57-EDD

Dot-Guide for 57-EDD instruments

57-EDD Fretboard is based on the formula (Scale_Length/(2^(x/57))). The most complex of Armodue resides here on 57-EDD. The 'but' with this, that is not comfortable for guitar, because the limt size between the cuts for put the frets is, in my consideration, 3,556mm (0.14"), and fretting a instrument with just 1 ditave is not very expansive nor generous. The solution with this system is, in the same cases of 46, 50 and 53 EDDs, applying it with a short bass scale length (818mm [32.2"]) with 84 frets.

In this first case, the dots are in Armodue position, favouring the scale 7 7 7 4 7 7 7 7 4, and the dots graphics a scale of 2L5s 11;7 Relation, in the places 11· 18· 25· 32· 39· 46· 57: 68· 75· & 82· (11 7 7 7 7 7 11) :

Step	Purdal size	Cent size
01	173,68	21.053
02	347,37	42.105
03	521,05	63.158
04	694,74	84.211
05	868,42	105.263
06	1042,11	126.316
07	1215,79	147.368
08	1389,47	168.421
09	1563,16	189.474
10	1736,84	210.526
11·	1910,53	231.579
12	2084,21	252.632
13	2257,89	273.684
14	2431,58	294.737
15	2605,26	315.789
16	2778,95	336.842
17	2952,63	357.895
18·	3126,32	378.947
19	3300	400
20	3473,68	421.053
21	3647,37	442.105
22	3821,05	463.158
23	3994,74	484.211
24	4168,42	505.263
25·	4342,11	526.316
26	4515,79	547.368
27	4689,47	568.421
28	4863,16	589.474
29	5036,84	610.526
30	5210,53	631.579
31	5384,21	652.632
32·	5557,89	673.684
33	5731,58	694.737
34	5905,26	715.789
35	6078,95	736.842
36	6252,63	757.895
37	6426,32	778.947
38	6600	800
39·	6773,68	821.053
40	6947,37	842.105
41	7121,05	863.158
42	7294,74	884.211
43	7468,42	905.263
44	7642,11	926.316
45	7815,79	947.368
46·	7989,47	968.421
47	8163,16	989.474
48	8336,84	1010.526
49	8510,53	1031.579
50	8684,21	1052.632
51	8857,89	1073.684
52	9031,58	1094.737
53	9205,26	1115.789
54	9378,95	1136.842
55	9552,63	1157.894
56	9726,32	1178.947
57\0:	9900\0	1200\0

Note that the 46th fret with the 6th mark is the note '8' quasi-perfect 7/4, just -3,3 Purd. of error (-0.41 Cents).

Another look for a 57-EDD fretboard is with this way:

The dots follows the scheme 7 3 7 3 7 3 7 3 7 3 7, a scale of 6L5s 7;3 Relation, in the places 7· 10· 17· 20· 27· 30· 37· 40· 47· 50· 57: 64· 67· 74· 77· & 84·

Step	Purdal size	Cent size
01	173,68	21.053
02	347,37	42.105
03	521,05	63.158
04	694,74	84.211
05	868,42	105.263
06	1042,11	126.316
07·	1215,79	147.368
08	1389,47	168.421
09	1563,16	189.474
10·	1736,84	210.526
11	1910,53	231.579
12	2084,21	252.632
13	2257,89	273.684
14	2431,58	294.737
15	2605,26	315.789
16	2778,95	336.842
17·	2952,63	357.895
18	3126,32	378.947
19	3300	400
20·	3473,68	421.053
21	3647,37	442.105
22	3821,05	463.158
23	3994,74	484.211
24	4168,42	505.263
25	4342,11	526.316
26	4515,79	547.368
27·	4689,47	568.421
28	4863,16	589.474
29	5036,84	610.526
30·	5210,53	631.579
31	5384,21	652.632
32	5557,89	673.684
33	5731,58	694.737
34	5905,26	715.789
35	6078,95	736.842
36	6252,63	757.895
37·	6426,32	778.947
38	6600	800
39	6773,68	821.053
40·	6947,37	842.105
41	7121,05	863.158
42	7294,74	884.211
43	7468,42	905.263
44	7642,11	926.316
45	7815,79	947.368
46	7989,47	968.421
47·	8163,16	989.474
48	8336,84	1010.526
49	8510,53	1031.579
50·	8684,21	1052.632
51	8857,89	1073.684
52	9031,58	1094.737
53	9205,26	1115.789
54	9378,95	1136.842
55	9552,63	1157.894
56	9726,32	1178.947
57\0:	9900\0	1200\0