tuned their major third between 1.253 : 1 and 1.258 : 1. A just major third is 1.25 : 1, an equal tempered major third is about 1.26 : 1, and the 55-EDO system mentioned in the book I referenced in my first comment would give a major third of about 1.255 : 1. Like I expected, they tuned their major third sharp with respect to just intonation, but still flat with respect to equal temperament.

tshaddox 5y ago
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.