Why Stringed Instruments Are Hard To Tune

All of us have probably seen a musician wrestling with being out of tune, and there are a surprising number of interesting reasons why this happens. The issues involved are physical things like the strings, the instrument and the environment, combined with human issues of hearing, and very mysterious things about music itself. The real truth is that tuning is a place where art and science intersect, and neither one clearly wins. You simply can't tune a piano to a stroboscope-- few players will want to play it. There are artistic compromises, and a startling number of "gotchas" that pop up, and I think it is only fair to offer somewhere in writing an attempt to explain some of this stuff. I have never seen a music instruction book anywhere that even started to go down this slippery slope, and they all just say "tune your instrument" as if it was a simple and straightforward thing. It is neither.

Let's start with the easier thorns.

PHYSICAL REASONS

Instrument strings are not perfect things, and though most new strings behave properly, a string can be "sour" and incapable of producing correct pitches, especially when it is old and well-worn. The gears and mechanisms of the tuning machines can be flawed or worn, or the strings can be poorly attached at one of the ends. Instruments themselves can be made improperly, so that all music is significantly out of tune, because the position of the nut, saddle or frets are incorrect. The neck angle can be wrong, which can cause problems, and if the action (height of the strings above the fingerboard) is too high, it can cause the strings to stretch out of tune as they are pressed down, especially on the higher frets.

During environmental changes, when sunlight, stage lighting, air currents and various thermal and humidity changes are impacting a wooden instrument, the hardwood, softwood, bone, metal and plastic parts of the instrument, tuners and strings themselves can expand or contract or absorb moisture differently and cause all sorts of tuning problems. Playing in sunlight or in front of a heat source like a fire can wreak havoc with tuning, since the back of the instrument (or even the back of the strings) may be in the shade, or even worse, there may be intermittent lighting or heating that causes non-stop fluctuations. Hot dry environments tend to cause wood to shrink. And changes in humidity or temperature such as heating or cooling systems in a building, or sun and clouds alternating outdoors, will cause instability in keeping an instrument in tune.

Now the more obscure stuff...

The whole idea of what it means to be "in tune" is a lot foggier and more imprecise than bystanders might imagine. Different cultures of the world have different ideas of what it means to be in tune, and the history of musical pitch is an extremely interesting subject. Human taste is a factor. A certain old bluesman's guitar always sounds of of tune to me, but he liked it that way and would "fix" it if someone tried to "tune" it when he wasn't looking.

If you tune a string or blow across a Coke bottle and produce a musical note, nature provides some other notes that are consonant with it. The most universal one is the "octave" which represents the integer 2. Shorten a vibrating string by half and it raises the pitch an octave; doubling its length lowers one octave. Each time you change the vibrating object by a power of 2, it changes another octave. Reducing the volume of air in the Coke bottle by half raises the pitch an octave. The note A is defined as 440 cycles per second. So the other octaves of A occur at 220, 110, 55, 27.5 and also at 880, 1760 etc. They are all producing different octaves of the note A. The octave is present in all musical systes on earth and is the fundamental building block of all music.

If you shorten a string that by 1/3 the length you get another note that is not the octave, generally called a musical "fifth", and an interval Westerners know as do-re-mi-fa-SOL-- the 5th scale of the do-re-mi "major scale." This is the next most important building block, and I believe it also appears in all music. When this note occurs in nature, acoustics people call it a Pythagorean interval, because it is generated from the harmonic series of overtones associated with the integers 2 and 3 that were so beloved by Pthagoras and the ancient Greeks. All vibrating objects emit a series of overtones, generally fainter than the "fundamental" and the way those overtones are present or not present is what makes a G note on a mandolin sound different than one on a guitar. What seems to be a simple musical note is almost never that simple, unless it is a tuning fork or an electronically generated sine wave. Most people have some idea of what this is about, and ancient Greeks got very excited and even religious about the relationship between integers and music.

However, things get messy really fast. If you have a string tuned to a C and then shorten it by 1/3 it makes what we call a G note, a 5th above. If you then make another note a 5th above that it is a D you can then make an A and an E (called a "circle of fifths"), and you can generate a whole series of notes this way. Trouble is, any series of numbers generated by the integer 3 will never yield a note that is commensurate with the powers of 2 that generate the octaves. 2 and 3 just are not ever multiples of each other. So if you started with an A at 440 cycles, and started making a series of 5ths, you would never ever land on an octave multiple of 440. What does this mean? That a musical scale based on pure Pythagorean 5ths spirals off into oblivion without ever returning to its starting point.

It turns out that the human ear really likes Pythagorean intervals and they sound "sweet" to us. If you bore holes in a flute using the Pythagorean math, melodies sound good. But if you start trying to form chords, things start to sound sour. Over the centures, various "tempering" systems have evolved, including "just" and "meantone" tempering, which allow certain compromises between these opposing forces. One of JS Bach's most important contributions to music was to celebrate a new system of tempering called "equal" or "well-tempered" in which these little errors were equally divided over the 12 notes in the Western scale. Bach wrote many works for the "well-tempered clavier" which was a way of tuning the piano. He wrote music that changed keys repeatedly and constantly and never sounded greatly out of tune like such things would do if played on an untempered system, and his endorsement and celebration of ths system signalled the beginning of the modern era of musical tuning. "Early Music" groups actually make a point to tune their instruments to differently tempered systems when playing music that was written during the pre-well-tempered era. They feel that the composers chose their notes partly because of the subtle nuances of the tempering, and that playing that music on well-tempered pianos does not sound the way it should.

In a well-tempered system, all notes are "equally and slightly" out of tune from their "natural" form. The octave ends up being divided into 12 equal pieces that are in the ratio to each other of the 12th root of two! So much for the integer beauty of the ancient Greeks, and welcome to listening to irrational numbers.

So how does this relate to the struggle to tune a guitar? Because it is actually not natural to hear well-tempered intervals. Our innate inclination when tuning notes to each other the way we often do on a guitar or a fiddle is to play them together and see if they sound "in tune." Well the adjacent strings on a guitar are generally a musical 4th apart, and almost no one can hear that interval accurately. Octaves and unisons we hear best, and quite less well the fifth, and after that almost no one can be trusted. So if a beginner tunes the open strings by ear, or tunes a G chord of a guitar till it sounds good, they will unwittingly tune the B string (the music 3rd of the chord) to a Pythagorean interval, and might even do that with the D or 5ths. Then when they play an E chord, the B string sounds very wrong. (Try it!) We actually have to become "civilized" and "learn" to hear and accept the tempered notes. Studies have shown that singers and violin players, who can adjust their pitches in ways that guitar or piano players cannot, will usually choose to "sweeten" any intervals they can, so the civilizing process and acceptance of the tempering is only on the surface, and our inner primitive selves still yearn to hear those integers, even among trained and disciplined musicians who are supposedly fully acclimated to the well-tempered world.

And as we start to play music, and learn to hear differences between notes, as our ability to listen improves, it is occuring alongside this other tempering thing, and we get confused. At the beginning, we might just play away and not give it a thought. As we start to realize we are out of tune, we try to use our newly acquired sense of "in tuneness" and it lets us down because our natural tendencies to tune to untempered notes clash with the rigid metal frets that are chopping these notes up into 12th roots of two every time we press then down to the fingerboard of our guitar. We simultaneously have to learn to hear and then shun our instincts and embrace slightly out of tune notes. It is very hard, and all musicians go through it. The only thing that makes it easier are electronic tuners that are almost universal now, and they provide a standard and a benchmark that gets the job done without anyone having to know how messy everything really is.

Like wild horses who are tamed, those of us who wish to embrace the Western musical world, with its scales, keys & chords, must also as a necessary consequence abandon our primitive desires to hear perfect 5ths and perfect 3rds. (The difference between a tempered and an untempered 5th is small, about 1/50 of a fret, but the difference between a tempered and untempered 3rd is closer to 1/5 of a fret, and even beginners can hear that. It becomes much thornier when you tune a guitar to an open chord. It is almost impossible not to tune the 3rd of the chord to a sweet notes, yet if you dont, the fretted notes sound sour. On a 5-string banjo, an instrument that is usually tuned to a G chord, manufacturers have started "compensating" the nut and often the saddle of the instrument, usually making the 2nd string a little longer than the others to help solve this. I know of a well-known bluegrass band who basically broke up because the guitar player and the dobro player (who tune their instruments G-B-D-G-B-D which is 1-3-5-1-3-5) could not agree on how the dobro player should tune his B strings. He wanted them flatted a little, and the guitar player wanted a more "equal"tempered" tuning, and they fought and eventually it got ugly.

Add to this one other thorny issue and I'll let you get away, even though there are some other strange and difficult concepts and phenomena in the world of tuning that I will spare you for now.

When you play any note, it generates a "harmonic series" on integers overtones. Notes just do that. Lower pitches notes make more audible overtones that higher ones, and when you play a low note on an instrument with a wide pitch range like a piano, its natural overtones clash with the tempered notes you are trying to use in the higher registers. The guitar has just enough pitch range for this to become a problem, and what piano tuners call "octave stretching" is an artistic decision, based on the tastes of the person tuning, to change things a little to make them sound more musical. The more resonant and rich an instrument is, the more pronounced the overtones will be, and the more this accentuates the octave stretching issue.

It's actually a pretty good argument for playing a lousy old guitar with old dead clunky strings (few overtones) in an open tuning with a slide, like the old bluesmen did, since no acoustician or oscilloscope on earth was going to get involved in that pure and funky little world of guitar tuning and 3rds to chords that bend and slide all over the place.