You might like the book "Equal Temperament Ruined Harmony." It makes the case that there is a long history of differentiating sharps and flats in western music (flats are just a bit sharper than sharps), while arguing that in practice the whole tone was subdivided into nine parts, with the major and minor half steps respectively 5 or 4 of those nine parts. I don't think the precise tuning system described by the book really happened, but it does collect evidence that "enharmonic" used to mean "finesse your intonation to make this sharp be that flat."
In my own experimentation, the just intonation intervals are jarringly perfect, and I'd say that the 5:4 major third is too narrow. Has anyone checked that barbershop quartets are actually singing such narrow major thirds? My understand is that many studies have shown that string instrumentalists and singers, even when they claim to be using just intonation, play their major thirds somewhere between 5:4 and equal temperament.
It's also extraordinarly difficult to really tune basic harmony justly. The ii V I progression is a fun one... if you're not careful you shift the tonic by a syntonic comma.
> Has anyone checked that barbershop quartets are actually singing such narrow major thirds?
I don’t know if anyone has checked, but why wouldn’t they want to? Surely the low integer ratios are best going to get the intended sound of barbershop harmony, unless there are other acoustic reasons why slightly changing the intervals would work better (something akin to octave stretching in pianos, although I’m not sure that sort of thing would be as relevant to barbershop harmony).
That's a nice thought in theory, but I can assure you that string quartets do not play 5:4 major thirds -- they're significantly sharper (but not quite equal tempered major thirds).
There's more to music than acoustics. Four-part harmony has a lot of moving parts (literally and figuratively), and you have to make concessions to acoustically pure intervals to make it sound like it's in tune through time.
This is true, there are even "comma pump" sequences that are literally impossible to play fully harmonically, being inherently based on conflating "close" ratios! (I think in theory, a very detailed Schenkerian-ish analysis of a piece would tell you quite a bit about where ratios should be made "nicer" and where they shouldn't - but that's a lot of work and involves a whole lot of personal judgment.)
I think one of the reasons ii V I is so compelling (versus IV V I) is that the ii (or ii7) is conflating many notes. In C major, using interval terms as a stand-in for "tuned justly":
Is the D a fourth below G or a minor (or harmonic) seventh below C? Once you've chosen your D, is A a perfect fifth above it? If so, what kind of major second relation does it now have to G?
Is the F a perfect fourth above C, or is it a major third above your D? Or is it supposed to be the minor (or harmonic) seventh above G?
I think barbershop tends to skirt these questions by instead using a II V I progression (a secondary dominant), since the F# doesn't have to stand in careful relation to other notes of the plain C major scale.
(That's interesting Schenkerian analysis can help understand these issues. I know only about it at a very thin surface level.)
I suppose a good rule of thumb is that "dissonant" notes (in the musical syntax sense) should be in a harmonic relation with the scale step they will ultimately resolve into - so D to C, A to G, F to C etc. This can and will create roughness in the vertical dimension, but that actually reflects their unstable "energy" that drives them to resolution. Of course one could just as well use microtonal shifts to play with this kind of stability whenever longer-range relations are involved. Perhaps this is part of what good performers do intuitively when playing a melodic instrument. The relevance of music-syntactical dissonance and resolution is what might make Schenkerian analysis a very useful tool to understand these possibilities!
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?).
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.
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?
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 (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.
I don't think it's very difficult. In the ii-V-I, slightly shifting the root of the ii sounds fine, and most other problems can be solved similarly. I've made plenty of music in just intonation, here's a recent example: https://www.youtube.com/watch?v=qkUs-BdxtN8 To me it sounds like very standard harmony, but "cleaner".
In my own experimentation, the just intonation intervals are jarringly perfect, and I'd say that the 5:4 major third is too narrow. Has anyone checked that barbershop quartets are actually singing such narrow major thirds? My understand is that many studies have shown that string instrumentalists and singers, even when they claim to be using just intonation, play their major thirds somewhere between 5:4 and equal temperament.
It's also extraordinarly difficult to really tune basic harmony justly. The ii V I progression is a fun one... if you're not careful you shift the tonic by a syntonic comma.