Why Your Guitar Won’t Play Perfectly in Tune—and Why That’s OK

I have two steel-string guitars, a nylon-string, and an electric. All are good brands, well maintained, with good strings, and have been set up by my local luthier. I simply cannot get them to play in tune all the way up and down the neck. No matter how carefully I try, some of the notes always just sound out, especially if I play with other instruments. What am I doing wrong? 
—Susan Richardson 

I feel your pain. So many parts of a guitar’s tone and vibe are subjective. Sustain, responsiveness, clarity—these are intangibles that make one guitar a favorite and another a dud. It seems as though tuning should be one thing we could simply measure—we have digital tuners, after all! Unfortunately, reality is more complex, and less satisfying. 

I have had clients at every skill level with this complaint. Whether seasoned players or golden-eared beginners, they came in assuming that their tuners could be trusted to make each note perfect, and in every case, I’ve had to explain using an intermediate physics lesson.

Before we get deep into the issue, let’s address the most common culprit: intonation and compensation. Different thicknesses of strings require different deviations from the theoretical bridge location. Many guitars have saddle locations that are essentially a best-fit compromise that gets within an allowable margin of error for the manufacturer, for an average set of strings. Since final adjustments should be made for each specific player’s preferred setup, it’s appropriate for luthiers or techs to do this last-mile work after the guitar is purchased.

If bridge adjustments cannot correct the intonation, particularly on specific strings, it’s worth looking at the nut. First, verify that the nut is correctly placed by capoing the guitar at the second or third fret and tuning those notes as closely as possible. Then, remove the capo and see if the open strings are still in tune. If they are consistently flat or sharp, the nut may not be placed correctly—a problem I’ve encountered on guitars at every price point.

If the open strings don’t all agree, the guitar might benefit from nut-end compensation, in which the nut is adjusted on a per-string basis. This is a relatively modern idea, and the physics have been proven mathematically by Trevor Gore. Empirically, the results have been sufficient to inspire aftermarket compensated nuts (such as the Earvana) and manufacturer-installed compensated nuts, such as those on MusicMan guitars. Many luthiers have not yet warmed up to this approach—if a straight first fret can intonate correctly, it seems logical that a straight nut should also. I’ll confess to having been in this camp, though I recently faced a situation that could only be corrected with a single-string nut compensation and must admit that it was effective.

Now, it’s time to face the elephant in the room: there is a compromise built into
the tuning of every fretted instrument. All are built using a system called 12-tone equal temperament. In this system, the octave is divided into 1,200 steps, called cents. Each half step corresponds to 100 cents, and the relationship between any two adjacent notes is a mathematically consistent proportion (for those who are wondering, it is the 12th root of two, or 1.0594630943…). Multiplying the frequency of any pitch by that number results in the frequency of the pitch one half step higher. Do this process 12 times, and you have gone up one octave. Guitar makers use the same math to calculate fret-to-fret spacing on fingerboards. Seems totally reasonable, right?

Unfortunately, mathematics has an objection, in the form of a different system called just intonation. This system is mathematically elegant, based on simple fractions and the equally graceful physics of vibrating strings. This system traces back to Pythagoras and even prior, and is seductively simple. The octave is double the frequency of the root note, and the string length is half. These simple fractions (2/1 and 1/2) repeat for the fifth (3/2 or 2/3), then the fourth (4/3 or 3/4), then the major third (5/4 or 4/5), and so on. We’ve all encountered this when we play harmonics on an open string. The harmonic at the seventh fret (the fifth of the scale) divides the string into thirds, or three equal parts. The fifth-fret harmonic (the fourth of the scale) divides the string into four equal parts.

As with equal temperament, you can apply these fractions both to the physical string and to the note frequencies, and this is where the trouble starts. If we start from the same note and apply the math of both systems, the resulting notes don’t line up as they should. For example, if we begin with a note of 100Hz, then the just fifth is found at 150Hz. If that instrument had a scale length of 25 inches, then the position for the seventh fret would be at 16.66666 inches.

Let’s compare that to the same note/fret with equal temperament. Starting from 100Hz, we end up with a fifth note at 100 times (1.05946 to the seventh power), or 158.74. This is a disagreement of nearly 6 percent. The fret location would be at 16.685 inches—a difference of about half a fret width on a vintage guitar. Some of the notes in the scale disagree even more. The major third is the worst offender, with a disagreement of over 13 percent between the two systems, equivalent to a difference in fret placement of over 1/8 inch!

This has caused problems for composers as well. Early polyphonic instruments were tuned to just intervals, which sound most harmonious in any given key, as the overtone series for the scale tones tend to align mathematically. However, this is problematic for any piece of music that includes a key change or modulation—the E natural in the key of C major is not quite the same as the E natural that is the sixth (5/3) of G major. If a composer wanted to make a straightforward modulation from G major to C major, the harpsichord would suddenly be slightly out of tune in the new key, audibly enough to cause problems.

This age-old problem was well known to the Pythagoreans, who wrestled with it without success. However, it remained mostly theoretical for centuries, as most instruments were either monophonic (flutes, for example), fretless (ouds, violins, etc.), or able to be fine-tuned (e.g., lutes, with their tied-on frets). Historically, string materials also were not precise enough to consistently deliver exact intonation on a daily basis.

With the advent of modern polyphonic instruments such as the harpsichord (and later, the piano), along with increasing sophistication in composition, an alternative to just intonation was necessary. The solution: the equal-tempered system that is now built into almost every guitar we play. Put simply, the concept was to distribute all the errors and disagreements evenly throughout the scale, making each note equally and minimally wrong. The mathematical irrationality of the numbers involved was offensive to many at first, and there was considerable resistance to the idea that every note in a scale could be somehow slightly wrong, and still would produce harmonious music.

J.S. Bach composed possibly the most famous piece of music to address this conundrum. His The Well-Tempered Clavier from 1722 was intended to prove the viability of the 12-tone equal-tempered system. It consists of 24 pieces, covering every key in both major and minor versions, and was meant to prove that a single instrument was capable of playing every piece without retuning, and could produce a musically satisfying result in each key.

So what does this mean for you and your guitar? What I suspect, and what I have found to be the case for many of my clients, is that you are both blessed and cursed with an ear capable of discerning the compromises inherent in 12-tone equal temperament. It may be that you use combinations of open strings and harmonics in your music, or when you tune your guitar. If so, then you will never avoid the disagreement between the naturally just-tuned harmonics and the equal-tempered fretted notes—the physics are simply against us.

I have encountered a few cases where the combination of the instrument and the choice of strings emphasized overtones in the notes, particularly in the low range. Strings with thicker coatings are especially prone to this. In one case, the open A contained an extremely prominent and audible major third harmonic, which clashed badly with the fretted major thirds in the arrangement. Again, that interval is the worst offender, with approximately a 13 percent disagreement between systems.

The best thing I can recommend is this: get the instrument set up as best as possible, with a focus on intonation. This could include adjustments at both the saddle and nut ends. Experiment with string gauges, to fine-tune any remaining issues specific to individual strings. Next, try to identify which notes sound wrong, and how. You may be hearing problems that can be resolved with adjustment and string selection. However, armed with a bit of knowledge about intonation systems, you may also discover that you are facing the same problem that has plagued composers, mathematicians, and luthiers for over 2,000 years. Unfortunately, there is no real solution available there.

In closing, I’ll offer this: these little idiosyncrasies of pitch are part of what makes guitars sound like guitars. Every recording we’ve ever heard of a guitar included them, and they are one of the colors in the overall picture of what the instrument is. A guitar that could break the laws of physics and sound exactly perfect at every note, all the time, might be nice, but it might also not sound like a guitar anymore. Furthermore, the nuances of pitch and vibrato that we all incorporate into our playing, and which give each of us our individual voice, are often much more substantial than these little split differences. I get as close as I can to make my clients’ guitars play in tune, but theoretical perfection is neither possible nor necessary for making good music.

This article originally appeared in the January/February 2025 issue of Acoustic Guitar magazine.