John Hendow

As guitarists and bassists develop better technique, we often discover there seem to be tuning inconsistencies with our instruments that can’t be addressed by plugging into a tuner. Over the years that I’ve played, I have discovered that there is an inherent problem with all of my instruments in a certain portion of the fretboard range. In the process of trying to understand the problem space, I had to do a little math and physics. See? Beneath its firebreathing veneer of rebellion and self-expressive freedom, rock and roll is actually science! And all this time we thought we were being so anti-establishment. Well, at least we can say we’re putting our science to work.

Let’s start at the beginning of the problem with “this thing isn’t in tune”… these issues need to be fully addressed before we can derive any benefit from discussion on microtuning.

Tuning Issues
If you find your guitar or bass won’t play in tune, there are several things worth examining.

1. First of all, make sure your strings are relatively new (less than one month old). Old strings, especially if they’re really dull looking and cruddy, will not properly stay in tune. If in doubt replace them and allow the new ones to stretch a bit before proceeding.
2. How is the neck relief? Sight down the guitar fretboard, looking from the bridge to the nut. If you see an obvious bow / curve / twist in the fretboard, you need to adjust the neck relief. You should also be able detect any serious fret problems this way (see #4 below). Adjusting the neck relief isn’t terribly difficult, but if you aren’t experienced in making this adjustment I’d suggest you have a luthier show you how it’s done. The key here is to make SMALL adjustments; no more than 1/4 turn of the adjustment nut at a time. Warning: overtightening can break the truss rod, and this is the very definition of the word “bummer”.
3. Your tuning issues might be due to improper string action. Check the height of the string above the fretboard. If there is too much distance from the string to the top of the fret, there will be too much deflection when you fret (you’ll always be pulling the string sharp when fretting). This needs to be adjusted at both the bridge and at the nut. Adjusting the bridge is simple. Adjusting the nut slots is not. I recommend you have a luthier handle any nut adjustments.
4. It could also be your frets. If the frets are improperly crowned you’ll find tuning isn’t consistent on fretted notes. Sight down the fretboard and take notice of any unusual frets. If you see deep ruts in the frets or they seem really tall, flat, or radically different from each other, it might be time to ask a good luthier for an assessment.

So if you’ve checked all these things and carefully tuned the open strings with a good tuner, only to find your guitar or bass still doesn’t seem in tune when you’re playing, it might be time to check your intonation.

Read the rest of this post for more information…

In Our Last Episode…
In a previous article I discussed the definition of Pythagorean tuning with a focus on how it applies to guitar. Many guitarists discover they have tuning issues when playing their instruments, and it is sometimes rooted in improper string intonation; in other words the scale length of each string may need to be adjusted. In order to make sense of general intonation, think of it as aligning the first harmonic node with its fret position. There is both (1) the harmonic center of the vibrating string and (2) the middle point on the fretboard, and they need to be in the same place. The important test is to make sure the first harmonic (node) has the same pitch as the corresponding fretted note. The first harmonic is a member of the Pythagorean scale (again, see this posting ) and will always occur exactly halfway along the string between the bridge saddle and the nut. In order for the frets to be equally tempered along the length of the string, the crown of the 12th fret must be exactly under the first harmonic. Since the frets are fixed in position, we adjust the overall scale length to relocate the node.

Each of the strings needs to be adjusted individually as follows:

• Play the 12th fret harmonic and tune the string using a tuner
• Fret the note at the 12th fret and observe the tuner
• If the fretted note is flatter than the harmonic, the scale length is too long on that string. Loosen the bridge saddle and move it toward the neck.
• If the fretted note is sharp vs the harmonic, the scale length is too short on that string. Loosen the bridge saddle and move it away from the neck.

When you’re done intonating the saddles, they will not be in a straight line. Each string will require different adjustment based on the string’s gauge and mass.

Assuming the frets were correctly placed on the fretboard, and that they are correctly crowned, you’ll be reasonably well in-tune. The only proper way to test for tuning is to check that the octaves sound in tune across the strings. Remember, the guitar uses an equal temperament scale for fret placement, so all the notes are adjusted slightly to make the notes equidistant within the 12 note octave. Guitarists and bassists often use harmonics for tuning; this is a common done by getting the harmonic at the 5th fret and 7th fret on adjacent strings to sound exactly the same.  As I explain in another article, this is not a good way to tune your instrument as these notes will never be in tune with their fretted counterparts. ONLY the octaves are truly in tune.

If you’ve checked your instrument for proper intonation, and have gotten the open strings and octaves in tune, begin to play some chords and listen to how they sound. Pay special attention to chords in the middle of the neck as well as open chords (first position). They should sound pretty good. If you have a keen ear, you’ll probably notice something is not completely right with open chords. They sound a little strident, and this is the crux of the tuning anomaly I’ve been hinting at.

Why Am I Having Tuning Problems With Open Chords?
Even after all that careful adjustment, and keeping in mind that our equal-temperament scale has inherent compromises, most fretted instruments will STILL have tuning issues, especially noticeable in the first position. I have discovered that all of my electric guitars have intonation issues in the first 4 or 5 frets. The notes in this range are noticeably sharp, with the B and G strings being particularly problematic. Any open chords played in this range will have a slight dissonance because the third will sound sharp. I’ve experimented with different strings on my guitars and this issue is endemic. I’ve verified this using a strobe tuner. Less noticeable, but also true is the opposite effect: the notes above the 18th fret seem strangely flat. The string is in tune. The intonation has been adjusted correctly. The frets are in the right place (at least from a mathematical standpoint). So what’s going on here?

Yep, it’s a physics problem. In order to understand the physics underlying the our tuning anomaly, it’s necessary to first discuss the harmonic overtone series.

Harmonic Overtone Series
If we consider the regular harmonic series, we can construct a simpy table showing the intervals and frequency ratios of the first nine harmonic overtones.

This harmonic overtone series is absolutely correct for columns of vibrating air, as with a pipe organ. However, with music instruments that have strings (piano, guitar, bass, etc) there is an error in these simple ratios due to inharmonicity. In short, vibrating strings don’t demonstrate these pure and simple overtones as expected.

Inharmonicity
Inharmonicity describes the magnitude of the error between the expected (see the table above) and actual frequencies of overtones resulting from vibrating strings. This is a subtle tuning issue that is familiar to pianists (especially to piano tuners). Most guitarists and bassists have also experienced the effect of this tuning anomaly, but it’s less pronounced due to their instrument’s (1) short scale length (2) relatively limited octave range and (3) comparatively slack string tension (all versus a piano). Still it’s noticeable and can be addressed if we understand the basis of the problem. What we need to do is make adjustments for the type of string size (thickness), the tension on the string, and the manner in which it is sounded.

Stretched Tuning
In order to compensate for inharmonicity, pianos are treated to a degree of additional scalar compensation known as “Stretched Tuning”. This means octave intervals, which we would expect to have a 2:1 ratio are intentionally moved slightly farther apart, with the intermediate scalar intervals being adjusted appropriately. By convention the note ‘A’ above Middle C is tuned to 440 Hz. Each successive octave is slightly compensated in the direction away from middle C (known as C4). 

• Notes are intentionally tuned flatter as you descend from Middle C down to the lowest note.
• Notes are intentionally tuned sharper as you ascend from Middle C up to the highest note.

So How Do We Fix This On Guitars And Basses?
Remember, we’re trying to adjust the intervals to address the highest and lowest notes, compensating for the string’s thickness and tension.

If you are the mad scientist type (actually more of a mad luthier), you could make yourself a compensating nut to fix this issue. It’s complex and you’ll need serious skills and a very good ear to do this yourself. Fortunately, there are two commercially available solutions that are actually pretty affordable and work quite well: the Earvana nut and Buzz Feiten tuning system. These are both adaptations designed to help address scalar intonation issues on guitars and they work by making micro-adjustments to intervallic distances.

The Earvana and Buzz Feiten systems replaces the stock nut on a guitar with one that slightly staggers the endpoint for each string. This small adjustment changes the length of the string scale, which has the greatest improvement effect on the low notes where the tuning is usually sharp. This is the simplest and least-invasive approach to addressing micro-intonation issues. The Buzz Feiten tuning system also includes a custom compensation for the bridge saddles, which is designed to address the issues on high frets as well. Since these modifications are non-permanent, one can easily revert to the stock nut if so desired.

OK, So It Can Be Fixed. Why Don’t Guitars And Basses Just Come This Way?
Good question. The compensation systems are available on some stock instruments, and as noted above, can be retrofitted onto most guitars and basses. Playing a guitar with corrected intonation will sell you on the benefit of the system. Playing complex chords (b9, #9 etc.) results in improved sonority.  Playing through a distorted amp really brings out the benefit of sweetened tuning; distortion emphasizes harmonic overtones and if the notes are nicely tuned the chord will be much richer. Most of the “mud” that results from open power chords is cleaned up.

Remember, this is just one step in the process of learning to play in tune. There are adjustments you can (and should) make with you left hand to help chords sound more in tune. Understanding when to make these adjustments requires a knowledge of music theory, and will be addressed in a future article.