Guitar fret decreasing down a guitar

In summary, the spacing decreases going down the neck of a guitar because the frequencies of the notes on the guitar scale are a geometric progression, with a factor of ##2^{1/12}## between each frequency. The string lengths decrease in the same ratio. The early guitar makers didn't know about partial differential equations, but they knew what worked in practice! They used (and still use) special rulers with the fret positions premarked. Nobody computes intervals fret-to-fret because of the inability to control cumulative error.
  • #1
ramly
9
0
why does the spacing decrease going down the neck of a guitar?

using physics concepts how would this be explained? (equations and concepts)
 
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  • #2
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.
 
  • #3
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.
 
  • #4
AlephZero said:
.

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.

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.
 
  • #5
willem2 said:
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.

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!
 
  • #6
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.
 
  • #7
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/
 

1. What is guitar fret decreasing?

Guitar fret decreasing is the process of adjusting the height of the frets on a guitar. This can be done to improve playability and intonation.

2. Why would I need to decrease the frets on my guitar?

Over time, the frets on a guitar can become worn down or uneven, causing buzzing or intonation issues. Decreasing the frets can fix these problems and improve the overall playability of the instrument.

3. Can I decrease the frets on my guitar myself?

While it is possible to decrease the frets on your guitar yourself, it is a delicate process that requires specialized tools and skills. It is recommended to have a professional guitar technician perform this task to avoid damaging your instrument.

4. How much does it cost to have the frets decreased on a guitar?

The cost of fret decreasing can vary depending on the guitar and the extent of the work needed. On average, it can range from $50-$100 for a basic fret level and crown, but more extensive work may cost more.

5. Will decreasing the frets affect the tone of my guitar?

Fret decreasing should not significantly affect the tone of your guitar. However, if the frets were severely worn down or uneven, fixing them may improve the overall sound of the instrument. It is important to have a professional perform the task to ensure minimal impact on the tone.

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