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 |
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KEY: |
Large |
small |
At start |
Changes made to tET at D22 overule other changes to L ratio at J6 |
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distance |
'n' tone ET |
octave |
default setting are |
Changing adjustable L&s from (F6 to F11) and (H6 to H11) sets (J6 and J7) |
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Logic of 5L+2s |
LucyTuned values |
v (Adjustable) v |
Used for fretting calculations |
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Intervals |
Ratio |
cents |
cents |
cent check |
Ratios |
Values |
Ratios |
cents |
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Large (II) |
L |
1.116633 |
190.9859 |
190.986 |
190.986 |
1.11663 |
Large (L) |
1.116633 |
190.99 |
Adjust |
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small (bII) |
s |
1.073344 |
122.5352 |
122.535 |
122.535 |
1.07334 |
small (s) |
1.073344 |
122.54 |
Adjust |
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Third (III) |
2L |
1.246869 |
381.9719 |
381.972 |
381.972 |
1.24687 |
Third |
1.246869 |
381.97 |
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Fourth (IV) |
2L+s |
1.338319 |
504.507 |
504.507 |
504.507 |
1.33832 |
Fourth |
1.338319 |
504.51 |
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Fifth (V) |
3L+s |
1.494412 |
695.493 |
695.493 |
695.493 |
1.49441 |
Fifth |
1.494412 |
695.49 |
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Octv (VIII) |
5L+2s |
2 |
1200 |
1200 |
1200.000 |
2.0000 |
Octave |
2.000000 |
1200.00 |
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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) |
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Fretting may be calculated for any 5L + 2s tuning system for any bridge to nut distance |
Large Ratio (L) @ [J6] |
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Values indicated "Adjustable" may be changed by user |
^ |
small ratio (s) @ [J7] |
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by changing Nut to Bridge distance (E12) |
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^ |
All fretting positions are |
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by changing ratios (H6, H7, or H11) |
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> > > |
^ |
calculated from (J6 & J7) |
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by cent values (F6, F7, or F11) |
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by specifying an equal temperament (D22) |
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For equal temperaments (tET) Eg. 12, 19, 31, 53 etc. |
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Change value of (D22) below V |
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Defaults for Column D at start |
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Equal intervals (units) per octave |
2 |
< Adjustable |
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2 |
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OCTAVE RATIO (adjustable) |
2.000000 |
< Adjustable |
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2.000000 |
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Cents per |
unit = |
600.00 |
Octave = |
1200.00 |
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Values |
Ratios |
cents |
Units |
Interval |
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II (L) |
1.000000 |
0.00 |
0 |
Large |
N.B. IF (D24) = other than 2 THEN Ratios (J6 & J7) are |
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bII (s) |
1.414214 |
600.00 |
1 |
small |
used to calculate fretting from L&s Ratios at (C26 & C27). |
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III (2L) |
1.000000 |
0.00 |
0 |
Third |
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IV (2L+s) |
1.414214 |
600.00 |
1 |
Fourth |
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V (3L+s) |
1.414214 |
600.00 |
1 |
Fifth |
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VIII (5L+2s) |
2.000000 |
1200.00 |
2 |
Octave |
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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 * |
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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. |
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For permission to publish or resell contact: |
lucy@lucytune.com |
http://www.lucytune.com |
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