Posted on Nov 23 2020 09:58 AM
Yep, the G! But there are more. Here is a quote from the article I linked to:
The western musical scale is made of 12 notes per octave that are equally spaced apart. This allows you to play in any key without having to stop and adjust your tuning for each key (this will become clearer in a moment). Each of the 12 notes is about 5.946% higher in frequency than the one below it. If you take A 440, and multiply it by exactly 1.05946, you get the frequency of A sharp, which is 466.162 Hz. Multiply that again by 1.05946 eleven more times, and you reach 880 Hz, the A an octave higher. In the studio, where sometimes you have to change tape speeds for tuning purposes, you can just remember it as "6% speed change equals one half-step" (or one fret on the guitar). Six percent is ballpark... then finetune by ear. (Also... each of the 12 notes in an octave is divided into 100 tiny intervals called "cents". So... one "cent" is about .06%. An octave is 1200 cents. Hey, I didn't invent this stuff...)
So far so good? Get out your old TI calculator and try multiplying anything by 1.05946, 12 times, and watch the number end up doubled. It happens that 1.05946 is the "twelfth root of two". This evil number, which we are stuck with, has caused tuning nightmares for entire civilizations.
The G (and B) string drives people crazy on the guitar. They tune it, then play a C chord or A minor chord, but the G string sounds wrong. Fuzz and distortion makes the wrongness even more apparent. So they tune the G string by ear so that chord is in tune... and then all the other chords they play sound wrong. Way down there at the first fret, all your intonation acrobatics (which mostly affect the other end of the string!) will be of little use, so what do you do? Sigh wearily... and look for another guitar, which might fix the problem... sorta.
The explanation won't make you happy. In the "first position," meaning for chord shapes that are mostly on the first couple frets on the guitar, the G string is often used for the upper part of a musical interval called a "third," either major or minor third. (This musical term is not to be confused with "third harmonics;" it's a totally different thing.) In an ideal world, a "major third" is two notes (a "diad") whose frequencies are in a ratio of 5 to 4, or 1.25, while a "minor third" is in a ratio of 6 to 5, or 1.2. If those ratios are true, these diads (note pairs) sound wonderfully in tune and harmonious.
Here's where it gets hairy. In our 12-tone Western scale, where all the notes are equally spaced, no pair of them are exactly in a 1.2 or 1.25 ratio. If you pull out your calculator and multiply 1.05946 by itself a few times, you'll land on 1.189 and, next, 1.2599! The first one is actually 15 cents flat from where your ears will want a minor third to be, and the second is 14 cents sharp from where a major third should be! So if you tune a chord that includes a major third "by ear" until it sounds perfect, that same chord with a minor third substituted in it will be 29 cents out of tune... almost a third of a half-step. (Cue: wailing and gnashing of teeth.)
For comparison, a "fourth," the frequency span from A down to E, should be in a ratio of 4 to 3, or 1.3333... and in our Western scale, it lands on 1.3348. Damn close... only 2 cents sharp. A "fifth" (E to B, the ultimate punk rock interval; one string over, 2 frets up) should be 3 to 2, or 1.5000, but it lands on 1.4983 in our scale... 2 cents flat. Fourths and fifths are definitely close enough for rock and roll.