53-EDD

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Dot-Guide for 53-EDD instruments

53-EDD Fretboard is based on the formula (Scale_Length/(2^(x/53))). This system is related as Extended Pythagorean Musical Scale System (more info here). A parallel indagation around of 53 notes per ditave explored on a guitar, was made by Eduardo Sábat-Garibaldi. His particular tuning was a kind of enharmonic system, blending Pythagorean and Ptolomeic theoric systems, that are about harmonics 3 & 5 limits for intonation, not being an EDD system.

For a practicalness reason, fret a guitar with normal scale length within 53-EDD looks in aspect ludicrous, because the sizes in the fingers not comforms with a irrational space of 0,8mm (0.0315") between frets in the last frets. The scheme in the picture below visualize the aspect of a Short Bass Scale Length (818mm [32.2"]) with 84 frets, not trespassing the space between the cuts for the frets under 3,556mm (0.14") for a best employment over the fretboard, and no neccesary string it with bass strings, with piccolo bass strings or custom extra-long guitar strings are adequate very well.

Normally a 53-EDD fretboard can be applied (with a first impression) with the 2L3s 13;9 Relation, 13 9 9 9 13 :

53-EDD Fibass 0.png

The dots are suited in the places 13· 22· 31· 40· 53: 66· 75· & 84·

Step Purdal size Cent size
01 186,79 22.642
02 373,58 45.283
03 560,38 67.925
04 747,17 90.566
05 933,96 113.208
06 1120,75 135.849
07 1307,55 158.491
08 1494,34 181.132
09 1681,13 203.774
10 1867,92 226.415
11 2054,72 249.057
12 2241,51 271.698
13· 2428,3 294.34
14 2615,09 316.981
15 2801,89 339.623
16 2988,68 362.264
17 3175,47 384.906
18 3362,26 407.547
19 3549,06 430.189
20 3735,85 452.83
21 3922,64 475.472
22· 4109,43 498.113
23 4296,23 520.755
24 4483,02 543.396
25 4669,81 566.038
26 4856,6 588.679
27 5043,4 611.321
28 5230,19 633.962
29 5416,98 656.604
30 5603,77 679.245
31· 5790,57 701.887
32 5977,36 724.528
33 6164,15 747.17
34 6350,94 769.811
35 6537,74 792.453
36 6724,53 815.094
37 6911,32 837.736
38 7098,11 860.377
39 7284,91 883.019
40· 7471,7 905.66
41 7658,49 928.302
42 7845,28 950.943
43 8032,08 973.585
44 8218,87 996.226
45 8405,66 1018.868
46 8592,45 1041.509
47 8779,25 1064.151
48 8966,04 1086.792
49 9152,83 1109.434
50 9339,62 1132.075
51 9526,42 1154.717
52 9713,21 1177.358
53\0: 9900\0 1200\0

But other type for dot a 53-EDD fretboard, maybe a bit similar with the first dot-guide, guards relation by similar way with 29-EDD :

53-EDD Fibass 1.png

This dots are in the places 9· 11· 20· 22· 31· 33· 42· 44· 53: 62· 64· 73· 75· 84· denoting a scale of 5L4s 9;2 Relation, 9 2 9 2 9 2 9 2 9.

Step Purdal size Cent size
1 186,79 22.642
2 373,58 45.283
3 560,38 67.925
4 747,17 90.566
5 933,96 113.208
6 1120,75 135.849
7 1307,55 158.491
8 1494,34 181.132
1681,13 203.774
10 1867,92 226.415
11· 2054,72 249.057
12 2241,51 271.698
13 2428,3 294.34
14 2615,09 316.981
15 2801,89 339.623
16 2988,68 362.264
17 3175,47 384.906
18 3362,26 407.547
19 3549,06 430.189
20· 3735,85 452.83
21 3922,64 475.472
22· 4109,43 498.113
23 4296,23 520.755
24 4483,02 543.396
25 4669,81 566.038
26 4856,6 588.679
27 5043,4 611.321
28 5230,19 633.962
29 5416,98 656.604
30 5603,77 679.245
31· 5790,57 701.887
32 5977,36 724.528
33· 6164,15 747.17
34 6350,94 769.811
35 6537,74 792.453
36 6724,53 815.094
37 6911,32 837.736
38 7098,11 860.377
39 7284,91 883.019
40 7471,7 905.66
41 7658,49 928.302
42· 7845,28 950.943
43 8032,08 973.585
44· 8218,87 996.226
45 8405,66 1018.868
46 8592,45 1041.509
47 8779,25 1064.151
48 8966,04 1086.792
49 9152,83 1109.434
50 9339,62 1132.075
51 9526,42 1154.717
52 9713,21 1177.358
53\0: 9900\0 1200\0