Why is it so hard to get the B string in tune?

August 1, 2008 7:35 PM

What is the deal with B strings on guitars? Is it just my ears? Doesn't matter which guitar I'm tuning, when I tune by ear it NEVER sounds right. And then, even with a tuner, I have to adjust it a bit after, I'm never satisfied. Finally sounds good with an Am chord, then you play a C and it's fucked up. Am I insane?
posted by chococat (31 comments total) 12 users marked this as a favorite

These two links offer some clues, I think. Guitars, with their frets, as opposed to individually-tuned strings like a piano, aren't as suited to exact equal temperment. When you tune using harmonics, you are tuning based on exact ratios, as in the righthand side of the "Comparison to Just Intonation" table halfway down the Equal Temperment page.

So if you tune all of the fourths (E to A, A to D, D to G and B to E) using harmonics, comparing 1/4 of the way up the string (the 5th fret harmonic) with 1/3 of the way up the string (the 7th fret harmonic), then the one place were you will hear most obviously that you've diverged from equal temperment (the standard piano tuning) is from the G to the B. There is more of a difference between equal and just tuning in the G to B interval (15 cents or 15% of one fret) versus the others (2 cents or 2% of one fret). So when you are fiddling with the B string in standard tuning, you are deciding to what extent you want to be in just versus equal temperment. Strictly just intonation will sound better in certain keys than others, while equal will be a bit off the same way in each key.

Equal temperment is a compromise that allows players to change keys all over the place without each key sounding different in terms of how far away from each other each note is, like Nigel's reference to D Minor being "the saddest of all keys" in Spinal Tap. In just intonation, different keys are slightly different in structure. This is also why a really good string quartet, being completely fretless, can adjust when they change keys a little tiny bit so that each key sounds really close to those 2/3 3/4 etc. ratios in a way that fretted instruments or pianos can't.

That got kind of dense. Please, tell me which parts of that don't make any sense whatsoever and I can try to clarify.
posted by umbú at 8:41 PM on August 1, 2008 [5 favorites]

On both of my electric guitars, the biggest trouble I have is with the G. Because I like the droning open B/Hi-E strings, I tend to do a lot of things on that G up near the 7th fret, but it's so sensitive to how I strum.

Even right after I check the intonation.
posted by chimaera at 9:06 PM on August 1, 2008

I had this same problem (actually, on certain electric guitars, it was all three high GBE strings), and I couldn't figure out why they never sounded right when tuning, but sounded okay when playing chords. The upper strings seem to have a much wider frequency quality to them -- in fact, all physical musical devices have varying harmonics, and it's just really noticeable on these strings (particularly on electric guitars). If you focus on the sound, you can hear the first harmonic. It's hard to explain, but if I concentrate on it, I can convince my brain to filter out the higher notes, and when I do that it sounds in-tune.

Now, throw in the fact that humans don't actually like perfect chromatic scales and instead prefer a very very slight alteration to the pitch depending on the key (especially when playing chords that involve the 3rds), and it makes sense why it doesn't sound quite right.
posted by spiderskull at 9:23 PM on August 1, 2008

I notice that the problem is much more diminished (ha!) after I take my guitar to an expert and have him set it up and fix the intonation.
posted by chillmost at 2:10 AM on August 2, 2008 [1 favorite]

Yes, if it's really far off, it's probably a problem with how the neck is seated.
posted by umbú at 6:37 AM on August 2, 2008

umbú just saved me some typing. I've learned over time to fudge my by-harmonics tuning a little bit to avoid the G-and-B blues.
posted by cortex at 7:26 AM on August 2, 2008

I've had this problem with EVERY GUITAR EVER and it drives me batty. I'm also really anal about tuning, and the b string drives me crazy.
posted by ORthey at 2:26 PM on August 2, 2008 [1 favorite]

I've never considered the b string to be that problematic, but I've been playing for twenty years and have yet to hear a g string that didn't sound awful and out of tune.
posted by bunnytricks at 1:00 AM on August 3, 2008 [1 favorite]

I myself am a fan of the g-string.
posted by Astro Zombie at 9:25 AM on August 3, 2008 [1 favorite]

umbú, that's a great answer that I should have found myself. Thanks a bunch. And thank goodness this isn't AskMe.
Your description is pretty much exactly what I've been doing; harmonics and then adjusting for the weird strings, but it's the playing in different keys or different places on the neck that always got me. It was only sometimes, which drove me crazy. I'd think I had a warped neck or something and feverishly check the intonation but then it would do the same on a different guitar, or I guess I'd get the sweet spot or something and it would be fine.
It doesn't help that my Gretsch has a floating bridge with a Bigsby that basically sends everything out of tune after one song and has me obsessively tuning before/during any kind of live thing, adding out-of-tune-phobia to my paralyzing fear of forgetting words.

Oh, and my brother David said something off-the-cuff many, many years ago that I say to this day to remember the string order:

EveryBody Gives Dave An Eraser.

Just try and unremember that.
posted by chococat at 10:45 PM on August 3, 2008

Having played in the Guitar Craft New Standard Tuning for a long time - CGDAEG - which evades some of the problems described here to some extent by being almost all fifths (like violins or cellos), I can state conclusively that it's physically impossible to tune a guitar, by which I mean it would violate the laws of physics.

(Interested parties might find this book to be of use.)

I mention it, because even though the strings are more consonant with each other (each string has the pitch of the string above it as a dominant harmonic, so the strings "support" each other better) and there's no pesky major third in the middle (there is a minor third on the top, but this is less tricky), it's still a bugger to tune. Not quite as much of a bugger, and not quite as frustrating when you work out where to compromise, but a bugger nonetheless. For example, in order to sound "right", the bottom strings need to be a bit lower than the harmonics alone would suggest.

That major third is a pain in the arse, though. Lute tuning put it a string lower (E A D F# B E) and I wonder if that might not be a bit better. I remember, in the early days, almost weeping with the frustration of it, before I went the easy route (selective tone-deafness).
posted by Grangousier at 12:17 AM on August 4, 2008

The B stands for Bitch string.
posted by Mr.Encyclopedia at 8:26 PM on August 4, 2008

This post kicks ass. This topic is one that has gone unexamined for far too long, IMHO (seriously).

I always wondered if this problem had anything to do with the mathematical imprecision inherent in the western musical scale. There's a thorough treatment of this problem here on this blog. I haven't had a chance to read that article in its entirety yet, but just from glancing over it, it seems to cover the issue pretty well (to the best of my limited understanding).

Can anyone with a better grasp of the mathematical problems with the musical scale discussed in the linked article confirm whether it plays any role in the more practical problem of the damn B-string's harmonic decay never sounding quite right in every possible chord position for a given tuning? Is it related at all--directly or indirectly--to this more basic music theory problem, or does it just come down to the physical properties of the guitar as an instrument, as umbú's excellent explanation suggests?
posted by saulgoodman at 10:05 AM on August 5, 2008

I always wondered if this problem had anything to do with the mathematical imprecision inherent in the western musical scale.

Well, I might be misunderstanding you, but I want to be clear that there's nothing mathematically imprecise about the now-common equal-tempered tuning: the ratio between any two semitones is precisely mathematically equal. Wikipedia's write-up on it is actually pretty decent.

But if what you're getting at is in part that a specific solution like equal temperamant is just one of several ways (and a late-comer to the party, at that) to analyze the idea of the western twelve-tone scale, yeah, that does come into this tuning mess—the tune-by-fifth (or fourths) thing that a lot of us do by stepping up a pair of strings at a time and using pure harmonic fifths to get the strings in tune is in direct conflict with the equal-tempered results that we're generally trying to achieve. But that's not mathematical imprecision, it's using two different models to try and solve the same problem, and standard tuning on a guitar just makes for a nice showcase of the problems with that.

(I used to feel a kind of snobbish desire to eschew electronic tuners. Now I have a sort of snobbish desire to make sure everybody is using an electronic tuner. Flip-flopper.)

All of this is aside from the fact that, as a few folks have alluded to already, shit intonation on you guitar will just ruin everything anyway. For along time I didn't even know that was an issue, and when I got guitar intonation it was a revelation.
posted by cortex at 10:46 AM on August 5, 2008

(Pragmatist that I am, I think of equal temperament not as a compromise but as Correct; heliocentricity was not as simple and clean an explanation as Ptolemy's old take on things, but it works. Apples and oranges there, yes, I know.)
posted by cortex at 10:49 AM on August 5, 2008

Here's what (maybe?) is the relevant point from that article I linked:

So here is the problem: we can’t choose the notes of the musical scale such that, from every note, an interval of a perfect octave and a perfect fifth is available. My next post will show how modern musical scale solves this problem.

Is the "equal temperament" solution you mention a solution to that specific problem? Or are these more or less unrelated issues? That's my question, I guess.
posted by saulgoodman at 10:55 AM on August 5, 2008

phew. trying to work through the stuff you linked, cortex, but it's mostly way over my head.
posted by saulgoodman at 11:11 AM on August 5, 2008

Equal temperament isn't a pure solution to the problem—the nature of perfect harmonics is that they don't actually lead to anything like equal temperament when carried to the limit, which is why that sort of intonation has problems in some contexts (but can sound very nice in others).

What equal temperament is is a pragmatic solution to the problem—normal human listeners can only discern differences in tones down to a certain degree of difference, and the differences that exist between e.g. a perfect harmonic fifth (a 3:2 or 1.5:1 ratio between tones) and an equal-tempered fifth (which is 27/12 ~ 1.498:1 ratio between tones) is small enough that they functionall sound the same or so very close to the same that music sounds good.

So equal temperament is a working solution because, unlike pure harmonic models and some other intonational models, there are no intervals in an equal tempered instrument that sound wrong. It is the least-wrong model going, but it's built on the axiomatic notion that it's okay for nothing to be perfect and built out of ratios of small integers.

Here's an article that talks about temperament and piano tuning that covers a lot of that stuff fairly well too; it concludes with a paragraph that begins thus:

The goal of musical instrument adjustment and tuning is an instrument that sounds good. The qualitative definition of what sounds good has been being developed by musicians and instrument makers for thousands of years. Modern technology has provided the tools to make very accurate quantitative measurements of these qualities.

Which is kind of the whole thing in a nutshell. Folks still disagree about the specifics of what "sounds good" means, but we've gotten to a point where (compared to 200 or 400 or 1000 years ago) we can be really specific about how any particular model for creating that good sound is accomplished. But much of that is maybe a good bit deeper into the weeds than most sane people want to get, heh.
posted by cortex at 11:27 AM on August 5, 2008

That's a really interesting link, saulgoodman. I can't admit to have worked through all the math, but I think his argument is basically sound. I jotted down a possible tuning scenario, and I think it helps clarify what's going on.

I think the easiest way to look at this is using the 'cents' system, which attributes 100 cents to the difference between one equally tempered note and the next--between one fret and the next. So from one octave to the next is 1200 cents, and between A and Bb is 100 cents.

It's pretty standard to use the A string as the reference point for tuning. If you do that, and use the technique of comparing 5th fret of one string to the 7th fret harmonic of the next, then you end up with a difference of approximately 498 cents, not exactly 500. If you then use the string you just tuned as the reference point for tuning the next string up pitch-wise, then a game of telephone ensues, with the tiny difference of 2 cents (2% of a fret) adds up until it can cause minor problems like this:

(in cents)

E -498
A 0
D +498
G +996

Now, here's something that explains why we all end up fiddling with the G, B and E strings longer than the lower ones when we're under pressure to start the next tune at a gig. If you tune the low E to the high E, then you're looking at:

E +1898 (2400 cents or two octaves above the low E)

But if you tune the A string (7th fret harmonic) to the high E, then you'll end up with:

E +1902 (1902 cents or one octave and a just fifth above the A)

Okay, so you've left the B string to the last. You have several options of how to tune it. If you tune the B (5th fret harmonic) to the high E (7th fret harmonic) then you'll end up with either:

B +1400 (subtracting 498 cents from E +1898)
B +1404 (subtracting 498 cents from E +1902)

Now, remember that the G string (which Astro Zombie notwithstanding, some folks pinpoint as as much of a problem or more than the B string) is at G +996, four cents below the equal tempered 1000 cent difference between an A and the G above it. So no matter which way you tune the high E string (unless you use a tuner), the interval between the G and the B strings is going to be larger than equal temperment, clocking in at either +404 or +408 cents, which is large enough to be audibly irritating.

E -498
A 0
D +498
G +996
B +1400 or +1404
E +1898 or +1902

And assuming that the frets are exactly 100 cents each, which they try to be, then if you tune by actually fourth-fretting the G and comparing it to the B, that'll be between 4 and 8 cents less. And each note on a given string follows lockstep from the tuning of that given open string, resulting in an instrument you have to constantly tweak.
posted by umbú at 11:47 AM on August 5, 2008 [5 favorites]

Independent of the math, however, cortex nails the really important point: that it's about competing views of what sounds good. It's qualitative. It's not that some scales are conforming to the laws of acoustics and others run counter.

I like the quote of Alexander Ellis, the physicist who worked out the 'cents' system:

"The Musical Scale is not one, not 'natural,' nor even founded necessarily on the laws of the constitution of musical sound...but very diverse, very artificial, and very capricious."
posted by umbú at 11:55 AM on August 5, 2008

Having never taken the time to sit down and figure out all this Equal Temperament stuff - it's on my list of things to do, eventually - I don't have much to contribute to this discussion except to ask a somewhat related question: When you tune the guitar by ear, do you tune a string to the string next to it - say, tune D to A, G to D and so on, as most guitarists are taught to - or do you tune all the strings to one string, as explained here?

To get around all this, I just use an electronic tuner most of the time.
posted by Ira_ at 12:09 PM on August 5, 2008

The Musical Scale is not one, not 'natural,'

Exactly. The "natural" intrinsics of musical acoustics are pretty damned limited from one view:

- it's a weird happy accident of acoustic cognition than notes a natural octave apart sound "the same" to us, and
- the relation between sub-octave intervals can be described in terms of discrete acoustic phenomena like "beats", but not at a level that's within the reaches of conceptual discrimination with normal tones (nobody counts the beats-per-second in an A4-E5 perfect fifth, even if beating is an acoustical component of how that interval sounds).

The human brain has the capacity to develop a powerfully complex appreciation of musical sounds, but as in the existence of a stunning variety of natural spoken languages in the world, the existence of starkly different musical scales and theory underlines that whatever the musical or linguistic capacity inherent in the brain, it's operating at a level much more fundamental than any particular language or scale. Octaves and semitones are a convention, not something that exists in the bedrock of the universe waiting to be discovered.
posted by cortex at 12:20 PM on August 5, 2008

Independent of the math, however, cortex nails the really important point: that it's about competing views of what sounds good. It's qualitative. It's not that some scales are conforming to the laws of acoustics and others run counter.

Makes sense to me (in an abstract sort of way). No tonal system (or scale, whatever) is perfect; in fact, 'perfection' isn't even a meaningful concept. There's quantitative fuzziness involved in every tonal system. And if you try to define 'perfection' in the classical sense as 'mathematically rational,' then all the musical scales are imperfect because they generate irrationals. And different rounding methods lead to subtly different tonal outcomes, which can only be judged qualitatively. And then the physical properties of instruments like guitars impose certain limits on what's acoustically possible for the instrument, too, and the use of conventional tunings imposes further limits, and within that context, this whole issue of "loose change" in the musical scale probably does figure into the B/G/E-string tuning problem in some way. Now I've got to stop thinking about this before it makes me crazy.
posted by saulgoodman at 12:22 PM on August 5, 2008

I use a tuner when I can help it. I tune string-by-string off another known-good instrument when I can't, and by harmonics+fudging when I can't do that either. The E2 writeup is more than I'm likely to bother internalizing, because I am lazy and stubborn and usually have a tuner with me. And because as middling as my own fudged tuning practices are, I'm usually more in tune than the other people around me if they're fudge-tuning as well, so, like, fuck it.

Also, I will sometimes tune off a dialtone if I have a way-out-of-tune guitar and no other way to get a reference note. Dialtone is approximately an F-A major third.

posted by cortex at 12:23 PM on August 5, 2008

cortex: I thought the basic idea of the E2 writeup was just to tune all strings to one string instead of the traditional way of tuning each string to the next one up/down, so as not to compound the inevitable small tuning errors between each string - it seems to make sense to me, so I was just trying to ask if you folks who know this stuff better than I do think that's right. But yeah, I generally can't be bothered with all this and just use a tuner too.
posted by Ira_ at 3:39 AM on August 6, 2008

Yeah, the basic idea of the E2 thing is solid, and I'm making it sound like it's more complicated than it actually looked at first glance. I'm just too lazy to try and work the harmonics like that.
posted by cortex at 8:02 AM on August 6, 2008

I spent last night reading up on intonation and tuning as I've just got a semi-acoustic with a moving bridge and suddenly need to learn a whole new bunch of things. Damned if I can find them now but I came across a couple of guitar forum discussions of the subject explaining that while all guitar tuning and intonation is effectively a compromise, guitar strings and guitars not being perfect theoretical objects, the two strings with the worst string mass / size / scale / intonation issues were the G and the B. This is why you can get days when all the open strings seem to be in tune, yet it starts sounding all out of tune as soon as you play, especially on the frets nearest the headstock.
posted by motty at 9:35 AM on August 7, 2008

You found my post! I'm the guy who wrote the The Imperfection of the Musical Scale posts over at Letters to Nature.

I'm a bass player myself and always wondered whether the method of tuning with harmonics is totally accurate. And, for the reasons I mentioned in my other post, it isn't. The key line was quoted above: we can’t choose the notes of the musical scale such that, from every note, an interval of a perfect octave and a perfect fifth is available. So we approximate the fifth.

But how much of a difference does it make? Suppose your G string is perfectly in tune: 97.99886 Hz. You now tune the D string so that the harmonic off the 7th fret of the G string is the same pitch as the harmonic off the 5th fret of the D string. You then tune the remaining strings in the same way. (Here's a more complete explanation.).

By the time you get down to the B string, assuming you're ear is perfect, you're B string is sharp by almost 8 cents. (I won't do the calculations here - I'm an astrophysicist by day). Even the E string is off by almost 6 cents. The human ear can hear a differences of 5 cents or more. I think this is enough to justify the purchase of an electric tuner.
posted by LukeBarnes at 5:17 AM on August 8, 2008

Ha! Hiya, Luke. Welcome aboard.
posted by cortex at 6:45 AM on August 8, 2008

Pythagoras is to blame. Check out Howard Goodall on the subject:

posted by chuckdarwin at 2:17 AM on November 18, 2008

Here's a really good in-depth presentation about this very subject. [Youtube, runs about an hour].
posted by knave at 10:59 PM on January 9, 2009

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