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Portland Guitar Pretty Good Intonation (PGPG) System

Short Version | Introduction | Intonation Errors | Analysis | PG Approach | Comparisons | Conclusion

PGPG Intonation

The Sources of Intonation Errors

To help flesh out all of the ways things can go wrong with a guitar’s intonation, the following is a list of possible sources of intonation error.  The magnitude of the errors varies, with some sources such as fretting the string causing large effects and others such as finger pressure producing small effects.  This list is probably incomplete and is not in any order, but for our purposes it should cover most of the bases.

Psychoacoustics:  In our musical convention, the interval from one note to the next is subdivided into 100 equal parts called cents.  Individuals have varying levels of ability to hear differences in pitch.  It has been reported that we can typically hear an intonation error of about 3 cents at 500 hz although this is not universally accepted as some people can hear better than others.  Someone with perfect pitch will hear errors far smaller than I ever can as I am relatively insensitive to pitch.  I have been tested and I can only reliably differentiate two tones 12 hz apart at 500 hz… not too good.L  Probably why I can’t really sing. 

No matter what the numbers from our sophisticated set of tools tells us, if the player says it doesn’t sound right, then it must be adjusted.  This is a consequence of the phenomenon that frequency does not equal pitch.  Frequency is how fast it vibrates; pitch is how we perceive it and the two just aren’t necessarily the same.  We humans have pitch meters not frequency meters in our heads.  The subject of psychoacoustics is the study of the perception of sound by the brain and is the last link in a long important chain from the pick to perception.

Fretting the String:  When a string is pressed down and fretted its total length increases slightly.  Consequently so too does its tension.  This increased tension will cause the note to play sharp. The higher the action the more the tension increases which causes the note to play sharper, the lower the action, the smaller the effect.  The amount of stretching and the intonation errors depend on where you play the note on the fretboard.

            String Height at the Nut: The height of the string at the nut largely determines the amount of additional stretching the string experiences when it is fretted near the nut. The higher the string the more stretching occurs and thus needs additional compensation.  This suggests that getting the nut height as low as possible may be advantageous although there are reasons to increase the nut action.  A common method to create a nut is to place a fret at the nut position, i.e., the Zero Fret.  This creates a nut action nearly identical to the action at the first fret. 

            Resonance Interactions: Sometimes the resonances of the guitar body can interfere with the string resonances and cause a note to play sharp or flat depending on circumstances.  These errors are real, reproducible, and difficult to track down and correct … so far.

Virtual Saddle Position: As the top vibrates the bridge is carried along with it meaning that our supposedly fixed saddle is no longer in a fixed position.  If this didn’t happen our guitars wouldn’t make much sound at all.  Imagine the string as it vibrates; it takes on a curved shape that comes to a point right at the saddle.  On a real guitar though the saddle is still moving, so the imaginary fixed point is behind the saddle a bit.  This effect has the result that the string thinks it is longer than it really is.  It is sort of like looking into a mirror that is slightly convex; objects are closer than they appear.  The problem for the string is to find the virtually fixed position of the saddle.  Fortunately it doesn’t find this hard to do.  This effect depends on the note, the resonant frequencies of the top of the guitar and how they interact. 

            String wear and tear: As strings are used they wear away in spots, particularly at the frets, and unevenly collect gunk from the oils, acids, and dirt on our hands.  Corrosion can occur anywhere along the string and is likely to be spotty.  All of these things cause the string to have an uneven density along its length.  This can cause the string to play sharp or flat depending on what has happened to it and where it is being fretted.

Systematic Errors: When a musician frets a note it is possible to push on the string parallel to the frets causing the note to play sharp.  This “bending” must be considered if the player systematically does this.  It is also possible to press on the string perpendicular to the fret either toward or away from the bridge causing the note to play sharp or flat (vibrato). When a string is pressed down between two frets the tension will increase as it is pushed and stretched further into place.  This will cause the note to play sharp.  The effect is small, but real, and the harder you push the sharper the note.  Someone with a very strong grip may play the note sharper than someone with a light touch.  Also, as you play you may change your finger pressure depending on the passage being played.  How a person plays has an effect on the intonation and is a factor when setting up the guitar.

Seasonal Changes to the Guitar: As the environment or seasons change, a wooden guitar will expand and contract along with the humidity (mostly) and temperature.  The length and shape of the guitar will actually alter slightly.  These changes will cause the intonation to drift either sharp or flat depending on the season.  The guitar certainly needs to be re-tuned and the IQ number may or may not be affected.

String Mechanics: If you carefully listen to or measure the frequency of a plucked note on a guitar you might notice the tone is not constant.  Generally, when the note is first plucked it will play a few cents sharp and then as it decays away the tone drifts back to an asymptote.   What is the right tone?  Well, that is pretty much up to you.  For example, if you play lots of black notes, i.e., notes of short duration, you might choose to intonate the guitar to the first part of the note.  If you play lots of really longs notes you might want to intonate to the asymptote.  This is truly a subjective decision.

Temperature Changes: Metal strings are particularly susceptible to changes in temperature.  The metal will expand as the temperature increases causing the string to lose tension and go flat.  Believe it or not, the strings actually warm up as they are played, but this effect is very small.  However, if you bring your guitar in from a cold car into a warm room, it will likely be out of tune.  Wood also expands and contracts with temperature, but much less than metal.

Changing Strings:  When changing strings, the type, make, and gauge of the strings will have differences that may or may not affect the intonation.  When changing to a new type of string you might expect the IQ number to change.  New strings will be different than old used strings of the same make.

Changes to the Setup: Sometimes you may want to change your playing style and choose to modify the setup, or the guitar gets old or sold or passed on.  A little lower action might be nice, or it might be good to just tighten things up once in a while.  This may change the intonation depending on what is done.  For example when the action is lowered, the strings will stretch less when they are fretted and the intonation errors will be different and require a different amount of compensation.

Neck and Body Creep: Our poor guitars are expected to withstand 160 pounds or so of tension for fifty years or more without deforming more than a millimeter.  You try that!  All the while the guitar is expected to be as lightly constructed as possible to enhance the acoustics of the instrument.  This might be considered a set of unreasonable expectations if one were reasonable, a trait sometimes lacking.  In the real world our guitars are in the slow motion process of collapsing under tension.  For a high performance guitar that is built on the cusp of self-destruction the effect might be expected to be larger than on an overbuilt off the shelf guitar.  Over time the neck angle will change, the top of the guitar deforms, and the woods age and mature.  All of these things can make the intonation change and might require the guitar to be adjusted, or worse a neck reset, or worse yet a new top!

Fret Position and Saddle Placement Errors:  We know with exquisite theoretical detail where the frets and the saddle belong on the instrument, but it can be difficult to get them positioned just right.  With our modern tools we can cut the fret slots to a few mil (1/1000”) accuracy.  When cut by hand the slot positions are probably less accurate.  When the frets are re-crowned it is important that the peak of the crown is directly over the slot.  If any of these things parameters are off even a little bit the only solution may be to rework the instrument.  It might be possible to compensate for the errors, but I can’t imagine that it will make the situation much better if the guitar is fundamentally flawed.

Bad Strings: Sometimes it has been reported that a string is unevenly wound or has other manufacturing problems.  The best solution if this is the case is to replace the string.

Saddle Slop: For a straight line slanted saddle, if the saddle doesn’t fit snuggly into the saddle slot it can tilt forward leading to errors. 


Setting up a Guitar

Among other things, the playability of a guitar is greatly influenced by the height of the strings above the fretboard (the action).  Generally, the higher the strings are set above the fretboard the harder it is to play, the lower the strings the easier it is to play.  The height of the strings also has an effect on the quality of the sound that the guitar makes.  Set the strings too low and the sound gets thin and ultimately starts to buzz as they hit the frets.  Make the strings too high above the fretboard and it sounds great but is too hard to play.  Once the action is ultimately set, a refinement is achieved by controlling the longitudinal shape of the neck with the truss rod.  Ideally there is a slight concave bow of about a millimeter or less at the 12th fret that helps to prevent buzzing.   So, for each and every guitar and musician there should be a setup that makes the player most happy.  Our objective is to find that happy medium and then make the guitar sound as good as we can with what we are given.  Once we have adjusted the action of the guitar and it plays the way the owner would like it to play, it may or may not play in tune; probably not.  What to do?

Fortunately, to improve the intonation, we can adjust (compensate) the scale length, defined as the distance from the nut to the bridge, by repositioning the nut and the saddle.  It has been traditional to compensate a guitar by making the bass side of the saddle about 1/8 inch farther away from the nut and then further modifying the saddle for each string.  This is the slanted saddle seen on most steel string acoustic guitars.  This slanted saddle has the effect of increasing the scale length of each string and typically will produce a good but not great intonation.  However, good may not do it when we are trying to build a high performance guitar. So we also have the option to adjust the position of the nut.  This is a bit more difficult than the saddle adjustment, but not impossible.  Nut Compensation has typically been done by fixing the type of strings that will be used, measuring the stiffness and action accurately and precisely, and then using that information and a theoretical formula to calculate the amount of compensation needed for each string.  A unique nut and saddle must next be crafted to fit these calculations.  Once manufactured the nut and saddle are not adjustable and must be replaced if alterations are necessary.  Your results may vary and predictions from the model may or may not match the realities of the actual instrument.



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