jamminjim
Well-known member
but this here thread is about neck math......
Last edited:
Who needs that 24th fret anyway!
.
No rocket science here.
The neck is just 2 frets longer.
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I love math
I also like 24 frets cause it makes the math easier for me.
Rob says he doesn't get math so we'll start there.
An open A string (when in tune) vibrates 110 times a second. That's it's frequency (Hz). When you cut the string length in half (fret at the 12th fret) given the same string tension and thickness the string is forced to vibrate twice as fast or 220 Hz. If you cut the string length in half again (fret at the 24th fret) the same thing happens again and you get A 440Hz. (This is where intonation becomes important but not now)
And now some stinking math:
Given A 110Hz and A 220Hz We can find all the frequencies for the other notes:
freq (A#) = Freq (A) * 2^(1/12)
116.54 = 110 * 2^(1/12)
You can check this with the chart below or your calculator
For fun
freq (unknown note) = freq (known note) * 2^(x/12)
x = distance between notes in half steps
And it's almost the same thing for string length. (From the fret to the bridge) We know open A (110 Hz) length is 25.5"
(For metric people just multiply all lengths by 2.54 to convert to cm.)
BTW We're going metric every inch of the way!i digress
StrLn (A#) = StrLn (A) / 2^(1/12)
24.07 = 25.5 / 2^(1/12)
Then you find the distance between frets by subtracting the differences between string lengths for adjacent notes
Fret 1 = StrLn (A) - StrLn (A#)
1.43 = 25.50 - 24.07
Fret__Note______Hz______String Length____Fret Length
0______A______110.00_____25.50
1______A#____116.54_____24.07___________1.43
2______B______123.47_____22.72___________1.35
3______C______130.81_____21.44___________1.28
4______C#____138.59_____20.24___________1.20
5______D______146.83_____19.10___________1.14
6______D#____155.56_____18.03___________1.07
7______E______164.81_____17.02___________1.01
8______F______174.61_____16.06___________0.96
9______F#_____185.00_____15.16___________0.90
10____G_______196.00_____14.31___________0.85
11____G#______207.65_____13.51___________0.80
12____A_______220.00_____12.75___________0.76
13____A#_____233.08_____12.03___________0.72
14____B_______246.94_____11.36___________0.68
15____C_______261.63_____10.72___________0.64
16____C#______277.18_____10.12___________0.60
17____D_______293.66_____9.55___________0.57
18____D#_____311.13_____9.02___________0.54
19____E_______329.63_____8.51___________0.51
20____F_______349.23_____8.03___________0.48
21____F#_____369.99_____7.58___________0.45
22____G______392.00_____7.16___________0.43
23____G#____415.30_____6.75___________0.40
24____A_______440.00_____6.38___________0.38
Like ShaneV said you can keep adding frets but they do get pretty small after a while
I didn't get my calipers out to check this but I wish someone would