guitar fret decreasing down a guitar

ramly

why does the spacing decrease going down the neck of a guitar?

using physics concepts how would this be explained? (equations and concepts)

truesearch

To double the frequency of a note the string length must halve (assuming tension is constant) To produce any fractional change in frequency the length must change by the same fraction (or1/fraction)
Every halving of the length results in a doubling of the frequency, the frets get closer.

AlephZero

The frequencies of the Western musical scale of 12 semitones in a octave are a geometric progression, with a factor of ##2^{1/12}## between each frequency. The string lengths decrease in the same ratio.

Incidentally, the value of ##2^{1/12}## is very close to 18/17, which was (and probably still us) the ratio used by traditional guitar makers, who positioned the frets by making a drawing with a straight-edge and compasses, not by calculating and measuring.

willem2

You might not be able to hear the difference betweeb 18/17 = 1.0588 and 2^(1/12) = 1.0594, but you'll definitely be able to hear the difference between (18/17)^12 = 1.9856 and 2, so the traditinal guitar makers can't have made all their intervals 18/17.

AlephZero

On a real guitar the fret positions are affected by the height of the action (the string tension changes as you press it down onto the fingerboard) and the inharmonicity of the string (it has its own instrinsic stiffness as well as the stiffeness generated by the tension). Both these increase the frequency of fretted notes relative to the theoretical fret positions.

The early guitar makers didn't know about partial differential equations, but they knew what worked in practice!

Antiphon

They used (and still do use) special rulers wih the fret positions premarked. This works because scale lengths are fairly standard.

Nobody computes intervals fret-to-fret because of the inability to control cumulative error.

starland

I agree your advice AlephZero. But my opinion Fret less guitars are fairly uncommon in most forms of western music and generally limited to the electrified instruments due to decreased acoustic volume and sustain in fret less instruments. Thanks!

www.starlandguitar.com/brown-eyed-girl/