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Why Guitars Are Hard To Tune

tuning fork...How do we tune our guitars, why they are so hard to keep in tune, and what does it mean to be in tune?

I went to see the acoustic super-group Goat Rodeo, consisting of Edgar Meyer (bass & piano), Stuart Duncan (fiddle), Chris Thile (mandolin, fiddle & guitar) and Yo Yo Ma (cello). They are all astounding musicians, and their repertoire for this group is very complex instrumental “chamber music,” mostly things they created for their group. When Thile played the guitar on one song, it was quite out of tune. It was the only thing in the entire evening that wasn’t in tune, and it jumped out and got me thinking about why the guitar always seems to be the instrument that's least in tune. Thile seems to be a reincarnation of Mozart, so I couldn’t blame him for not knowing better. I also know there was nothing wrong with the guitar, since they made a point to tell us that it was an Olson guitar (one of the most respected modern luthiers) that was borrowed from James Taylor.

All of us have likely seen a guitar player wrestling with being out of tune, though I suspect that few of us know the surprising number of non-obvious reasons why this happens. Tuning is actually a very complex subject, and not just a matter of the musician being incompetent, drunk, careless or tired. Since I have never seen a thorough and detailed discussion of why the subject is so complicated, I’m going to offer one here, and I apologize up front if it's more than you wanted to know.

Now that electronic tuners are so inexpensive and accurate, it can be argued that there is no longer any need for anyone to learn anything about how to get in tune, or to even bother to understand the surprising complexity that underlies the seemingly routine act of tuning. I started playing guitar before there were electronic tuners, and the first thing to learn was how to get in tune. 50 years later I'm still learning how.

Tuning is one of those disciplines where science and art meet head-on, and neither is supreme. Only a few people are trusted to tune the pianos of the great pianists, and though electronic equipment has drastically improved, the methods of tuning used at the highest levels of music require human judgement and decisions to be made that are beyond the realm of just measurement and science. You could tune a piano to a stroboscope- but few good pianists would enjoy playing it. The whole idea of what it means to be “in tune” is foggier and more imprecise than bystanders or beginners might imagine. Varying cultures of the world also have different ideas of what it means to be in tune, and the history of musical pitch is itself an extremely interesting and convoluted subject. Personal taste is even a factor. A certain old bluesman’s guitar always sounds out of tune to me on his recordings, but he reportedly liked it that way and would “fix” it when someone tried to “tune” it when he wasn’t looking. Maybe if we understand what underlies the seemingly simple act of tuning we might feel better or blame themselves less next time we are struggling to get in tune.

One set of issues in guitar tuning involve the physical things like the strings, the instrument and the environment. A second set of concerns involve human issues of hearing and judgement, and there is a third and very mysterious set of issues that involve the music itself. I have never seen a guitar instruction resource anywhere that even started to go down this slippery slope, and they all just say "tune your guitar" as if it was a simple and straightforward thing. It can be the simple act it seems to be, though bubbling just below the surface are a startling number of mysterious issues. Not only is the tuning of musical instruments scientifically complex, but the social and political questions appear immediately about who is in charge of tuning and who notices or fixes it if something is determined to be out of tune. There aren’t any “tuning police,” and I have told students and audiences for years that the worse ear you have, the more music you can enjoy.

This will take a while, so settle into a comfortable chair...


There are two types of being "in tune:"

• The strings of a guitar can be in "relative tune" so that the notes generated on the various strings are consonant with each other

• Whether or not those notes match up to the "absolute tuning" standard that civilization has decreed is what we should tune to is another matter.

If you are playing alone, it doesn't matter that much if your A string is not tuned to 110 hertz exactly as long as you are in relative tune to yourself. If you are in a band, it does matter. Instruments and strings are manufactured for the tension of standard pitch, and tuning to a very different pitch can cause strings or instruments to underperform or to break. If you are singing with your guitar, then your vocal range becomes part of the situation, and singing songs by other artists might cause you to keep your guitar tuned to standard pitch or perhaps not to. For about 30 years I always slack-tuned my guitar down 1 fret to Eb because I liked the extra resonance, I liked singing in Eb more than in E, and I always performed solo so it didn't matter if I was playing in weird keys like Ab or C#. It did make it hard to jam along with other people, since I had to retune or put a capo on the first fret, which is disorienting.

“STANDARD” PITCH
Electronic tuners may tell you that a perfect A is 440 hz. (cycles per second) but they do not tell you that number was essentially invented out of thin air at the International Standards Association meeting in London in 1939 after a lot of bickering and compromise. The system based on 440A is usually called “Standard Pitch” or “Concert Pitch” and it evolved to solve real problems, and is a triumph of civilization over barbarism. The choice of 440 cycles does not seem to be connected with any scientific, religious or other phenomenon, and except for the fact that other people use it, there is no real reason why you have to tune to standard pitch if you are not performing with anyone else. Over the centuries, from town to town and country to country, the pitches of instruments have varied all over the place, with 440 A ranging from over 500 and to a low of below 400. This especially challenged traveling singers, who had to sing along with whatever pipe organs, pianos and horns they encountered.

For most of the human time on earth, there was no way to establish pitch, though new research and theories at megalithic sites like Stonehenge indicate that the stones they used were an unusual kind that were musically resonant. They may have been tuned to pitches and struck like massive stone bells. Do a web search for something like “Stonehenge musical stones” and you’ll find all sorts of tantalizing information, ideas and theories. Scientists now think that the best cave paintings are in the locations in the caves where the acoustics are the best, which makes total sense. Of course primitive people paid very close attention to sound. The Aurignacian (and possibly Neanderthal) flutes they dug up have holes drilled in very precise places, and show that Paleolithic humans knew about music very long ago.

In 1834 scientists first developed the ability to measure musical pitches and assign numerical frequencies to them. The tuning fork was invented earlier, by Englishman John Shore in 1711. Its two tines cleverly cancel out overtones and generate a pure pitch. Tuning forks were hard to obtain and very valuable, and kept like precious jewelry by their owners. Museums have a number of tuning forks that belonged to celebrities of the past, and it is interesting to measure what they are calibrated to. Mozart’s tuning fork reportedly was A=421.6 cycles, and Handel’s quite close at 422.5.

The first attempt to standardize pitch was in 1859 when the French government decreed that a musical A be 435 cycles at 15 degrees centigrade (59 Fahrenheit), reportedly to solve problems with military bands. In 1889 conventioneers decided on 435.4 cycles for A and then changed their minds and kicked it up to 440 hz. several decades years later, where it has remained ever since. Some “early music” groups tune to A=415 cycles, since apparently a lot of music was written centuries ago for this pitch range. (https://www.piano-tuners.org/history/pitch.html has more than you’ll ever need to know about the history of pitch.)

REFERENCE NOTES

Violin players still typically tune one string to a reference note, and then the players use their ears to tune the other 3 strings to that one. There are a number of systems of guitar tuning that players used to always learn, that are strategies of how to tune 5 strings to a reference note.

Tuning forks

tuning fork

Tuning forks were a huge breakthrough when they were invented, and they marked the beginning of establishing pitch standards. Most of them made currently generate the note A= 440 cycles, though I used to have a larger guitar fork that gave the pitch for the high E string of the guitar. They work best when you place the ball end on the bridge of your instrument, though I always liked to hold them in my teeth, so I had both hands free to tune. Get them ringing before you put them in your teeth to save on dental bills.

 

Pitch pipes

pitch pipe

Guitars were commonly sold with a "pitch pipe" years ago, that sounded a lot like a goose call to me, but they were a little better than just having a tuning fork to generate one note. I can't find my old one that had 6 little pipes, one for each of the guitar strings.They helped train your ear as you compared notes, and they at least could get you close to where you needed to be. If you were wildly out of tune they were often more helpful than an electronic tuner, which can sometimes send you off toward notes that are 12 frets too high or low from where you want to be.

Electronic tuners

Most guitar players now use an electronic tuner or smartphone app for tuning. I recommend getting a "chromatic tuner" which is capable of tuning to any note. Cheaper tuners and apps that are sometimes called "guitar tuners" just help you tune the 6 open strings, and don't help much if you are in a non-standard tuning, or using a capo. Most tuners are chromatic now, but not all. Many tuners just show a green light for in tune and a red light for out of tune, though more commonly now you'll also find a or yellow light for "almost there." We often need more information than that. Learn to observe the songs or situations where the music sounds in or out of tune, use the tuner to measure what your artistic self likes or dislikes so you can perhaps re-create it whenever you want to by using the tuner as a measuring tool. If you consistently don’t like what your tuner tells you, you might try a different brand. I like the TU-12 tuner by Boss (pic). I’ve used it to tune on most of my recordings for over 35 years, and I don’t ever listen back to the recordings now and think they are out of tune.

Boss tunerpitch pipebuilt in tunerpitch pipe"Snark" tuner

Problems with electronic tuners
You might as well know that you don’t always get perfect or consistent results even when you tune an instrument with an electronic tuner. All electronic tuners are not identical, and one brand of tuner might say you are in tune and another might disagree slightly. This may be a matter of how “fussy” and precise the tuner is, and one tuner may give something a passing grade and another might flunk it. It may also have to do with how the tuner's microphone "hears" (or doesn't hear) or its algorithms process the various overtones of the string.

I prefer tuners that have a needle that shows you what is going on, and do not just have the colored lights. With a particular instrument, two tuners might possibly both give readings that a good musician’s ear would disagree slightly with. Some brands of tuners have indicator needles or lights that bounce around a lot, get confused by the overtones from bass strings, or even change their mind as a note decays, leaving you to do some guessing. We learn how to use our tuners, and not just do everything they say. Sometimes we learn that it can be best to tune an open string, and at other times we might get better results using a fretted pitch or a harmonic. Even if you don't have a good ear, you can use an electronic tuner to observe and measure what is going, and find your way, though you will need a good quality chromatic tuner to do it.

Phone apps are convenient, and you're likely to have your tuner with you, but you can't use them effectively on stage, they only work by listening with the microphone, and are pretty valuable to be using constantly at a music festival, party or bonfire. A $20 electronic tuner might make more sense to use than a $700 phone. Many of us musicians like the Cleartone app that costs around $5. It has a sensitivity preference and seems to work better on "less sensitive" so the "needle" doesn't bounce around as much, though I still prefer the Boss TU-12.

Many guitars now have tuners built into them (pic) , and many of those are now pretty good, though they run off a 9 volt battery that powers the built-in guitar pickup system and that can be dead when you need to get in tune. The best ones not only give accurate readings, but also turn off after a minute or so and stop using up the battery when you stop using them. The so-called "snark" tuners (pic) seem to be very popular, and they clip onto the headstock, so you don't need a pickup built into your guitar or a cord to plug into them, and they are unaffected by wind noise or conversation around you. Tuners that rely on a microphone to listen to the notes need quiet to work right. I have a very nice tuner built into a Planet Waves capo. It's a good capo and a good tuner, though it is a bit large, and expensive.

Other sources

• If there is a piano nearby, chances are it is at least close to proper pitch.

• You can of course tune to another guitar. A great trick I learned long ago is to have the other player play minor chords for you to tune to. Instead of the other player sounding their E string for you to match, have them strum an E minor chord. For some reason it works much better than if they play an E major chord or just the single string note. The have them play Am, Gm, Dm and Bm chords so you can tune the other 4 strings.

• We have a foghorn here on the coast of Maine that is a lovely A, but not on sunny days.

• My old Chevy van had a horn than sounded a near-perfect A .

• Dial tone on a phone is a perfect F, which is a little hard to use since no common stringed instruments have an F string.

PHYSICAL PROBLEMS WTH TUNING

STRINGS
My best guess is that the strings on Thile's guitar had been recently changed and had stretched since they were tuned. Instrument strings are also not perfect things, and though most new strings behave properly once they have stretched a little, there is always a possibility that a string might be defective or damaged. A string can become faulty or "sour" and fail to produce correct pitches, even though there may be nothing visibly wrong with it. Old strings are generally done stretching, and the problems they cause may give the instrument poor tone, or certain overtones may be not in tune, but I doubt that old strings are what caused Thile’s problems. If you find yourself unable to get your instrument in tune, replacing strings is the first thing to do before you look for deeper causes. Strings may also be improperly attached at either end, which can allow them to slip unpredictably.

Strings that have low tension on them can sound permanently unmusical and out of tune. This is a common issue with smaller-scale children’s instruments, since in order to tune the shorter strings to standard pitch they need to have significantly less tension, and your natural inclination is to put thinner strings on an instrument for a child. Tuning smaller guitars 2 or 3 frets sharp or using thicker strings can solve this problem, but in turn cause other problems. (The guitar is no longer tuned to standard pitch, and the thicker or tighter strings are harder to press down, which is not ideal for children. I have written extensively on children's guitar issues.)

THE INSTRUMENT
It is possible for an instrument to not be capable of producing correct musical pitches over its fingerboard. The positions of the nut, saddle and frets collectively determine the intonation. Luthiers develop a formula for where they place the parts of the fingerboard that establish proper intonation, and manufacturers generally work out these tolerances to the point that you needn’t worry. Modern guitars are generally made more precisely than instruments of the past, and computer and laser-controlled cutters now often put the parts in place to an accuracy of ten-thousandths of an inch. Even inexpensive instruments now generally play in pretty good tune, and are often better than relatively expensive instruments of 50 or more years ago.

Since errors are proportionately larger, shorter-scale instruments such as guitars for children should be made more precisely than full-size guitars, but usually are not. Don’t expect a $99 children’s guitar to play in perfect tune, but don't be surprised if it does.

Guitars can have or develop improper intonation, which means that they do not produce correct pitches over the fretboard. Open strings might be in tune but a fretted string might not be. A particular string may be “off,” or perhaps notes higher up the fingerboard may be progressively out of tune.

A common problem with guitars is caused by string tension pulling the neck slightly upward. This causes the strings to sit higher above the fingerboard than they should. In my experience the string height (known as the “action”) of my acoustic guitars goes up in the summer and down in the winter, presumably due mostly to humidity. If the action is too high, it can cause the strings to stretch a little (go sharp) as they are pressed down, especially on the higher frets where they are highest above the fingerboard. The thicker gauge strings you use, the more stretching will occur in this situation. Most guitars made in the last 40 years have a threaded “truss rod” inside the neck that can be adjusted to increase or decrease the amount of “pulling” that the neck does when the strings are tightened. Optimizing this is part of what is called “setting up” a guitar.

If you put on different gauge strings than the instrument was designed for, it can slightly aggravate tuning issues. The ends of the strings rest in grooves cut in the saddle and the nut, and thinner strings might sit too deeply in the nut grooves, and thicker ones slightly higher up above the fretboard. If the slots in the nut are too narrow or the strings thicker than normal, they can also pinch a string and cause it to stick and perhaps jump up or down unpredictably when you operate the tuning pegs. A tiny amount of dry lubricant like graphite powder can remedy this. It’s a simple but delicate job to widen the notch cut in the nut, though without the right tools and knowledge you can cause other problems.

A strap attached to the headstock can pull on the neck and put an instrument out of tune. Most professionals attach both ends of the strap to the body and not the neck or headstock like Woody Guthrie did.

The gears and mechanisms of the tuning machines can also be flawed, loose or worn. They might slip a little at times and cause chronic random out-of-tuneness. Tighten all the screws and look for obvious problems. It's not a big deal to replace a tuning machine, though it hurts the resale value of vinatge guitars if they don't have original parts.

Frets can be worn down by a lot of use. This isn't uncommon, and can cause a string to be stopped at an imperfect place, though these errors are quite small. Fret wear usually just causes strings to buzz or rattle a little.

The neck angle can be wrong. This can easily be caused by string tension, and can cause various intonation problems. It may mean that to prevent rattling or buzzing of the strings, the action has to be higher than it optimally should be. This causes sharping when the strings are pressed down, since they stretch a little, especially toward the middle of the string where it is highest above the fretboard. Correcting the neck angle of a guitar is called a "neck reset" and can be a quite expensive repair on some brands and models. A number of leading brands of guitar (pioneered by Taylor Guitars) make the necks easy to remove and adjust to solve this chronic guitar problem.

ENVIRONMENT
Changes in humidity or temperature such as heating or cooling systems in a building, or sun and clouds alternating outdoors, can make it hard to keep a stringed instrument in tune, as can moving the instrument in and out of cars and buildings that have different temperatures and humidities. They are the other likely culprit in putting Chris Thile’s guitar out of tune. It is likely that his guitar went out of tune because it had a larger quantity of wood than the mandolin or fiddle, making it more susceptible to environmental changes than a smaller mandolin or violin. That doesn’t explain why Yo Yo Ma’s cello sounded fine, but with a fretless instrument a good musician can constantly make pitch corrections that a guitarist can't.

Changes in the environment can put you out of tune. Your instrument might sit for weeks at home where it stabilizes, having absorbed a certain amount of moisture. When you take it outside, in a car, and in and out of a heated or cooled building, it can take quite some time to settle down. When sunlight, stage lighting, air currents and various thermal and humidity changes impact an instrument, the hardwood, softwood, bone, metal, seashell and plastic parts of the instrument, tuners and strings themselves will expand, contract and absorb moisture differently, causing all manner of tuning problems. When I play a concert, I try to let my instruments sit as long as possible in the place where they are going to be played before I tune them. Often I will get to a gig, and notice that my autoharp (with 36 strings) is out of tune. If I tune it right away, it will almost certainly go out of tune again by showtime, and I am usually better off if I wait until right before show time to tune it, after it has adjusted somewhat. I prefer not to tune in the backstage or "green room" because it might have a different climate than the stage.

Playing in sunlight or in front of a heat source like a fire can wreak havoc with tuning. The front of the instrument (or even of the strings) may be in the sun or heat with the back in the shade, or even worse, there may be intermittent lighting or heating that causes non-stop fluctuations, such as what happens as clouds pass by. If I tune my autoharp for an outdoor gig and then the sun falls directly on it an hour later toward the end of the show, I’m in trouble, and I even have to plan for the sunlight conditions for the near future. Hot and wet environments can cause wood to swell and expand, while cool and dry environments cause wood to shrink. Because the different materials that make up our instruments and strings respond differently to environmental factors, the results can be unpredictable, and it is not a simple matter of knowing that a particular thing happens on a particular kind of weather day.

Theaters sometimes are cold when the audience arrives, since each audience member generates about 100 watts of heat. People also constantly exhale moisture, so a concert room may get significantly warmer and moister over the course of a 2 or 3-hour concert. Again this is not a recipe for perfect tuning.

MOVING AIR
Try to play guitar and sing in front of a window fan that's running on high speed. It’s awful, and the sound is chopped up and sounds like a phase shifter or tremolo pedal. The same thing happens to a smaller degree when even slight air movements from heating and cooling systems are present. Performing outdoors on a windy day can be very problematic as the sound is blown around, and I have had awful experiences trying to hear properly when even a small fan is blowing on me. It’s quite possible that forced-air heating systems that circulate air around a room can not only put your instrument out of tune, but also slightly interfere with your hearing. Some states even have laws requiring a number of cubic feet per minute of air to be circulated through a concert hall, and this can help or hinder performers who are trying to stay in tune.

CAPOS
Capos also usually throw guitars out of tune a little, especially by sharping the thicker strings. Unnecessarily over-tightening a capo can push you further out of tune, and possibly prevent you from making smooth tuning adjustments once it is in place. I use a lot of partial capos, and they wreak havoc on a fingerboard, since you are mixing open strings together with strings clamped by the capo. Capo first, then tune.

60-CYCLE HUM
Our electric grid uses alternating current, that reverses direction 60 times a second. (This was an idea pioneered by Nikolai Tesla, in opposition to Thomas Edison, who favored direct current.) Wires carrying the weaker signals from instruments or microphones need to be shielded to prevent interference from much-stronger electric current that is passing through nearby wires and electronic devices. A common symptom of this interference is a “60-cycle hum” that can permeate your sound system when you are performing and make it very hard for you to tune by ear. The faint hum of electrical motors and equipment can make musicians crazy, especially when they are trying to tune an electric guitar near an ice machine with a pinball machine and a neon sign nearby.

60 cycles is not a note in the modern pitch system (B is technically 61.7354 and Bb is 58.2705) and a 55 cycle (which is a perfect A) electrical grid would cause thousands of musicians to not drink too much at their gigs to drown out the awful clashing of music and electrical current. I have been told that parts of Tokyo were once 55 cycles, and it appears that worldwide now only on the island of Guam is the electric current still running at 55 cycles, so musicians there can tune to the ice machines and neon signs.

If your guitar pickup is not working right or shielded well, or if you are in an electrically “hostile” environment, surrounded by neon or fluorescent lights, it is also not uncommon to discover a 60 cycle hum mixed with the signal coming out of your instrument cable. This will compromise your situation if you plug into an electronic tuner and may prevent you from getting an accurate reading from your tuner. If you use a battery-powered clip-on style tuner on your instrument headstock you should be OK, since it works on vibrations in the instrument’s body and not on an electrical signal in a wire. Instrument pickups that rely on magnets are generally more susceptible to interference problems than the types that use piezo-electric materials.

THE MUSIC SYSTEM ITSELF IS A LITTLE "OUT OF TUNE"

The actual physics of tuning is a surprisingly convoluted subject, since a bystander might just think tuning a few strings to specified pitches is a routine and boring thing. It’s worth knowing about the subtler points involved, largely so you won’t always blame yourself or your instruments when you can’t seem to get in tune. If you are going to be a musician you should know about them, and they are not part of any music curriculum I am aware of. Buckle your seatbelt.

The whole idea of what it means to be "in tune" is much foggier and more imprecise than bystanders might imagine. Measuring and standardizing musical pitch are things we take for granted, as if they are set in stone, and the more you learn about the subject the less certain you may feel.

OVERTONES
All vibrating objects emit a series of overtones, generally fainter to our ears than the "fundamental" and the way those overtones are present or not present is what makes various instruments sound different even though they may be playing the same pitch. 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.

If you vibrate a string or blow across a Coke bottle and produce almost any musical note on any instrument, nature automatically provides the Pythagorean “harmonic series” of overtones, consisting of other notes with frequencies in integer multiples of 2x, 3x, 4x etc. that are mixed together with the so-called “fundamental” tone. Many of the overtones are very consonant with the fundamental tone. Many people have some idea that this has to do with those mysterious things that music and math have in common. The reason that the same pitched note sounds different when played on different instruments depends largely on how much of the various overtones are present in each note, though the “attack” of how the note is struck or created is also a vital component in what gives each instrument its signature sound.

When “integer notes” occur in nature, acoustics people refer to them as Pythagorean pitches, because they are generated from the harmonic series of overtones so beloved by Pythagoras and other ancient Greeks. It’s quite startling how much the people of antiquity seemed to understand these issues, but they were also predicting eclipses and accurately calculating the diameter of the Earth in quite ancient times. Some old cultures got very excited and even religious about the relationship between integers and music.

 
THE OCTAVE
The first overtone is the "octave,” which essentially gives us a way to listen to the integer 2. Shorten a vibrating string by half and it raises the pitch an octave; doubling its length lowers it one octave. Each time you change the vibrating object by a factor of 2, it changes another octave. Reducing the volume of air in a Coke bottle by half when you blow across the opening raises the pitch an octave, and doubling the air volume lowers it an octave. Since A has been defined as 440 cycles per second, 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 what we call the musical note A. The octave is present in all musical systems on earth and is the fundamental building block of all music. A guitar spans about 4 octaves in pitch, and a piano close to 8.


THE FIFTH
If you shorten a string by 1/3 its length you get the 2nd overtone, which is a new note that is not the octave. It is generally called a musical "fifth", an interval Westerners know as do-re-mi-fa-SOL-- the 5th scale of the do-re-mi "major scale." (Shortening a string to 1/3 actually generates a pitch that is an octave plus a fifth higher...) This is the next most important building block, and I believe it also appears in music of all cultures. When this note occurs in nature, it is a Pythagorean interval, because it is embedded in the note you hear coming from the instrument, generated from the harmonic series of overtones. Shortening a string to 1/4 of its length, 1/5 or 1/6 all make harmonious overtones. 1/7 is the first dissonant overtone, and this has contributed to the eternally shadowy reputation of the number 7. The next dissonant overtones are 11 and 13, which also have their own reputations.

TEMPERING
Unfortunately, things get messy really fast when you try to build a musical system with just integers and fractions. 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, and 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. The bad news is that 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 keep getting new notes that were not octaves (multiples of 2) from your starting point. You’d get notes generated by multiples of 3 and you would never ever land on A again, an octave (power of 2) multiple of 440.

What does this mean? It means that a musical scale based on pure Pythagorean 5ths spirals off into oblivion without ever returning to its starting point, and you can’t build much of a consistent music landscape with only Pythagorean integer-generated pitches. Many things will sound great, but some things will sound really sour. The ancient Greeks even knew this, and developed their own tempering systems thousands of years ago, to adjust the sacred integer-based musical pitches to solve problems that arise and make the music work better.

The notes we tune to now are not those created by the mystical integers that so intrigued the ancient Greeks. Temperings are systems of tuning that are intended to minimize the errors inherent in musical pitches. Guitar students had to learn to tune before there were cheap electronic tuners everywhere, and some techniques were developed to help us get the instrument in tune by tuning one string to a tuning fork and then tuning the other 5 to it with various recipes. We have to learn to use a “tempered” musical system that is not based on integers, and repress our primal selves who seem to want those mystical Pythagorean pitches.

The human ear apparently likes Pythagorean intervals, and they sound "sweet" to us. If you bore holes in a flute using the Pythagorean math, some but not all melodies sound good. But if you start trying to form chords or play in different keys, things start to sound out of tune, and so-called "wolf tones" appear. Over the centuries, various "tempering" systems have evolved, including "just" and "meantone" tempering, which allow various compromises between these opposing forces.

One of J.S. Bach's most important contributions to music was to celebrate and endorse a new system of tempering called "well-tempered" in which these little errors were better divided over the 12 notes in the Western scale. Bach wrote many works for the "well-tempered clavier,” which was a new way of tuning the piano. He wrote music that changed keys repeatedly and never sounded greatly out of tune, which such music would do if played on an untempered system. His enthusiastic adopting of this system signaled 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 music composed before well-tempering on well-tempered pianos does not sound the way it should.

In an equal-tempered system, all notes are "equally and slightly" out of tune from their "natural" form. The octave is 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. (Be careful reading explanations of the differences between well-tempering and equal tempering since they read like physics books and can overwhelm you with their complexity. It's probably more than any of us need to know)

What nobody ever tells troubadours is that the frets on the guitar are placed according to irrational numbers, not integers. The ratio of the length of each guitar fret to the previous one is actually the very irrational 12th root of 2, though many luthiers develop and adopt their own systems of fret and bridge placement that are not purely mathematical and may deviate slightly from this. The confusing but interesting Buzz Feiten Tuning System that some people swear by is a recent attempt to address the fundamental out-of-tune-ness of guitars by slightly altering the placements of tuning, nut, saddle and even fret shape.

Making a guitar with tempered frets is also a possibility, such as this one here (http://www.truetemperament.com/) that looks like a bad photograph but is actually somebody's solution to the guitar tuning problem. This is essentially what violin & cello players are doing all the time on their fretless fingerboards.


true tempered fets

Seeing a little more depth in the struggle to tune a guitar?

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" with each other. The adjacent strings on a guitar are generally a musical 4th apart, and unfortunately almost no one can hear that interval accurately. Octaves and unisons we hear best, less well but still reliably the fifth, which is what violin and cello players do. Almost no one can be trusted to properly tune two strings to each other by ear if they are not an octave or a fifth apart in pitch.

Most guitarists know that guitars are often out of tune, and play a “test” chord when they first pick up a guitar. The choice of that chord can make a difference. If you are the type who tests with a G chord, then if the guitar was tuned by someone who plays a D or an E to test the guitar, there will be disagreements. Some people even think that if you are a player with a good ear who likes the A chord, you’ll always be a little unhappy unless you alter your guitar set-up. (My personal guess is that Buzz Feiten likes the A chord.)

So if a beginner tunes the open guitar strings by ear, or tunes a G chord of a guitar till it sounds good, they will likely tune the B string (the music 3rd of the chord) to a Pythagorean interval. Then when they play an E chord, the B string will sound very wrong. (Try it!) If you must tune by ear, try tuning the 2nd string so it sounds good in an A or D chord, and then it will be in-between the pitches you like when you tune to either a G or an E chord. I'm even thinking here that it's possible that the brands of guitars that have come to be associated with certain styles of music may have something to do with the intonation preferences of the manuacturers that ended up slightly favoring certain musical keys. The fact that so many young musicians seem to be writing songs in G makes me wonder if there is a trend in guitar-making involved.

Imperfect is the new perfect.

We actually have to become “civilized” and learn to hear and accept the tempered notes. The “correct” thing to do is to average out the error, and make it so that all pitches “equally and slightly” out of tune. The truth is, our whole musical system is designed to be a little out of tune, and electronic tuners are manufactured to give us those 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. This is true even among trained and disciplined musicians who are supposedly fully acclimated to the well-tempered world. If you think about it, all the instruments in an orchestra are capable of adjusting the pitch so that the musicians can temper their harmony to sound right. Pianos and guitars that play fixed pitches are not normal parts of orchestras, and can inject intonation problems into the ensemble when they play with other instruments or each other. (I once spent several hours trying to get my autoharp in tune with a piano. I wish I had filmed it, because I may never try it again.)

As we start to play music and learn to hear differences between notes, as our ability to listen improves, it is occurring alongside this other tempering thing, and we can easily get confused right when we are learning to hear musical pitches better. As beginners, we might just play away and not give it a thought. There are a number of older recordings (I won’t mention any names) I used to enjoy, but now that my ear has improved I am quite aware of instruments or singers being out of tune. Maybe my fond memories of campfire guitar are rooted in the fact that I had a less-critical ear when I was a teenager. Now I dread the thought of trying to get a guitar to stay in tune at a campfire.

As we start to hear better, and realize we are out of tune, our newly acquired sense of "in tuneness" 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 irrational 12th roots of two when we press then down to the fingerboard. We simultaneously have to learn to hear, and then to 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 us having to know or deal with how messy everything really is. Once your ear is really trained, you will likely start noticing that electronic tuners are not always to be treated as omniscient or totally authoritarian.

Like wild horses who are tamed, those of us who wish to embrace the Western musical world, with its scales, keys & chords, must 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 about 1/7 of a fret. Even beginners can hear that.

When you tune an instrument like a banjo, dulcimer or dobro that is commonly tuned to an open chord, or an autoharp that only plays in 1 or 2 keys, these issues assert themselves strongly. Tune your guitar to an open chord tuning, like a D chord (D-A-D-F#-A-D), and you get more trouble, since your ear REALLY wants to flat the 3rd of the chord (the 3rd string) closer to its Pythagorean resting place, but the frets relentlessly give out their irrational numbers and tempered pitches. Since banjos are usually tuned to an open G chord, the banjo world has recently dealt with this in an interesting way: most 5-string banjos now have a 2nd (B) string (the musical 3rd of the G chord G-D-G-B-D the instrument is usually tuned to) a little bit different length than the other strings. This is done on banjos with a “compensated” saddle and sometimes even a staggered nut that makes the B string a slightly different length than the others.

compensated saddle

In the last 30 years or so, most fretted-instrument saddles have been “compensated,” which means that some of the strings (commonly the 2nd and 3rd strings on guitar- the 2nd string as shown here) are slightly different in length than the others. The places where the strings cross the saddle do not form a straight line. If done correctly, this can make a huge difference in the instrument’s intonation, and may be the largest reason why older guitars sound out of tune compared to modern ones. Guitar saddles are now made thicker than they were 50 years ago for this reason, and a good luthier can fine-tune the length of the strings in ways that can’t be done with a thin saddle. It’s a common alteration often made to older guitars to widen the saddle slot in the bridge (if there is room), and install a wider, compensated saddle.

MORE PROBLEMS WITH OVERTONES
Tuning even gets even another level messier when you consider more deeply the overtones an instrument is producing. This isn’t fantasy, and it causes genuine though subtle problems. Since the natural Pythagorean harmonic overtones of a lower-pitched vibrating string are always there, they may overlap and clash with either higher-pitched open strings or the fretted, untempered pitches produced on the fretboard. Any note generates a harmonic series of integer overtones, but lower-pitched notes are more problematic, since they generate overtones that are easier to hear than those made by higher-pitched strings, and they land in the same audible pitch range as other notes you are playing on the instrument. 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 using in the higher registers.

The guitar has enough pitch range for this to be a real problem. If you tune your guitar down low and plug it in on stage, you aggravate these issues by greatly amplifying the overtones from the bass strings. A surprisingly complex and fuzzy thing that some call “inharmonicity” and piano tuners often call “octave stretching” enters in. The more resonant and rich an instrument is, the more pronounced the overtones will be, and the more this accentuates this octave-stretching issue. The solution involves an artistic decision, based on the tastes of the person who is tuning and the persons who are going to play the instrument, to override the math and electronics, and change things a little to make everything sound more musical. There is a complex world of things like “wide fifths” and “narrow fifths” and “French temperament ordinaire,” which are things piano tuners have developed to reconcile the resonances of their instruments, the physics and realities of mathematics, together with our ears and artistic sensibilities. Bass players who borrow a tuner from a guitar player may face the “octave stretching” problem because the untempered overtones from the bass (whose open strings are tuned to the tempered electronic tuner) can clash slightly with the tempered open-string and Pythagorean overtones from guitar pitches.

Skilled players will sometimes make slight adjustments to their tuning in these situations if they hear something they don't like. Some tuners are designed for bass players, and some tuners have a switch to select guitar or bass to address this issue. The more resonant and rich an instrument is, the more pronounced the overtones will be, and this can accentuate the need for octave stretching. Our ears can sometimes hear the slight discrepancies, but we don’t all hear it the same. Beginners often don’t hear these kinds of things at all, and then as their ears gets better, they may start to notice that things are out of tune. What I do is to spend a long time listening, playing and tuning, and I use a very accurate electronic tuner as a measuring device, not as a rigid guideline. Some of us will use an electronic tuner as a measuring tool only, so we can carefully and repeatedly tune certain things a little “out of tune” in order to sound more “in tune.” Sometimes we’ll do this just for a particular song, tuning or instrument. As an experienced artist you are allowed to override a tuner, and you can use your tuner to purposely tune the B string a couple cents flat for certain songs, for example. This can be true especially if they involve an open tuning or a partial capo. A few great players like Steve Vai and Eddie van Halen have posted comments about tuning, and mention that they sometimes make small adjustments to certain strings and ignore the advice of their electronic tuners, sometimes just for certain songs.

COMBINATION (GHOST) TONES
You may think I have gone off the deep end when I venture into this one, so I'll skim it, and I’ll give you some searchable words so you can do your own internet research, which of course will leave you more confused than when you start. There are words like “resultant tones,” “combination tones,” “multiphonics” and “subjective tones” that will scramble your brain a bit, since they involve auditory phenomena that are both imaginary and real, and might actually be dark demons confusing us when we are innocently trying to tune our guitars so we can sing a song. And there may be days when we hear them better than other days. The sounds themselves are quite interesting, as are the history of when and how people discovered them. Now that we have wave-generating machines, oscilloscopes and all sorts of tools to analyze and generate sounds, we can only marvel at the things people figured out and were mystified by long ago when they had very few tools.

Play any note and it is well-known that unless it is a tuning fork, it automatically generates the "harmonic series" of integer overtones. There are also little-known, hard-to-hear but quite real “sum tones” and “difference tones” that show up when two or more notes are played at the same time, and you can never discount the possibility that they are entering into our tuning considerations. Sum tones are higher-pitched, and are the sum of the frequencies of two notes being played, but the difference tones, the difference of the two frequencies, cause more trouble. They were first discovered a few centuries ago, and show up quite clearly when you play a high, loud double-stop (two notes at once) way up the neck on a violin, or especially when two flutes are playing together in higher registers. You’ll hear the two notes being played, but there is also a much lower note, that is sometimes quite dissonant and often not musically related to the two notes that generate it. I have heard an arrangement of Jingle Bells, where two flutes play strange, seemingly un-melodic notes, with the “ghost tones” eerily sounding the melody of the song. These difference tones don’t actually show up on an oscilloscope, and are an auditory illusion created in the listener's ears and brain. They have nothing to do with us having two ears or other theories people have come up with. They don’t actually exist in the physical world. Yet we hear them loud and clear sometimes, though they do sound like they are being created in our head, because they are.

The real "kicker" of difference tones is illustrated by an experiment that involves what is called the "missing fundamental." Imagine 10 pitch-generating machines that are collectively sounding 10 octaves of an A note all together. This would mean 55hz, 110, 220, 440, 880, 1760 and so on. Supposedy switching off any one of them does not affect the sound, since the others are creating sum and difference tones with each other. I read that all you need is any 3 consecutive octaves sounding and what we humans hear is the same. (In this era of "fake news" it's hard not to be skeptical and to want to hear that with our own ears. Maybe there is a web site that does it for us somewhere.) A telephone cord cannot transmit sounds lower than 300 hz., yet male voices sound fine even when they are pitched below that. Supposedly the low notes on our guitars and even the low string on a violin are "phantom fundamentals" and when we measure the sound with electronic measuring tools we find that a guitar string really does not put much energy into the fundamental, but we hear it as a low note. This is downright creepy, and the more you read about missing fundamentals the creepier it all gets, since it seems to say that much of what we hear is created in our brains.

Here are some links you can explore, so you know I am not making this up. This kind of thing could be interfering with our ability to hear and our ability to tune. I tried to warn you that tuning is complicated, though if you made it this far I do salute your bravery and persistence.

THE POLITICS & PSYCHOLOGY OF TUNING
There are still more issues overshadowing the tuning issue, which involve emotions, psychology and even politics. Any time there are humans involved, human concerns come into play, and science and physics do not rule the roost.

Different cultures of the world have different ideas of what it means to be in tune. The history of musical pitch itself is an extremely interesting and complex subject. Human taste is even a factor. We have emotions, and a host of small but real physical and psychological things affect our abilities to decide on what we think is in tune or not in tune. Players from one part of the world or from a remote rural area may tune differently than those from a different country or an intellectual or urban culture. If you playing strictly primitive, pentatonic music, you might need to make slightly different choices about tuning than someone who is playing a lot of extended jazz chords.

Tuning is political also. If you are in a band or disagree with someone with more authority than you, then politics enter immediately. There may be deep and lasting disagreements that are not just a matter of one person being right and another person wrong. A well-known bluegrass band that I knew personally essentially broke up because the guitar player and the dobro player (who typically 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 (“sweetened” is the word usually used for this) a little, and the guitar player wanted a more “equal-tempered” tuning. They couldn’t agree and their mutual frustration was a factor when they quit playing together. Piano tuners argue among each other endlessly, and there is no widespread agreement of either how to tune a piano, or what methods to use to achieve a desired system of tuning.

US
One of the biggest variables in the whole tuning situation is actually us, the humans. There seem to be yet another set of issues underlying the notion of what it means to be “in tune.” When I first started to play guitar, tuning wasn’t an issue, and I played happily as a 14 year old kid, presumably wildly out of tune but not knowing or caring. I have also have had untold numbers of somewhat mysterious experiences, that I could superstitiously attribute to “good tuning days” or “bad tuning days,” or maybe blame on some hex put on me by a witch doctor. I suspect that my musician friends would agree with me on this one. There are often times when everything sounds awful and out of tune, and I put the guitar down in frustration, thinking the strings are shot or that I need a different guitar. Then I’ll pick it up the next day in the same room, with the same strings, and play happily for hours and never touch the tuning pegs. We may listen to the same recording on different days and feel differently about how “in tune” it sounds, which means that the only possible cause for the discrepancy is us, the gloriously flawed human who might actually have a better ear one day than another. That kind of knowledge is tricky to extract

from a science experiment, since the enemy of all science is the flawed observer.

Our ears are not precise scientific instruments, and our brains that process what our ears tell us do not behave entirely like machines. The term “psycho-acoustics” is often used to describe this shadowy world. Our emotional state, and probably chemical and hormonal levels also affect either our ability to hear or our ability to interpret what we hear, and any discussion of tuning that fails to mention this is being unreasonably shallow. There are days when we feel more religious or more energetic, and possibly there are some days when we have more precise musical ears than others. There is no certainty that our ears behave the same at all times. Our ear canals and sinus cavities are always doing different things as allergens and moist and dry air interact with them, and it is quite possible (and likely) that our whole hearing mechanism is a much less reliable system than we might at first imagine. We hear differently when we are tired than when rested. When I work in the recording studio, I try to not work for more than about 4 hours, and other colleagues of mine, both musicians and sound engineers have agreed that our “ears get tired.” Don’t count on those dramatic overnight marathons on the studio, because you can make big mistakes in listening or tuning if you’ve done it all day long.

When we compare two pitches, we tend to hear the lower note as being correct, and want to always adjust the higher-pitched of two notes. If it is the lower of the 2 notes that is incorrect, it’s harder to spot. This is why we usually tune starting at the bass end, and why when a folksinger puts on a capo, that pushes the bass string a little sharp, which can easily lead to the error of tuning higher-pitched strings to the now incorrect lower strings. Musicians jamming at a party or festival who don’t have electronic tuners tend to drift upward in pitch over time, and I think this is the explanation.

The time delay between two notes we are comparing is vital also. If they are simultaneous it’s hard to compare them, and if there is too much time between them it’s also hard in a different way. We need to learn for ourselves how to play the lower of the two notes, leave a short pause then play the upper note, then mentally vote on what to do to adjust the 2nd note to match the first. If you’ve ever listened to a good musician tuning, this is what they usually do, because it best suits the way our ears work and don’t work.

So what do you do with this knowledge?

I think the answer is to gain as much experience as you can, be open-minded, always be as careful as you can, and make sure you use an electronic tuner or phone app that is accurate to within “one cent,” which means 1/100th of a fret.

The fundamental out-of-tuneness of guitars is actually a pretty good argument for playing a lousy 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 is going to call the shots in that pure and funky little world of guitar tuning where 3rds and 7ths of chords bend and slide all over the place, and the guitar and vocal notes swoop around.

If you made it this far, reward yourself and go play your guitar happily. Do your best to get in tune, and maybe even try not to think too much about all the "dark knowledge" you've read here. Go play your guitar happily.


This is another posting where I'm trying to raise issues, questions and awareness in the world of modern troubadours... You deserve a reward or a door prize for making it to the end. Please check back to look for new posts as I get them done. I plan to cover a wide range of issues and topics.  I don't have a way for you to comment here, but I welcome your emails with your reactions. Feel free to cheer me on, or to disagree...

Chordally yours,

HARVEY REID

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