Fretting over under and around fret placement

2^(1/12) Along The Diagonal

The twelfth root of two

Found Along the

 

Di a~G on L

Hemming in the Visual 

Spectrum 

with the sound

heard all a~round

While the light is

Seen at the sine of the line

drawn

from the center

of the scene

The notes in the twelve note scale

often referred to as an octave are

separated by the twelfth root of two 

This is the diagonal

in a square matrix composed of

the product of the powers

The powers of three by The powers of two

        As Every note then is a function of 

the twelfth root of two

as 432 = 3^3 Χ 2^4

The notes that are in the Audible

spectrum of the energy

continuum are

always orGan ized in the same

sequence at the same spacing

and the interval

is 6 percent of the root

which is going to be two or three

or some multiple of the sum of the powers of

two and three of

which one is one

Meaning every form has the form

X^2 + Y^2 + Z^2

Resulting in the Ripple felt at 

the square root of 

Φ aka 5

Bonacci where 

the root is the reason

Each Fibbonacci number

is squenced into the sequence

of powers of the powers of three

piled by the power of two

leaving intervals in between

where the golden mean

finds the

complimentary hole

ready for a pole

to hang some wires on

with that caternary bend

Where the middle is an end

and the end is a middle

depending on 

the one

point of view

taken

as

a

Given

when

the given

is taken

with a grain

of co centric

salt

ion

s

F5(n) = (Φ^n - Φ^-n)cos(nπ)    / sqrt(5)

Φ(n) = (Φ^n - (1-Φ)^n)  / sqrt(5)

Here's how to calculate fret placement:

Understanding the Math

The placement of frets on a guitar follows a mathematical formula based on the principle of equal temperament. This system divides the octave into 12 equal semitones, and the distance between frets decreases as you move from the nut towards the bridge.¹

The Formula

The distance from the nut to a given fret can be calculated using the following formula:

Fret Distance = Scale Length - (Scale Length / (2^(Fret Number / 12)))

Where:

• Scale Length: The total length of the string from the nut to the bridge.
• Fret Number: The number of the fret you're calculating (starting from 1 at the first fret).

Explanation

1. 2^(Fret Number / 12): This part of the formula calculates the frequency ratio for the given fret. Each fret represents a semitone, and there are 12 semitones in an octave.² Raising a frequency by an octave means multiplying it by 2.³

2. Scale Length / (2^(Fret Number / 12)): Dividing the scale length by the frequency ratio gives you the distance from the bridge to the fret.

3. Scale Length - (Scale Length / (2^(Fret Number / 12))): Subtracting the distance from the bridge to the fret from the total scale length gives you the distance from the nut to the fret.

Let me know if you'd like to calculate the fret positions for a specific guitar!