This is an example of the fretting spreadsheet, which will run in M$ Excel, M$Works,
and many other spreadsheet programs including GnuMeric
It can be used to calculate values and positions for any 5 Large + 2 small meantone or equal temperament tuning system.
This example shows LucyTuned values and fret positions for 650mm (nut to bridge) fretboard.
Fretting positions for LucyTuned guitars and other fretted instruments using 5 Large plus 2 small intervals per octave
KEY: Large small At start Changes made to tET at D22 overule other changes to L ratio at J6
distance 'n' tone ET octave default setting are Changing adjustable L&s from (F6 to F11) and (H6 to H11) sets (J6 and J7)
Logic of 5L+2s LucyTuned values v (Adjustable) v Used for fretting calculations
Intervals Ratio cents cents cent check Ratios Values Ratios cents
Large (II) L 1.116633 190.9859 190.986 190.986 1.11663 Large (L) 1.116633 190.99 Adjust
small (bII) s 1.073344 122.5352 122.535 122.535 1.07334 small (s) 1.073344 122.54 Adjust
Third (III) 2L 1.246869 381.9719 381.972 381.972 1.24687 Third 1.246869 381.97
Fourth (IV) 2L+s 1.338319 504.507 504.507 504.507 1.33832 Fourth 1.338319 504.51
Fifth (V) 3L+s 1.494412 695.493 695.493 695.493 1.49441 Fifth 1.494412 695.49
Octv (VIII) 5L+2s 2 1200 1200 1200.000 2.0000 Octave 2.000000 1200.00
mm or inch Nut to bridge distance = 650 < ^ Adjustable ^ > see below table for tET adjustments
(Current values are set for LucyTuning with 650 millimetres nut to bridge) ^
Fretting may be calculated for any 5L + 2s tuning system for any bridge to nut distance Large Ratio (L) @ [J6]
Values indicated "Adjustable" may be changed by user ^ small ratio (s) @ [J7]
by changing Nut to Bridge distance (E12) ^ All fretting positions are
by changing ratios (H6, H7, or H11) > > > ^ calculated from (J6 & J7)
by cent values (F6, F7, or F11)
by specifying an equal temperament (D22)
For equal temperaments (tET) Eg. 12, 19, 31, 53 etc.
Change value of (D22) below V Defaults for Column D at start
Equal intervals (units) per octave 2 < Adjustable 2
OCTAVE RATIO (adjustable) 2.000000 < Adjustable 2.000000
Cents per unit = 600.00 Octave = 1200.00
Values Ratios cents Units Interval
II (L) 1.000000 0.00 0 Large N.B. IF (D24) = other than 2 THEN Ratios (J6 & J7) are
bII (s) 1.414214 600.00 1 small used to calculate fretting from L&s Ratios at (C26 & C27).
III (2L) 1.000000 0.00 0 Third
IV (2L+s) 1.414214 600.00 1 Fourth
V (3L+s) 1.414214 600.00 1 Fifth
VIII (5L+2s) 2.000000 1200.00 2 Octave
Cents *=fretboard landmarks FIRST OCTAVE L & s SECOND OCTAVE
from Notename Scale Nut to Fret Fret Fret intervals Nut to Fret Fret Fret
Open on Fifth (A) Position Fret Number Number Number from Open Fret Number Number Number
2nd Octave string from A Distance (0-19) (0-31) (0-53) 2nd Octave Distance (0-19) (0-31) (0-53)
add 1200 A I 0.000 Nut Nut Nut add 5L+2s 325.000 19 31 53
14.37 Gx# xVII 5.372 - - 1 2L-3s 327.686 - - 54
54.08 Bbb bbII 19.992 - 1 2 2s-L 334.996 - 32 55
68.45 A# #I 25.199 1 2 3 L-s 337.599 20 33 56
82.82 Gxx x#VII 30.362 - - 4 3L-4s 340.181 - - 57
108.17 Cbbb bbbbIII 39.370 - - 5 4s-2L 344.685 - - 58
122.54 Bb bII 44.416 2 3 6 s 347.208 21 34 59
136.90 Ax xI 49.421 - 4 7 2L-2s 349.710 - 35 60
176.62 Cbb bbbIII 63.042 - - 8 3s-L 356.521 - - 61
190.99 B II 67.893 3 5 9 L 358.946 22 36 62
205.35 Ax# x#I 72.703 - - 10 3L-3s 361.352 - - 63
245.07 Cb bbIII 85.797 - 6 11 2s 367.898 - 37 64
259.44 B# #II 90.460 4 7 12 2L-s 370.230 23 38 65
299.15 Dbbb bbbIV 103.150 - - 13 4s-L 376.575 - - 66
313.52 C * bIII 107.670 * 5 * * 8 * * 14 * * L+s * 378.835 * 24 * * 39 * * 67 *
327.89 Bx xII 112.151 - - 15 3L-2s 381.076 - - 68
367.61 Dbb bbIV 124.350 - 9 16 3s 387.175 - 40 69
381.97 C# III 128.694 6 10 17 2L 389.347 25 41 70
396.34 Bx# x#II 133.002 - - 18 4L-3s 391.501 - - 71
436.06 Db bIV 144.728 7 11 19 L+2s 397.364 26 42 72
450.42 Cx #III 148.904 - 12 20 3L-s 399.452 - 43 73
490.14 Ebbb bbbV 160.269 - - 21 4s 405.135 - - 74
504.51 D * * IV 164.316 * 8 * * 13 * * 22 * * 2L+s * 407.158 * 27 * * 44 * * 75 *
518.87 Cx# xIII 168.330 - - 23 4L-2s 409.165 - - 76
558.59 Ebb bbV 179.255 - 14 24 L+3s 414.627 - 45 77
572.96 D# #IV 183.145 9 15 25 3L 416.572 28 46 78
587.32 Cxx x#III 187.003 - - 26 5L-3s 418.501 - - 79
612.68 Fbbb bbbbVI 193.734 - - 27 5s 421.867 - - 80
627.04 Eb bV 197.504 10 16 28 2L+2s 423.752 29 47 81
641.41 Dx xIV 201.244 - 17 29 4L-s 425.622 - 48 82
681.13 Fbb bbbVI 211.422 - - 30 L+4s 430.711 - - 83
695.49 E * * V 215.046 * 11 * * 18 * * 31 * * 3L+s * 432.523 * 30 * * 49 * * 84 *
709.86 Dx# x#IV 218.641 - - 32 5L-2s 434.320 - - 85
749.58 Fb bbVI 228.424 - 19 33 2L+3s 439.212 - 50 86
763.94 E# #V 231.908 12 20 34 4L 440.954 31 51 87
803.66 Gbbb bbbbVII 241.391 - - 35 L+5s 445.695 - - 88
818.03 F bVI 244.768 13 21 36 3L+2s 447.384 32 52 89
832.39 Ex xV 248.116 - 22 37 5L-s 449.058 - 53 90
872.11 Gbb bbbVII 257.231 - - 38 2L+4s 453.616 - - 91
886.48 F# * * VI 260.477 * 14 * * 23 * * 39 * * 4L+s * 455.239 * 33 * * 54 * * 92 *
900.85 Ex# x#V 263.696 - - 40 6L-2s 456.848 - - 93
940.56 Gb bbVII 272.458 15 24 41 3L+3s 461.229 34 55 94
954.93 Fx #VI 275.578 - 25 42 5L 462.789 - 56 95
994.65 Abbb bbbVIII 284.070 - - 43 2L+5s 467.035 - - 96
1009.01 G bVII 287.094 16 26 44 4L+2s 468.547 35 57 97
1023.38 Fx# xVI 290.093 - - 45 6L-s 470.047 - - 98
1063.10 Abb bbVIII 298.256 - 27 46 3L+4s 474.128 - 58 99
1077.46 G# VII 301.163 17 28 47 5L+s 475.582 36 59 100
1091.83 Fxx x#VI 304.046 - - 48 7L-2s 477.023 - - 101
1117.18 Bbbbb bbbbIX 309.075 - - 49 2L+6s 479.538 - - 102
1131.55 Ab bVIII 311.892 18 29 50 4L+3s 480.946 37 60 103
1145.92 Gx #VII 314.687 - 30 51 6L 482.343 - 61 104
1185.63 Bbbb bbbII 322.292 - - 52 3L+5s 486.146 - - 105
1200.00 A ** VIIII 325.000 * 19 * * 31 * * 53 * * 5L+2s * 487.500 * 38 * * 62 * * 106 *
The contents of this spreadsheet for fretting, (which runs with Microsoft Works 4.0), are copyright LucyScaleDevelopments 1998,
It is provided free of charge for personal use and may only be resold with by the express permission of the copyright owner.
For permission to publish or resell contact: lucy@lucytune.com http://www.lucytune.com
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