Maths on Tunning

[Blaze]

Some of my guitars have a G string tunning problem and i m not the only one , is nt ?

Could it be the nut or the string or wathever ??..Try a wounded G string, etc,etc...few explanations are suggested..

Trying to find a trick to fix it ,i found this article about tunning.. mathematic involve here ...

Come on fretters, tell us your tips & tricks..




Brute-force explanation of equal-temperament:

1) Two different notes sound "good" together only if their frequencies are simple integer fractional multiples of each other; i.e. four wavelengths of one note equals three wavelengths of the other, or five equals four, or seven equals five. [For example, E at 660 Hz, has a 3/2 ratio to A at 440 Hz. Three waves of that E are the same physical length as two waves of that A.] For an octave, the ratio is a simple as it gets: two wavelengths of the higher note equal one wavelength of the lower one. [For example, two A notes: 880 Hz and 440 Hz, a ratio of 2 to 1.]

2) "Chords" represent stacked ratios of these wavelengths; for instance, seven wavelengths of the high note will equal five wavelengths of the next one down, or four wavelengths of the lowest note. The notes are all "in tune" with each other when these ratios are exact.

3) 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.

But... pile on a bunch of fuzz/distortion (which nakedly reveals tuning problems) and place those "third" notes right on the pesky first fret of the guitar, and you can have the ultimate homicidal-suicidal tuning nightmare. There's not much you can do. When a musician with a song including lots of first position complex chords notices this problem, he (and you) can go nuts trying to get his guitar in tune. There are actually chord progressions that simply cannot be played completely in tune on some guitars, period; you have to tune by ear for part of the chord progression, record it, then retune for the other part of the chord progression, and punch all those parts in... with very fast fingers. Or get another guitar... and hope!

You can try to suggest transposing the chord to some other part of the neck. Sometimes it works, if you can convince the musician. I had one client with a beat-to-hell Strat and a song with a first-position chord sequence that could not be tuned. No way, no how. We almost went insane, because he WOULD not use another guitar. It was a simple song, yet we spent hours trying to get a track done that did not sound horribly sour.

What could I do? Nothing... except try to learn why. That started me on the journey which led to this article. Thanks for reading, and good luck in the future... with all those keyboards, loops and samples! Hey, electric guitar's not dead, it just smells funny...

[Kodiak3D]

Thanks for posting! I am a scientist, so that was actually rather fascinating. The basis of music is the physics of sound waves. I love reading about the science of what makes something sound good to the human ear.

[Blaze]

Thanks for posting! I am a scientist, so that was actually rather fascinating. The basis of music is the physics of sound waves. I love reading about the science of what makes something sound good to the human ear.

Here s the complete article...

http://www.endino.com/archive/tuningnightmares.html

[Rampant]

Cheerz dude.

This post made me feel all comfortable and warm and in harmony with the world. As a meticulous thinker with a life (nee Job) built around numbers, maths and engineering I feel good to know there is a reason. It's even better to be told what the reason is. Even if I don't remember it.

Relaxed

[Robert****]

That was interesting.

I have more tuning "issues" with the B string though, not the G string.

[Jipes***]

Very interesting post and of course as lot's of players I had my bunch of tuning nightmare but that's even more freaky when I pass form one Open tuning to another

[kiteman]

I'm aware of the equal temperament tuning on a guitar. I just tune my As on the strings to the open A string. Fine tune with other octaves and I'm ready to go.

[Goose]

If you guys liked the math and science behind this, checkout the resulting engineering!
http://www.truetemperament.com/site/index.php

[Eric***]

Wow, that was interesting, encouraging (to know I'm not the only one), depressing, and a whole bunch of other things. Good to know. Thanks for the article.