“I don’t get it, I can’t keep my guitar in tune anymore,” the guy said, passing his guitar over the counter. “I play a couple of songs and it just goes right out again. It used to work just fine.”
I look it over. It’s a mid-priced, slightly used acoustic guitar, about ten years old. The strings sound a bit dull, and the action is a little high.
“How long have you had it,” I ask, looking at the slightly worn frets. I play a few notes.
“I bought it new. It’s always worked real good. I’ve traveled with it all over the world with it. I can’t figure out what happened.”
I ask him to show me how he normally tunes it. He shows me a common tuning method, matching fretted strings with open ones (5, 5, 5, 4, 5).
He then strums a D chord.
“This sounds ok, but listen when I play a C chord,” he says.
The C chord sounds out of tune. Grimacing, he tries retuning a couple of strings to make it sound better, then tries the D chord again. Now it sounds wrong. He frantically starts readjusting the tuning, trying chord after chord until it’s completely out of tune again.
“See what I mean? It’s broke!”
So what’s going on here?
LET’S DO SCIENCE!
Let’s pause this sad scene for a moment and look at a little science that might help shed some light on the problem. Sound and music are actually made up of groups of pressure waves traveling through air. Every sound has a unique mix of harmonics, which is why you can tell the difference between the sound of a car horn and an elephant trumpeting.
Quite some time ago someone discovered that you could actually kind of ‘pull apart’ sounds and hear their harmonics separately. Try this – touch a string over the 12th fret of a guitar and pluck it. You’ll hear a bell-like tone that’s twice the pitch of the open string. This produces a ‘standing wave harmonic’, which is actually part of the sound of the open string, normally heard at a much lower level. Touching the string over the 5th fret and plucking produces another tone an octave higher than that. Try this over all other frets you’ll hear other tones as well. Notice how some of them don’t quite sound ‘in tune’? The harmonics produced don’t ‘quite’ match their mathematical ideals, due to the size and stiffness of the physical string.
MUSIC AND THE LAW (OF NATURE)
Believe it or not, a lot of early music was created based on these naturally occurring out-of-tune harmonics produced by string and wind instruments. As long as a song kept droning on and on in the same key everything sounded fine, but once it shifted to a different key (especially one with more than 7 notes) problems began. It sounded out of tune – The notes of one key didn’t quite match the notes of another. A player would still have to stop and re-tune during performances. The more sophisticated the music the worse the problem got.
You ever notice how perfectly in tune a good orchestra always sounds? Wind instrument players (and vocalists) listen to one another as they perform and sublty re-tune their notes to match the notes they’re playing together. This creates more pure-sounding natural chords than are possible with a fixed pitch instruments. A note played in one chord does not necessarily match the same note in another. While this can result in quite lovely sounding music, keyboards and guitars can’t do this trick. A lot of tuning systems (such as just intonation) have been tried over the years to fix this with limited success. As time went on gradually it became obvious that some compromise was necessary. So equal temperament was born.
It works like this – instead of using harmonics to work out the notes, you take a perfect octave then divide it into equal 12 parts, each exactly the same distance in pitch from the other. The relationship between notes is then the same no matter what key is played, and though the notes aren’t quite the same as more natural sounding ones, they’re pretty close. Once everybody got used to hearing music played ever-so-slightly out of tune this way it became a worldwide standard. It’s so normal and accepted now that nobody gives it a second thought – Which brings us back to our guitar tuning problem.
Since guitars are fixed pitch instruments and the frets are laid out using the equal-tempered system, by design every note (except unisons and octaves) are always slightly out of tune with every other note. You see why it’s impossible to tune to chords? None of them can ever be perfectly in tune. The only notes that are close to perfect interval are a fifth and a fourth, which is why they’re used so much in rock and metal music. Unlike other pitches in the scale, they still sound smooth when distorted.
Another problem is that a stretched string is not ‘mathematically’ perfect – it plays more out of tune towards the end than the middle, and the size of string and height from the frets have an effect as well. Acoustic guitar designers try to compensate for this by installing the bridge saddle to make the string length just a little bit longer which brings the pitches closer to their ideal positions. Every manufacturer has their own recipe for this, but due to physical variables and other real-world uncertainties none of them do the job perfectly. However, for all practical purposes, this approach works fairly well.
Let’s get back to our frustrated guitarist. I pointed out that while the guitar probably worked fine when it was new, over time it has changed – the strings have been steadily pulling up and warping the neck and body, raising the action. The top has bellied up and the bridge has tipped forward slightly. The body joint was warped, and the string length was slightly shorter and higher than it used to be. The relationship between frets, body and bridge that worked so well when it was new was now broken. No matter what he does, the guitar will no longer be tune-able.
Fortunately in this case most of the warping and twisting that was likely to ever likely to happen was pretty done, so I was able to compensate for all the changes without doing a massive rebuild. I adjusted the truss rod, cut down the saddle a little and re-shaped it to compensate for the tipping bridge, then leveled and crowned the warped upper frets to get them back out of the way of the strings again. Once the guitar was restrung and set it up to factory spec, I demonstrated how to double check the ‘5th fret’ tuning method using unisons and octaves to help compensate for accumulative tuning errors, and cautioned him not to use 7th fret harmonics since they are actually out of tune with the fretted notes. When it was all done the guitar played and stayed much better in tune. He left a happy man.
To learn more about equal temperament and tuning:
© 2014 Leo Bidne