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:| | | * | | * | | * | | * | | |- ... |: | :| | | * | | * | | * | | * | | |- ... |: | ||
Open C :| C# | D | D# | E | F | F# | G | G# | A | A# | B |- ... |: | Open C :| C# | D | D# | E | F | F# | G | G# | A | A# | B |- ... |: | ||
− | Nut 0:| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11|- ... |: Bridge | + | Nut 0:| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11|- ... |: Bridge |
+ | #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: | ||
+ | #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: | ||
+ | #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: | ||
+ | #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: | ||
+ | #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: | ||
+ | ########|###########|########|########|###########|###########|########|- ... |: | ||
+ | ########|###########|########|########|###########|###########|########|- ... |: | ||
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Revision as of 19:16, 28 January 2016
Contents
- 1 Rough fret positions
- 2 Fret layout
- 3 Taylor Formula
- 4 Air resonance
- 5 Ukulele Variant
- 6 Ukulele Tunings
- 7 Common fret board scale lengths
- 8 Equal Temperament
- 9 Tables for some common fret board lengths (scale length)
- 9.1 6 inch scale length
- 9.2 8 inch scale length
- 9.3 10 inch scale length
- 9.4 12 inch scale length
- 9.5 14 inch scale length
- 9.6 16 inch scale length
- 9.7 18 inch scale length
- 9.8 20 inch scale length
- 9.9 22 inch scale length
- 9.10 24 inch scale length
- 9.11 32 inch scale length
- 9.12 36 inch scale length
- 9.13 42 inch scale length
Rough fret positions
12th fret: 1/2 of the string's length
9th fret: 2/5 of the string's length
7th fret: 1/3 of the string's length
5th fret: 1/4 of the string's length
4th fret: 1/5 of the string's length
Fret layout
D X D X D D X D X D Xb D :| | | * | | * | | * | | * | | |- ... |: Open C :| C# | D | D# | E | F | F# | G | G# | A | A# | B |- ... |: Nut 0:| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11|- ... |: Bridge #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: #####| |#####| |#####|#####| |#####| |#####| |#####|- ... |: ########|###########|########|########|###########|###########|########|- ... |: ########|###########|########|########|###########|###########|########|- ... |:
Diatonic only (common with dulcimer)
D D D D D D D :| | | * | * | * | |- ... |: Open C :| D | E | F | G | A | B |- ... |: Nut 0:| 2| 4| 5| 7| 9| 11|- ... |: Bridge
Dulcimer with "blue note":
D D D D D D Xb D :| | | * | * | * | | |- ... |: Open C :| D | E | F | G | A | A# | B |- ... |: Nut 0:| 2| 4| 5| 7| 9| 10| 11|- ... |: Bridge
Taylor Formula
For precise calculations.
Taylor formula:
- string tension
- F
- string length
- l
- frequency
- f
- string diameter
- d
- string density
- Ro
- Pi=3.14159
- π
F = (2l/f)2*π*d2/4*Ro
Air resonance
A Standard Soprano Ukulele has an air resonance of about 260 Hz, which is Middle C, the third string.
Ukulele Variant
See Tahitian Ukuleles also known as the Tahitian Banjo, These are constructed similar to a banjo with the bridge on a thin disk of wood rather than a drum. Usually strung with 8 strings in 4 courses, tuned like a Ukulele to G4 C4 E4 A4.
Ukulele Tunings
The Ukulele descended from the Rajão, which was tuned in D G C E A. The Ukulele keeps the strings, GCEA.
- Common Soprano (reentrant, or high 4th tuning)
- G4 C4 E4 A4
- Low G Soprano (or low 4th tuning)
- G3 C4 E4 A4
- D6 or D tuning, (AKA "Mainland"), also reentrant, a step higher than GCEA)
- A4 D4 F#4 B4
Common fret board scale lengths
- Ukulele Sopranissimo Scale (pocket Ukulele)
- 11 inches
- Ukulele Sopranino or Bambino Ukulele
- 12 inches (one found as 11.9")
- Ukulele Soprano (minimum length mentioned)
- 13 inches (approximately 330 mm)
- Ukulele Soprano (common length mentioned)
- 13.5 inches
- Ukulele Soprano (from "Martin Guitars - A History" by Mike Longworth)
- 13-5/8 inches (13.625")
- Ukulele Soprano Kamaka
- 13-9/16 inches (13.5625")
- Ukulele Soprano Kala/Makala
- 13-11/16 inches (13.6875", approximately 348 mm rounds to 13.7")
- Ukulele Concert
- 15 inches (also found reference giving 14-3/4)
- Ukulele Tenor
- 17 inches
- Ukulele Baritone
- 21-1/8 inches (also found references giving 19)
- Mandolin Gibson F style
- 13.875 inches
- Mandolin Gibson A style
- 14.125 inches
- Guitar Tenor short scale
- 21 inches
- Guitar Tenor long scale
- 23 inches
- Guitar short scale
- 24.5 inches
- Guitar from Gibson, Standard, and Guild
- 24.75 inches
- Guitar from Paul Reed Smith, National, and Dobro
- 25 inches
- Guitar models Fender Telecaster and Stratocaster
- 25.5 inches
- Guitar Baritone
- 27.5 inches
- Guitar Bass Fender short scale
- 30 inches
- Guitar Bass Fender long scale
- 34 inches
Equal Temperament
To calculate distance from FretA to FretB divide the Scale Length Remaining (FretA to bridge) by 17.817. Three digits of precision is impossible. In fact in the old days they just used 18 instead of 17.817. You might also see 17.835 in old references. This value was used to add in a fudge factor to accommodate the musical tastes of the time (sort of how the standard for the pitch of A above middle C wasn't always 440 Hz (Concert Pitch)).
fret # factor 1 0.056126 2 0.109101 3 0.159104 4 0.206291 5 0.250847 6 0.292893 7 0.33258 8 0.370039 9 0.405396 10 0.438769 11 0.470268 12 0.5 13 0.528063 14 0.554551 15 0.579552 16 0.60315 17 0.625423 18 0.646447 19 0.66629 20 0.68502 21 0.702698 22 0.719385 23 0.735134 24 0.75
d = s – (s / 2(n / 12))
- d
- distance from nut to fret number, n
- s
- scale or string length
- n
- fret number
Here is a little Python script that will output fret positions given a string length.
#!/usr/bin/env python # This will print the distance from the nut to each fret # over a two octave range given an open string length. import sys # Set string length here. Units don't matter. Output is in the same units. string_length = 14.0 fret_length_factors = [ 0.056126, 0.109101, 0.159104, 0.206291, 0.250847, 0.292893, 0.33258, 0.370039, 0.405396, 0.438769, 0.470268, 0.5, 0.528063, 0.554551, 0.579552, 0.60315, 0.625423, 0.646447, 0.66629, 0.68502, 0.702698, 0.719385, 0.735134, 0.75 ] fret_number = 1 for length_factor in fret_length_factors: sys.stdout.write('%3d %5.2f'%(fret_number, (length_factor * string_length))) sys.stdout.write('\n') fret_number += 1 sys.stdout.write('\n') # This should give the same results. # This calculates the same information in a different way. for fret_number in range(1,25): fret_distance = string_length - (string_length / (2 ** (fret_number/12.0))) sys.stdout.write('%3d %5.2f'%(fret_number, fret_distance)) sys.stdout.write('\n')
Gives the following table:
fret distance from number nut to fret 1 0.79 2 1.53 3 2.23 4 2.89 5 3.51 6 4.10 7 4.66 8 5.18 9 5.68 10 6.14 11 6.58 12 7.00 13 7.39 14 7.76 15 8.11 16 8.44 17 8.76 18 9.05 19 9.33 20 9.59 21 9.84 22 10.07 23 10.29 24 10.50
Tables for some common fret board lengths (scale length)
Column definitions: 1: Fret number 2: Distance from nut to fret in your units, to thousandths. 3: your units rounded to 32ths. 4: your units rounded to 16ths. 5: your units as inches converted to millimeters. Ignore this if your units were not in inches.
6 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 0.337 0+11/32 0+ 5/16 8.554mm 2 0.655 0+21/32 0+10/16 16.627mm 3 0.955 0+31/32 0+15/16 24.247mm 4 1.238 1+ 8/32 1+ 4/16 31.440mm 5 1.505 1+16/32 1+ 8/16 38.229mm 6 1.757 1+24/32 1+12/16 44.637mm 7 1.995 1+32/32 1+16/16 50.685mm 8 2.220 2+ 7/32 2+ 4/16 56.394mm 9 2.432 2+14/32 2+ 7/16 61.782mm 10 2.633 2+20/32 2+10/16 66.868mm 11 2.822 2+26/32 2+13/16 71.669mm 12 3.000 3+ 0/32 3+ 0/16 76.200mm 13 3.168 3+ 5/32 3+ 3/16 80.477mm 14 3.327 3+10/32 3+ 5/16 84.514mm 15 3.477 3+15/32 3+ 8/16 88.324mm 16 3.619 3+20/32 3+10/16 91.920mm 17 3.753 3+24/32 3+12/16 95.315mm 18 3.879 3+28/32 3+14/16 98.518mm 19 3.998 3+32/32 3+16/16 101.543mm 20 4.110 4+ 4/32 4+ 2/16 104.397mm 21 4.216 4+ 7/32 4+ 3/16 107.091mm 22 4.316 4+10/32 4+ 5/16 109.634mm 23 4.411 4+13/32 4+ 7/16 112.034mm 24 4.500 4+16/32 4+ 8/16 114.300mm
8 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 0.449 0+14/32 0+ 7/16 11.405mm 2 0.873 0+28/32 0+14/16 22.169mm 3 1.273 1+ 9/32 1+ 4/16 32.330mm 4 1.650 1+21/32 1+10/16 41.920mm 5 2.007 2+ 0/32 2+ 0/16 50.972mm 6 2.343 2+11/32 2+ 5/16 59.516mm 7 2.661 2+21/32 2+11/16 67.580mm 8 2.960 2+31/32 2+15/16 75.192mm 9 3.243 3+ 8/32 3+ 4/16 82.377mm 10 3.510 3+16/32 3+ 8/16 89.158mm 11 3.762 3+24/32 3+12/16 95.559mm 12 4.000 4+ 0/32 4+ 0/16 101.600mm 13 4.225 4+ 7/32 4+ 4/16 107.302mm 14 4.436 4+14/32 4+ 7/16 112.685mm 15 4.636 4+20/32 4+10/16 117.765mm 16 4.825 4+26/32 4+13/16 122.560mm 17 5.003 5+ 0/32 5+ 0/16 127.086mm 18 5.172 5+ 5/32 5+ 3/16 131.358mm 19 5.330 5+11/32 5+ 5/16 135.390mm 20 5.480 5+15/32 5+ 8/16 139.196mm 21 5.622 5+20/32 5+10/16 142.788mm 22 5.755 5+24/32 5+12/16 146.179mm 23 5.881 5+28/32 5+14/16 149.379mm 24 6.000 6+ 0/32 6+ 0/16 152.400mm
10 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 0.561 0+18/32 0+ 9/16 14.256mm 2 1.091 1+ 3/32 1+ 1/16 27.712mm 3 1.591 1+19/32 1+ 9/16 40.412mm 4 2.063 2+ 2/32 2+ 1/16 52.400mm 5 2.508 2+16/32 2+ 8/16 63.715mm 6 2.929 2+30/32 2+15/16 74.395mm 7 3.326 3+10/32 3+ 5/16 84.475mm 8 3.700 3+22/32 3+11/16 93.990mm 9 4.054 4+ 2/32 4+ 1/16 102.971mm 10 4.388 4+12/32 4+ 6/16 111.447mm 11 4.703 4+22/32 4+11/16 119.448mm 12 5.000 5+ 0/32 5+ 0/16 127.000mm 13 5.281 5+ 9/32 5+ 4/16 134.128mm 14 5.546 5+17/32 5+ 9/16 140.856mm 15 5.796 5+25/32 5+13/16 147.206mm 16 6.031 6+ 1/32 6+ 1/16 153.200mm 17 6.254 6+ 8/32 6+ 4/16 158.858mm 18 6.464 6+15/32 6+ 7/16 164.197mm 19 6.663 6+21/32 6+11/16 169.238mm 20 6.850 6+27/32 6+14/16 173.995mm 21 7.027 7+ 1/32 7+ 0/16 178.485mm 22 7.194 7+ 6/32 7+ 3/16 182.724mm 23 7.351 7+11/32 7+ 6/16 186.724mm 24 7.500 7+16/32 7+ 8/16 190.500mm
12 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 0.674 0+22/32 0+11/16 17.107mm 2 1.309 1+10/32 1+ 5/16 33.254mm 3 1.909 1+29/32 1+15/16 48.495mm 4 2.476 2+15/32 2+ 8/16 62.880mm 5 3.010 3+ 0/32 3+ 0/16 76.458mm 6 3.515 3+16/32 3+ 8/16 89.274mm 7 3.991 3+32/32 3+16/16 101.370mm 8 4.440 4+14/32 4+ 7/16 112.788mm 9 4.865 4+28/32 4+14/16 123.565mm 10 5.265 5+ 8/32 5+ 4/16 133.737mm 11 5.643 5+21/32 5+10/16 143.338mm 12 6.000 6+ 0/32 6+ 0/16 152.400mm 13 6.337 6+11/32 6+ 5/16 160.954mm 14 6.655 6+21/32 6+10/16 169.027mm 15 6.955 6+31/32 6+15/16 176.647mm 16 7.238 7+ 8/32 7+ 4/16 183.840mm 17 7.505 7+16/32 7+ 8/16 190.629mm 18 7.757 7+24/32 7+12/16 197.037mm 19 7.995 7+32/32 7+16/16 203.085mm 20 8.220 8+ 7/32 8+ 4/16 208.794mm 21 8.432 8+14/32 8+ 7/16 214.182mm 22 8.633 8+20/32 8+10/16 219.268mm 23 8.822 8+26/32 8+13/16 224.069mm 24 9.000 9+ 0/32 9+ 0/16 228.600mm
14 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 0.786 0+25/32 0+13/16 19.958mm 2 1.527 1+17/32 1+ 8/16 38.796mm 3 2.227 2+ 7/32 2+ 4/16 56.577mm 4 2.888 2+28/32 2+14/16 73.360mm 5 3.512 3+16/32 3+ 8/16 89.201mm 6 4.101 4+ 3/32 4+ 2/16 104.153mm 7 4.656 4+21/32 4+10/16 118.265mm 8 5.181 5+ 6/32 5+ 3/16 131.586mm 9 5.676 5+22/32 5+11/16 144.159mm 10 6.143 6+ 5/32 6+ 2/16 156.026mm 11 6.584 6+19/32 6+ 9/16 167.227mm 12 7.000 7+ 0/32 7+ 0/16 177.800mm 13 7.393 7+13/32 7+ 6/16 187.779mm 14 7.764 7+24/32 7+12/16 197.198mm 15 8.114 8+ 4/32 8+ 2/16 206.089mm 16 8.444 8+14/32 8+ 7/16 214.480mm 17 8.756 8+24/32 8+12/16 222.401mm 18 9.050 9+ 2/32 9+ 1/16 229.876mm 19 9.328 9+10/32 9+ 5/16 236.933mm 20 9.590 9+19/32 9+ 9/16 243.593mm 21 9.838 9+27/32 9+13/16 249.879mm 22 10.071 10+ 2/32 10+ 1/16 255.813mm 23 10.292 10+ 9/32 10+ 5/16 261.414mm 24 10.500 10+16/32 10+ 8/16 266.700mm
16 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 0.898 0+29/32 0+14/16 22.809mm 2 1.746 1+24/32 1+12/16 44.339mm 3 2.546 2+17/32 2+ 9/16 64.660mm 4 3.301 3+10/32 3+ 5/16 83.840mm 5 4.014 4+ 0/32 4+ 0/16 101.944mm 6 4.686 4+22/32 4+11/16 119.032mm 7 5.321 5+10/32 5+ 5/16 135.161mm 8 5.921 5+29/32 5+15/16 150.384mm 9 6.486 6+16/32 6+ 8/16 164.753mm 10 7.020 7+ 1/32 7+ 0/16 178.316mm 11 7.524 7+17/32 7+ 8/16 191.117mm 12 8.000 8+ 0/32 8+ 0/16 203.200mm 13 8.449 8+14/32 8+ 7/16 214.605mm 14 8.873 8+28/32 8+14/16 225.369mm 15 9.273 9+ 9/32 9+ 4/16 235.530mm 16 9.650 9+21/32 9+10/16 245.120mm 17 10.007 10+ 0/32 10+ 0/16 254.172mm 18 10.343 10+11/32 10+ 5/16 262.716mm 19 10.661 10+21/32 10+11/16 270.780mm 20 10.960 10+31/32 10+15/16 278.392mm 21 11.243 11+ 8/32 11+ 4/16 285.577mm 22 11.510 11+16/32 11+ 8/16 292.358mm 23 11.762 11+24/32 11+12/16 298.759mm 24 12.000 12+ 0/32 12+ 0/16 304.800mm
18 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 1.010 1+ 0/32 1+ 0/16 25.661mm 2 1.964 1+31/32 1+15/16 49.881mm 3 2.864 2+28/32 2+14/16 72.742mm 4 3.713 3+23/32 3+11/16 94.320mm 5 4.515 4+16/32 4+ 8/16 114.687mm 6 5.272 5+ 9/32 5+ 4/16 133.911mm 7 5.986 5+32/32 5+16/16 152.056mm 8 6.661 6+21/32 6+11/16 169.182mm 9 7.297 7+10/32 7+ 5/16 185.347mm 10 7.898 7+29/32 7+14/16 200.605mm 11 8.465 8+15/32 8+ 7/16 215.007mm 12 9.000 9+ 0/32 9+ 0/16 228.600mm 13 9.505 9+16/32 9+ 8/16 241.430mm 14 9.982 9+31/32 9+16/16 253.541mm 15 10.432 10+14/32 10+ 7/16 264.971mm 16 10.857 10+27/32 10+14/16 275.760mm 17 11.258 11+ 8/32 11+ 4/16 285.944mm 18 11.636 11+20/32 11+10/16 295.555mm 19 11.993 11+32/32 11+16/16 304.628mm 20 12.330 12+11/32 12+ 5/16 313.191mm 21 12.649 12+21/32 12+10/16 321.274mm 22 12.949 12+30/32 12+15/16 328.903mm 23 13.232 13+ 7/32 13+ 4/16 336.103mm 24 13.500 13+16/32 13+ 8/16 342.900mm
20 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 1.123 1+ 4/32 1+ 2/16 28.512mm 2 2.182 2+ 6/32 2+ 3/16 55.423mm 3 3.182 3+ 6/32 3+ 3/16 80.825mm 4 4.126 4+ 4/32 4+ 2/16 104.800mm 5 5.017 5+ 1/32 5+ 0/16 127.430mm 6 5.858 5+27/32 5+14/16 148.790mm 7 6.652 6+21/32 6+10/16 168.951mm 8 7.401 7+13/32 7+ 6/16 187.980mm 9 8.108 8+ 3/32 8+ 2/16 205.941mm 10 8.775 8+25/32 8+12/16 222.895mm 11 9.405 9+13/32 9+ 6/16 238.896mm 12 10.000 10+ 0/32 10+ 0/16 254.000mm 13 10.561 10+18/32 10+ 9/16 268.256mm 14 11.091 11+ 3/32 11+ 1/16 281.712mm 15 11.591 11+19/32 11+ 9/16 294.412mm 16 12.063 12+ 2/32 12+ 1/16 306.400mm 17 12.508 12+16/32 12+ 8/16 317.715mm 18 12.929 12+30/32 12+15/16 328.395mm 19 13.326 13+10/32 13+ 5/16 338.475mm 20 13.700 13+22/32 13+11/16 347.990mm 21 14.054 14+ 2/32 14+ 1/16 356.971mm 22 14.388 14+12/32 14+ 6/16 365.447mm 23 14.703 14+22/32 14+11/16 373.448mm 24 15.000 15+ 0/32 15+ 0/16 381.000mm
22 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 1.235 1+ 8/32 1+ 4/16 31.363mm 2 2.400 2+13/32 2+ 6/16 60.966mm 3 3.500 3+16/32 3+ 8/16 88.907mm 4 4.539 4+17/32 4+ 9/16 115.280mm 5 5.519 5+17/32 5+ 8/16 140.173mm 6 6.444 6+14/32 6+ 7/16 163.669mm 7 7.317 7+10/32 7+ 5/16 185.846mm 8 8.141 8+ 5/32 8+ 2/16 206.778mm 9 8.919 8+29/32 8+15/16 226.536mm 10 9.653 9+21/32 9+10/16 245.184mm 11 10.346 10+11/32 10+ 6/16 262.786mm 12 11.000 11+ 0/32 11+ 0/16 279.400mm 13 11.617 11+20/32 11+10/16 295.082mm 14 12.200 12+ 6/32 12+ 3/16 309.883mm 15 12.750 12+24/32 12+12/16 323.854mm 16 13.269 13+ 9/32 13+ 4/16 337.040mm 17 13.759 13+24/32 13+12/16 349.487mm 18 14.222 14+ 7/32 14+ 4/16 361.234mm 19 14.658 14+21/32 14+11/16 372.323mm 20 15.070 15+ 2/32 15+ 1/16 382.789mm 21 15.459 15+15/32 15+ 7/16 392.668mm 22 15.826 15+26/32 15+13/16 401.992mm 23 16.173 16+ 6/32 16+ 3/16 410.793mm 24 16.500 16+16/32 16+ 8/16 419.100mm
24 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 1.347 1+11/32 1+ 6/16 34.214mm 2 2.618 2+20/32 2+10/16 66.508mm 3 3.818 3+26/32 3+13/16 96.990mm 4 4.951 4+30/32 4+15/16 125.760mm 5 6.020 6+ 1/32 6+ 0/16 152.916mm 6 7.029 7+ 1/32 7+ 0/16 178.548mm 7 7.982 7+31/32 7+16/16 202.741mm 8 8.881 8+28/32 8+14/16 225.576mm 9 9.730 9+23/32 9+12/16 247.130mm 10 10.530 10+17/32 10+ 8/16 267.474mm 11 11.286 11+ 9/32 11+ 5/16 286.676mm 12 12.000 12+ 0/32 12+ 0/16 304.800mm 13 12.674 12+22/32 12+11/16 321.907mm 14 13.309 13+10/32 13+ 5/16 338.054mm 15 13.909 13+29/32 13+15/16 353.295mm 16 14.476 14+15/32 14+ 8/16 367.680mm 17 15.010 15+ 0/32 15+ 0/16 381.258mm 18 15.515 15+16/32 15+ 8/16 394.074mm 19 15.991 15+32/32 15+16/16 406.170mm 20 16.440 16+14/32 16+ 7/16 417.588mm 21 16.865 16+28/32 16+14/16 428.365mm 22 17.265 17+ 8/32 17+ 4/16 438.537mm 23 17.643 17+21/32 17+10/16 448.138mm 24 18.000 18+ 0/32 18+ 0/16 457.200mm
32 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 1.796 1+25/32 1+13/16 45.619mm 2 3.491 3+16/32 3+ 8/16 88.678mm 3 5.091 5+ 3/32 5+ 1/16 129.319mm 4 6.602 6+19/32 6+10/16 167.680mm 5 8.027 8+ 1/32 8+ 0/16 203.888mm 6 9.373 9+12/32 9+ 6/16 238.064mm 7 10.643 10+21/32 10+10/16 270.321mm 8 11.841 11+27/32 11+13/16 300.768mm 9 12.973 12+31/32 12+16/16 329.506mm 10 14.041 14+ 1/32 14+ 1/16 356.631mm 11 15.049 15+ 2/32 15+ 1/16 382.234mm 12 16.000 16+ 0/32 16+ 0/16 406.400mm 13 16.898 16+29/32 16+14/16 429.209mm 14 17.746 17+24/32 17+12/16 450.739mm 15 18.546 18+17/32 18+ 9/16 471.060mm 16 19.301 19+10/32 19+ 5/16 490.240mm 17 20.014 20+ 0/32 20+ 0/16 508.344mm 18 20.686 20+22/32 20+11/16 525.432mm 19 21.321 21+10/32 21+ 5/16 541.561mm 20 21.921 21+29/32 21+15/16 556.784mm 21 22.486 22+16/32 22+ 8/16 571.153mm 22 23.020 23+ 1/32 23+ 0/16 584.716mm 23 23.524 23+17/32 23+ 8/16 597.517mm 24 24.000 24+ 0/32 24+ 0/16 609.600mm
36 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 2.021 2+ 1/32 2+ 0/16 51.321mm 2 3.928 3+30/32 3+15/16 99.762mm 3 5.728 5+23/32 5+12/16 145.484mm 4 7.427 7+14/32 7+ 7/16 188.640mm 5 9.030 9+ 1/32 9+ 0/16 229.374mm 6 10.544 10+17/32 10+ 9/16 267.822mm 7 11.973 11+31/32 11+16/16 304.111mm 8 13.321 13+10/32 13+ 5/16 338.364mm 9 14.594 14+19/32 14+10/16 370.695mm 10 15.796 15+25/32 15+13/16 401.210mm 11 16.930 16+30/32 16+15/16 430.013mm 12 18.000 18+ 0/32 18+ 0/16 457.200mm 13 19.010 19+ 0/32 19+ 0/16 482.861mm 14 19.964 19+31/32 19+15/16 507.081mm 15 20.864 20+28/32 20+14/16 529.942mm 16 21.713 21+23/32 21+11/16 551.520mm 17 22.515 22+16/32 22+ 8/16 571.887mm 18 23.272 23+ 9/32 23+ 4/16 591.111mm 19 23.986 23+32/32 23+16/16 609.256mm 20 24.661 24+21/32 24+11/16 626.382mm 21 25.297 25+10/32 25+ 5/16 642.547mm 22 25.898 25+29/32 25+14/16 657.805mm 23 26.465 26+15/32 26+ 7/16 672.207mm 24 27.000 27+ 0/32 27+ 0/16 685.800mm
42 inch scale length
1: 2: 3: 4: 5: ------------------------------------------------------------------------------- 1 2.357 2+11/32 2+ 6/16 59.875mm 2 4.582 4+19/32 4+ 9/16 116.389mm 3 6.682 6+22/32 6+11/16 169.732mm 4 8.665 8+21/32 8+11/16 220.080mm 5 10.536 10+17/32 10+ 9/16 267.603mm 6 12.302 12+10/32 12+ 5/16 312.458mm 7 13.968 13+31/32 13+15/16 354.796mm 8 15.542 15+17/32 15+ 9/16 394.758mm 9 17.027 17+ 1/32 17+ 0/16 432.477mm 10 18.428 18+14/32 18+ 7/16 468.079mm 11 19.751 19+24/32 19+12/16 501.682mm 12 21.000 21+ 0/32 21+ 0/16 533.400mm 13 22.179 22+ 6/32 22+ 3/16 563.337mm 14 23.291 23+ 9/32 23+ 5/16 591.595mm 15 24.341 24+11/32 24+ 5/16 618.266mm 16 25.332 25+11/32 25+ 5/16 643.440mm 17 26.268 26+ 9/32 26+ 4/16 667.202mm 18 27.151 27+ 5/32 27+ 2/16 689.629mm 19 27.984 27+31/32 27+16/16 710.798mm 20 28.771 28+25/32 28+12/16 730.779mm 21 29.513 29+16/32 29+ 8/16 749.638mm 22 30.214 30+ 7/32 30+ 3/16 767.439mm 23 30.876 30+28/32 30+14/16 784.241mm 24 31.500 31+16/32 31+ 8/16 800.100mm
For a 16" fret board (with fractions of an inch rounded to 16ths) use:
fret | distance from nut to fret number | in three different precisions -------+---------------------------------- # | hundredths 32nds 16ths ------------------------------------------ 1 | 0.90 29/32 14/16 2 | 1.75 1+24/32 1+12/16 3 | 2.55 2+17/32 2+ 9/16 4 | 3.30 3+10/32 3+ 5/16 5 | 4.01 4+ 0/32 4+ 0/16 6 | 4.69 4+22/32 4+11/16 7 | 5.32 5+10/32 5+ 5/16 8 | 5.92 5+29/32 5+15/16 9 | 6.49 6+16/32 6+ 8/16 10 | 7.02 7+ 1/32 7+ 0/16 11 | 7.52 7+17/32 7+ 8/16 12 | 8.00 8+ 0/32 8+ 0/16 ___ 1 octave 13 | 8.45 8+14/32 8+ 7/16 14 | 8.87 8+28/32 8+14/16 15 | 9.27 9+ 9/32 9+ 4/16 16 | 9.65 9+21/32 9+10/16 17 | 10.01 10+ 0/32 10+0/16 18 | 10.34 10+11/32 10+5/16 _ _ _ one and a half octaves 19 | 10.66 10+21/32 10+11/16 20 | 10.96 10+31/32 10+15/16 21 | 11.24 11+ 8/32 11+ 4/16 22 | 11.51 11+16/32 11+ 8/16 23 | 11.76 11+24/32 11+12/16 24 | 12.00 12+ 0/32 12+ 0/16 ___ 2 octaves