Did you know that it’s impossible to tune a guitar perfectly? I don’t mean impossible as in, “It’s impossible to play an entire gig without some joker yelling ‘Freebird!’” I’m sure that’s happened somewhere. I mean impossible as in, Swedish-physicists-in-lab-coats-standing-around-a-guitar-shaking-their-heads impossible.
To fully explain why, we’d need to talk about Greek philosophers experimenting with harps, and Bach’s contemporaries arguing about how to get an orchestra in tune, and there’d be lots of charts, graphs, and ratios involved. I’m unqualified to do any of this.
Here’s a brief explanation though, to the best of my knowledge
Looking at the fretboard of the guitar, you’d get the impression that our musical system is very orderly. Those perfect parallel frets line up so nicely, diminishing in width at an even rate as they move up the neck, like the world’s straightest sidewalk stretching into the distance. What if I told you that in order to get the guitar to play perfectly in tune, that sidewalk would look like a bomb landed on it? And even then, you could only play it in one key? This is what I’m talking about.
Time for an example. Most of you know the way of tuning your guitar by ear, where you tune pairs of strings by playing the 5th or 4th fret of the lower-pitched string. Those of you who are really sensitive to tuning have probably noticed that by the time you’re done, you compare your 1st string to your 6th (both E notes) and that 1st string is sharp! “Arrgh! I knew I should have bought that extended warranty!”
Actually, there’s nothing wrong with your guitar. Or rather, David Gilmore’s Strat has the same problem. The problem is, the note you play on the 5th fret of your guitar is ever-so-slightly sharp compared to the open string note. Every time you tune a string, you introduce a little bit more sharpness, so that by the time you get to the first string, you’ve drifted out of tune. It’s like the game of telephone—error on top of error on top of error.
The distance between an open-string note and a 5th fret note is called an interval of a fourth. Where things really start sounding out-of-tune is when you play the interval of a third. Try tuning your guitar with an electric tuner, and then play the open third and second strings—this is an interval of a third. That second string sounds a tiny bit sharp.
Why is this? Basically, nature handed us a spiral, and for the last 500 years we’ve been trying to figure out how to squish it into a circle. The best we’ve come up with so far is the system we use today, called “equal temperment”. Google this term and you can learn more. Be prepared for some math.
In the meantime, how should you tune your guitar? First of all, the electric tuner is superior to that fretting-the-fifth-fret method. It appalls me how often I hear about guitar teachers who force their students to always tune by ear using that method. Sure, it trains your ear, but shouldn’t the primary goal be to get the thing in tune?
There is a tuning-by-ear technique that does work great, described by Richard Lloyd (guitarist for the awesome 70’s punk band Television). It’s harder to memorize, but it’s worth it! You can find it on his website’s FAQ here, second question down.
But ultimately, you’re going to have to put up with your guitar being a bit out-of tune. If it’s any consolation, pianos and other fixed-pitch instruments have the same problem.
And if you just can’t stand it, you can always switch to an instrument like trombone, where you have full control of your pitch.
Of course, you can’t play a trombone behind your head or light it on fire….
I don’t know if you have ever heard of the Buzz Feiten tuning system, but here is their website. Check it out! I would be interested in attending workshop if you ever do put one on again. Hope all is well!!!
This is a really timely piece of info. I use an electric tuner which allows the user to set pitch at intervals of 5Hz from 335 Hz upward. I have absolutely no idea what use this is! Can anyone enlighten me please??
I had a look at the web site of Richard Lloyd, which you refer to. I wouldn’t like anyone to take his explanation at face value as it doesn’t seem that he really understands the causes of the problem. For example, he says “equal temperament […] The way that this is done is simply to take the difference in frequency between a note and its natural octave and divide by 12”. This is not so, which you will see if you read, for example, the Wikipedia article at http://en.wikipedia.org/wiki/Equal_temperament.
The main point I wanted to make and the one hinted at by the Randall’s reference to the Buzz Feiten system is that there is another effect at play with guitars as well as the subtleties of equal temperament, which is this. The principle of the guitar is that you shorten the resonant length of the string to make the note higher. Each fret is about seventeen eighteenths nearer the bridge than the one before it. When you’ve had 12 frets, you’ve had 17/18 of 17/18 twelve times over (or 17/18 to the power of 12), which equals 0.5. i.e. The octave is a resonant length a half of it’s root.
The problem with the guitar, and steel strings in particular, is that when you fret a string near the nut, you not only shorten its resonant length, you stretch it slightly by moving it down towards the fretboard. This makes notes near the nut go sharp. Buzz Feiten’s system compensates for this by moving the nut nearer the first fret. The resonant length when you’re on the first fret is therefore not quite so far removed from the root (as the approx. 17/18 amount). The stretch puts the note to where it should be.
This isn’t perfect but is better than an uncorrected guitar. Buzz worked out the optimum distance of the nut so as to produce the best average correction (and patented the system).
There are also modified tunings for the guitar which attempt to correct the most obvious problems introduced with equal temperament tuning. For example, Peterson strobe tuners (www.petersontuners.com) have “sweetened” tunings, which help common guitar chords to sound more in tune. They also have a clear explanation of the problem at http://www.petersontuners.com/index.cfm?category=85&sub=59.
Randy – Great to hear from you! You turned me on to the Buzz Feiten system a couple years ago–very cool. I’m still hoping I’ll get my hands on a BF guitar someday so I can check it out.
About workshops—I haven’t done any in two years. I can’t see how I can fit any in anytime soon. I’ve got you on the contact list, though.
Kev G – That’s a calibration feature that allows people to tune their instrumet to another instrument that’s out-of-tune. 99% of musicians never need that function (I’ve never used it), but 99% of my students get screwed up by it by accidentally bumping the calibration button. You should keep the number at 440 Hz, which is concert pitch for the “A” note, the standard reference point for tuning.
Julian Gall – Thanks for bringing up the issue of notes fretted closer to the nut sounding sharp—I’m sure many readers have gotten their guitars in perfect tune playing an open G chord, and then they switched to an E and that 3rd string, 1st fret note was way sharp. Now you know why.
I still don’t understand Richard Lloyd’s misunderstanding of equal temperment. I’ve read the first half of the Wikipedia article, and then I start bleeding from the eyes. Could you spell it out for me (us)?
i am a “guitar neophyte” (though not a music neophyte, i used to play accordion ha!) . . .
i use an electronic tuner to tune my guitar . . . and i learned a lesson even just using that . . .
i kept turning the tuning knob on the guitar so that the red light on the electronic tuner would turn green on the display indicating that the string was in tune . . . i turned it a little more . . . and then a little more . . and then . . twang! the string snapped. why? because i was turning the right knob but plunking and listening to the wrong string! ha!
i had never changed a guitar string, so i had to go back to the music store and ask them if they would change the string for me and shsow me just how it’s done. and the guy there did that for me . . . now if i can “remember” exactly how to do it myself because i’m sure that won’t be the last string i snap! 🙂
oh, yeah, he also cautioned me that some electonic tuners will tune give us the correct note but not distinguish or discern the “octave” and if you begin an octave too high . . . twang! snap! there goes another string! 🙂
Here is an example of how equal temperament is not quite accurate.
Equal temperament divides the octave equally into twelve half notes or semitones. The ratio of each half note to the next is exactly the same – 1.059463. In other words, if the frequency of A is 440Hz, the frequency of A# is 440 x 1.059463 = 466.16Hz. B is 466.16 x 1.059463 = 493.88Hz, etc. By the time you’ve multipled by 1.059463 twelve times, you have the A an octave higher being 880Hz. At twice the frequency, this is exactly right.
Going up a piano keyboard on black and white keys or going up the fretboard on a guitar takes these equal steps.
Now, “natural” harmonies occur where the frequsncies of the notes are in simple ratios. A perfect fifth, for example, should be 3/2 or 1.5 times the frequsncy of the root. However, multiplying 440 by 1.059463 7 times gives a frequency of 659.26Hz. This is actually 1.498 times the root, rather than 1.5. In the case of the fifth, the difference is small, but it illustrates why equal temperament is an approximation. With the minor seventh, the ratio should be 7/4 (770Hz) but equal temperament gives 784Hz, a far bigger error.
So to summarise, the guitar suffers from the mathematical errors of equal temperament, although Bach obviously found this acceptable 🙂 And it also suffers from string stretching sharpening the notes when fretted, particularly with steel strings and near the nut.
This is great. Thanks for your clear explanation.
And I see now how Richard Lloyd’s description of equal temperament is inaccurate. “Take the difference in frequency between a note and its natural octave and divide by 12” makes it sound like you can just divide the frequency of a pitch by 12, and then add that number to create the next pitch. But the actual formula is logarithmic—you multiply your pitch by the magic number (1.059463) to get the next pitch, which if you graphed it would look like a curve instead of a the straight line that Richard Lloyd’s formula would create.
As you can see, I’m straining my memory of high school math here, but is that right?
As you say, ultimately the goal is to get the guitar in tune. So as long as my students understand the concept of, and have the ability to, tune by ear I recommend electronic tuners for ease…not to mention their necessity in noisy environments.
The big issue is equal temperament. The biggest issue is the major third and all those muddy harmonics that it produces in equal temperament. I am teaching myself lap slide on my old beater.The strings are set high to prevent fretting. If I dont have a tuner to hand I pretty much have to go by ear. I usually use Open D or Open G which leave me with 2-3 strings each tuned to the I and V notes of the scale( which I pick easily) and one to the III. I had been tuning the III to the point where the beats all resolved. I only recently understood that I am tuning to just intonation rather than equal temperament. Interestingly an unaccompanied singer will tend to choose the “Just” third, rather than the equal temperament third.
True…the main goal is really to get in tune. However, it’s not enough to tune the open strings, the EADGBE strings. For me, I used a octave tuning because I can hear that high pitch sounds of each strings better than the open strings…after that I try to tune the guitar to itself. How, I compare the open strings with the 12th fret note ..but I don’t do this often, I do it to check out whether my guitar neck is in need of adjustment or whether my guitar strings needed to be changed.
All these factors affect our tuning…the strings and the neck should be checked when you’ve got the time to spend.
I find that electronic tuners helps a lot…try using BOSS guitar tuner. Quite bulky by very acurate.
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