Why the frets get closer together.

mike721
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Sat Jan 20, 2018 11:31 am

Since everyone was so good and thoughtful to me here at TotallyGuitars, I thought I'd like to share something.

The ancient Greeks, found three intervals particularly pleasing to the ear and it follows common mathematical ratios. If you take any open string and pluck the note and then play the string again by shortening its length by a half (it's the 12th fret), you get an octave, the first two notes of "Somewhere over the Rainbow." or a 2:1 ratio. Whereas if you pluck any open string and then shorten the string by a third of its original length (it's the 7th fret) you get a Perfect Fifth or the first few notes of "Twinkle, Twinkle Little Star." or a 3:2 ratio. Finally, if you shorten any string by a fourth of its original length (it's the 5th fret), you get an perfect fourth, the first two notes of "Here comes the Bride." or a 4:3 ratio.

To see what I mean. Put the guitar down flat on something, I use my couch and play it like it were a piano; this is so you can see the proportions. Grab a capo and let's make a perfect fourth. Let's use the sixth string, but it doesn't matter which one, pluck it and then pluck it with the left finger on the fifth fret and listen; you can play "here comes the bride." Now look down at the string and try to eyeball that you shortened it by a quarter of its original length. Clamp the capo on the fifth fret.

Now ask yourself, where is the next fourth up from where the capo is? Well, it's again shortening the sixth string by a quarter from the capo to the bridge. Eye ball the proportion and you'll see your finger is on the 10th fret and you can play "here comes the bride."

With a tape measure of some sort, measure the distance from the nut to the capo (fifth fret); that was the first interval we played. Next, measure the distance from the capo to the 10th fret. On my guitar, the former was six and a half inches and the latter is four and three quarter inches. So, the interval length of the string for a fourth is diminishing in length, as so are all the other intervals, as we move towards the bridge. This is why the frets get closer together.

Try it sometime! It's fascinating!


spinland
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Sun Jan 21, 2018 9:18 pm

Nice! I love geeking over the science of how this stuff works. Thanks for the share!


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