nekomatic wrote: ↑Tue Sep 07, 2021 7:32 am
In a discussion elsewhere on the tuning of fretted versus fretless instruments, it was stated that barbershop quartets sound like they do because they use just intonation.
‘I did not know that’, I thought, and went looking for confirmation. It turns out
it’s a bit more complicated than that
Strangely enough, I've been doing a *lot* of thinking about just intonation (and what evidence there is to support some of the common claims) while on holiday for the last couple of weeks. I also came across a different Sundberg paper - one where he summarised a lot of musical acoustics/psychoacoustics work in this area, including the barbershop paper you linked to.
In this broader Sundberg review, he summarised a bunch of studies measuring typical interval sizes for vocal and instrumental musical pieces (where one might expect just intonation to be used). He measured both harmonic intervals (when an unaccompanied melody jumps to a new note) as well as dyads, when two tones sound simaltaneously. Short answer is: measured intervals were not well matched to just intonation, were somewhat more closely matched to 12-tone equal temperament (12TET), but in most cases were somewhat wider than 12TET. The minor second and diminished 5th were outliers to this pattern, and I think he raised some possible reasonings for this.
I've heard it claimed so many times that solo instrument players and some vocal music uses just intonation, because this "sounds better". But I haven't found any good evidence to support this, and Sundberg's summary (and Barbershop paper linked above) show this is clearly not the case.
And also, people talk about just intonation as if it's a single, well-defined thing. In terms of what integer ratios are used to define different intervals, you quickly find there are several schools of thought (e.g. for minor 7ths, minor 3rds), e.g. Pythagorean system using ratios created only using powers of 2 and 3 (so "standard" just major 3rd is 5/4, but pythagorean major 3rd is 81/64)
My personal take: tuning is all about compromise. There is no tuning or temperament system that is "perfectly in tune". It just depends what you're used to, what the musical context is, and what musical effect you want to achieve.
There were some interesting psychoacoustic experiment results Sundberg referenced, where trained musicians were asked to adjust a tone frequency, so that when played with a lower tone, the intervals "sounded best". They also didn't use just intervals here, and tended to tune intervals a little wider than 12TET.
One really interesting result: when they were asked to tune octaves, even these were tuned wider than a simple 1:2 ratio! In other words, trained musicians think that an octave sounds best when it's tuned so the upper note is 5 or 10 cents sharper than a strict 1:2 ratio.
I don't know how much this is influenced by stretched octave tuning on pianos (assuming most musicians spend a good deal of time listening to or playing pianos in their musical education). There are also really interesting questions around whether these results apply in a similar way or not to musicians from very different musical backgrounds (from around the world).
One final comment: just intonation and the use of simple integer ratios is based on an ideal string, where the harmonics above the fundamental have a frequency n times larger than the fundamental (f, 2f, 3f, 4f...). Because of the awkwardness of reality (mainly string stiffness), the harmonics you get on a real string start to drift sharp of this ideal fairly quickly, which *might* be a reason for a preference for wider than 12TET intervals.
Really interesting area!