Intonation is an extremely tricky subject, and the study of it is one of my hobbies. Historical tuning systems, the mathematics behind various temperaments and scale degrees, and application of new theories is absolutely fascinating. Yes, I’m a serious nerd.
Delving into intonation is a daunting task, but I’ll try to distill it to it’s most simple essence, and get to the gist of how it relates to your guitar. The division of an octave is rooted in physics and mathematics, and has been a source of considerable debate over the last several thousand years or so. It began in earnest with Pythagoras, who began studying the relationships of string vibrational ratios and the division of the octave into equal parts. He determined that a root note and the octave of that root have a relationship ratio of 1:2 – for example, a note at a frequency of 100 cycles per second (hertz, or Hz) is one octave above a note at 50 cycles per second. Make sense? So by having a note at 100Hz, you can tune it’s octaves without any complicated math, and it’s very easy to hear when they’re in tune or not, as they are essentially the same note. Now, music with just octaves isn’t terribly exciting (Bulls On Parade being an exception), so we need another note to spice things up. So Pythagoras again applied a pure ratio to divide the octave, 1:3, which gives us a perfect 5th (so if we apply that to our 100Hz note, the next note is 66.66Hz). Both the pure octave and the pure 5th sound very pleasing to the ear, as their individual vibrational patterns don’t clash with each other. Now that we’ve got two distinct notes, we can proceed to find all the other notes in the 12 tone scale, simply by applying the 1:3 ratio to each new note and finding our circle of 5ths. Each 5th will be a perfect 5th from the previous note… but by the time we get back to the original note, the octave is almost a quarter-step sharp! The math simply doesn’t work: it’s impossible to divide the octave into equal steps using pure ratios.
Music theorists over the years have played around with a lot of different ways of tempering the scale, which is a fancy way of saying they’re changing the pure intervals to something less pure, in an effort to make every note sound equally out of tune, instead of just one or two notes being grossly out of tune. That’s right: ALL the music you listen to is out of tune. You’ve simply gotten used to it, which is why I often say that intonation is a social construct.
So what? Well, now that you understand that your guitar is already out of tune with itself and always will be, the trick now is to make sure that it’s at least equally out of tune with itself all the way up and down the neck. First, it’s important to understand this: intonation can’t be set accurately with a poorly set up guitar. If your action is too high, or your nut is cut unevenly, or if your frets are worn, you’re never going to get decent intonation on your guitar. Don’t even bother. Get it set up first.
Guitar intonation is actually pretty simple, once the guitar is properly set up, you have the proper tools, and know a few tricks. Setting the intonation is accomplished by moving the individual string saddles back and forth, making up for the different string gauges and type. At it’s most simple, it’s just a matter of making the open string and the 12th fret note perfectly in tune. Accuracy is key here: it has to be within about a cent or so, or you will hear it. I recommend using a strobe tuner. My favorites are the Peterson tuners, which can be a bit expensive, but certainly worth it. If you’ve got a iPhone, I highly recommend Planet Waves TuneUp app, which can be had for only 99¢ (Bonus! It also is capable of tuning Buzz Feiten equipped guitars for an extra $20).
I hope this makes sense – distilling such a tricky subject into just a few paragraphs is not easy. The takeaway here is this: get your guitar set up and intonated properly. It WILL sound better, I guarantee it.
Questions? Give me a call or shoot me an email and I’ll be glad to take you down the intonation rabbit hole.