Warning: wordy blog post!
For a while now I've wanted to put out my own views on intonation (with a few points on the side about guitar set ups). Hopefully my thoughts will be of interest to guitarists looking to better understand their own guitar. I should expect that most of what I'm about to say applies to all fretted strings instruments (probably!) but I'll write in the context of guitars.
So what is intonation? Intonation is the adjustment made to a guitar to improve it's ability to pitch any given note accurately. To begin with lets ask why a note on a guitar might sound wrong.
In an ideal world the positions of the frets along the neck exactly determine the pitch of each note. However in practice when a note is fretted, the string will be forced slightly over the fret and this increases the tensile stress in the string. Any increase of tension will increase the pitch, so generally most fretted notes will sound sharper. In practice the this effect is most extreme on the thicker, lower strings.*
The solution to this problem is normally to 'compensate' at the bridge. This means slightly increasing the string length, usually by about 1mm on the high e string, and 3-4mm on the low E string, resulting in a slanted saddle (sometimes split at the point between the G and B strings for added accuracy due to the wound strings. You'll often see this on Lowdens and Takamines). This gives a pretty good workable approximation. Normally further fine tuning on an acoustic guitar can be made by slanting the saddle for each string, which is normally 2-3mm wide. On an electric guitar there are often adjustable pieces for each string, making adjustment even easier.
Most guitarists are aware of saddle compensation and get their heads around it pretty easily. What I want to bring everyone's attention to are all the OTHER things that make a HUGE difference to intonation! They are all interrelated and are listed as follows:
1) String choice
That's right! The easiest way to improve your intonation is use thicker gauge strings. If you've been playing with 9s or 10s on your guitar but intonation is bothering you, I strongly recommend going up to 11s or 12s. Thicker strings will allow you to set the action lower because the strings deflect slightly less when they are plucked. Closer to the frets means less tension going into the strings when you fret notes. They also bend less over the fret because the higher tension in the string offers added resistance. It's also worth saying that a new set of strings will greatly improve intonation too - once your strings get really old, the uneven mass along the string (i.e. finger gunk residue!) starts to have an audible effect.
Also: play in odd tunings? Find the appropriate strings for your favourite tuning. It's no wonder that drop C tuning sounds so dodgy when you play the low E on the 12th fret! D'addario have very kindly created an online string calculator for this very reason.
2) Scale length
This is kind of related to 1) above, but if you have a favourite set of strings (that you buy in bulk on the internet for example) but use them on all your guitars, you will experience different intonation issues on each one (even assuming they are all set up exactly the same). This is because you will get lower string tension on the shorter scale length guitars, resulting in poorer intonation. So match your string gauges to your scale lengths, if necessary!
3) Fret height
The first thing I'll say is that strings are NOT supposed to touch the fretboard when you fret them. Often fingers will touch the fingerboard, but the string actually doesn't quite make it. So in a sense changing fret heights doesn't mean anything with regard to intonation. However I believe that higher and bigger frets make more insensitive players more inclined to push a little harder down, introducing some of that unwanted tensile stress and making intonation worse.
4) Action
Lower action means less string deflection when fretting notes, meaning better intonation! This is all related to what I was saying above about string choice affecting action too. Everything is connected!
5) Playing style
I'm saving the most important until last. When you next pick up your guitar, gently fret a note on the low E string, play it, and then push into the fingerboard quite hard. You'll normally find the note pitch increases quite significantly. The way the fingers fret the notes is the single biggest factor in affecting intonation, in my experience shifting the note as much as 50 cents. This is WAY more than most saddle compensation adjustments will ever make.
A good guitar repairer will admit that they can only take the intonation on a guitar so far. There is no such thing as a guitar that plays itself perfectly in tune!** It needs a good player to bring it to life, and a set up that is matched to the playing style of the guitarist. I always ask my customers what kind of player they are, and what kind of guitarists they are into. A gentle fingerpicking folk guitarist will require a very different set up to a traditional gypsy jazz guitarist. For the former a low action with decent strings will result in perfectly workable intonation without much saddle compensation. But for the gypsy jazz guitarists a higher action is normally preferably, but the intonation has to be matched accordingly. As a result, normally a fair bit more compensation at the bridge will be required.
It's no wonder that all guitars can sound great in the right hands. A sensitive player will adapt to any guitar they play, smoothing out any tuning inconsistencies and they will 'feel' their way around the guitars own quirks. But conversely a well set up guitar will bring out the very best in every guitarist! Thanks for reading :D
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*I've often assumed this must be due to the fact that the thicker strings bend over the fret more, compared to the finer high strings. It could also be that the same amount of deflection makes a proportionally bigger effect on the lower frequency notes. Would be interested to know your opinions in the comments box below!
**I'm keen to explore this in more detail in a blog post further down the line. Not many people consider what it means to be in tune in the context of equal temperament and this interests me greatly. If you have a well developed ear and you prefer to tune your guitar by listening to the fourths intervals between the lower strings and then can't figure out why your B string (a major third interval) ends up so flat according to your tuner, this will be explained! I love this kind of stuff...