On the microtonality of barbershop

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nekomatic
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On the microtonality of barbershop

Post by nekomatic » 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
Dervict stanord

IvanV
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Re: On the microtonality of barbershop

Post by IvanV » Tue Sep 07, 2021 6:41 pm

Having done some workshops in one-to-a-part unaccompanied singing, then I would say there's two aspects going on. And it doesn't really matter whether its barbershop or Brahms.

First, there is not that much music we sing, outside the folk music room, that is so simple harmonically that it would work in a purely just intonation sense. Even in barbershop they do a lot of jazz chords and chromaticisms that you can't conceive of within a just intonation. So, there has to be some sense of equal temperament going on for it not to sound odd overall. That probably comes through the pitching of individual lines, which other people then correct to - just as it says in the paper you quote - they tune to the part that mostly has the tune, the 2nd part down in barbershop. But you probably also hang onto some common reference points, at least I try to - the tonic and dominant for example - which it is often possible to keep a strong sense of in mind. If I've been singing a piece in D for a while, for example, then I tend to find "the room" now has a strong sense of what a D and an A is, and I can easily sing them on request, even though I don't have perfect pitch, and will soon forget them once we move on to singing in C# minor for a while.

And second, when you are adjusting your intonation vertically to keep the chord in tune - which you should do a lot when singing a capella, and which is easiest when you have landed in a simple diatonic chord - then you will likely be naturally doing that in a just intonation. Because that is what singers and violinists and trombonists and the like naturally do.

One of the things I have often wondered about is why do conductors shout at you so much to keep your major thirds sharp, when a just major third is a long way flat of an equal tempered major third.* I used to think the difference is larger on the major third than any other degree of the scale, though that article suggests minor second is largest. So it ought to sound good to be a bit flat of equal temperament when you are singing the third in a major chord. But I guess the problem is what you sing next. From that just major third, your next note might be sharper than you would imagine from starting point, on a purely note to note basis, so you'll tend to sing the next note flat of where it needs to be.

*An equal temperament major third is a frequency ratio of 2^(4/12) = 1.25992 as against a ratio of 5:4 = 1.25 for just tuning. So if A=440Hz, then a just tuned C# is 550 Hz vs 554 Hz for equal tempered. That seems to be a difference of 14 cents, which is much larger than the typical tuning errors cited in that paper. (1 cent is a frequency ratio such that c^100 = 2^(1/12), equivalently 100 cents is an equal tempered semitone, which is a frequency ratio of 2^(1/12).)

plodder
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Re: On the microtonality of barbershop

Post by plodder » Mon Sep 20, 2021 12:09 pm

Not sure if I'll add much to the conversation by saying that, as someone who plays open-tuned instruments (i.e. tuned to a chord rather than, say, standard guitar tuning) I always tune the major 3rd to be slightly flat in order that it functions as a 3rd. Trick is to get it close enough to work for the other inversions up the neck (when the string stops hosting the 3rd, and provides a different chord tone).

Also, not barbershop but certainly very flexible. I wonder what these guys do? They seem to be aiming to create beats in some places: https://www.youtube.com/watch?v=9t6Gar_2Zv4

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Re: On the microtonality of barbershop

Post by hakwright » Mon Sep 20, 2021 12:14 pm

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!

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