53-EDD

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 :

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 :

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
9·	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