41-EDD
Dot-Guide for 41-EDD instruments
41-EDD Fretboard is based on the formula (Scale_Length/(2^(x/41))). 41-EDD is the third EDD (after of 19 & 31 EDDs for Classic formers, and 16 & 25 for Armodue formers) with a great importance for musical intonation.
Aaron Andrew Hunt had advocate in his complex (but necessary) keyboards with the 41-EDD as elemental basis for his proper musical praxis with the 205-EDD (each interval is a JND), a triumph achieved inside his musical academic trajectory (and a great respect to his person).
Now, referring to fretted string instruments, 41-EDD have much variety for notation schemes, between those are Diatonic, Superdiatonic (Armodue), Bohlen-Pierce and 88cET approx, just for mention a few.
A new level ground for dot-guiding a 41-EDD fretboard is with this :
The dots are in the places 8· 13· 18· 23· 28· 33· 41: 49· 54· 59· 64· & 69· denoting a scale of 2L5s 8;5 Relation, 8 5 5 5 5 5 8.
A second 'Badass' dot-guide is this :
The dots are in the places 5· 6· 11· 12· 17· 18· 23· 24· 29· 30· 35· 36· 41: 46· 47· 52· 53· 58· 59· 64· 65· & 70 denoting a scale of 7L6s 5;1 Relation, 5 1 5 1 5 1 5 1 5 1 5 1 5.
Step (form 1) | Purdal size | Cent size | | | Step (form 2) | Purdal size | Cent size |
01 | 241,46 | 29.268 | | | 01 | 241,46 | 29.268 |
02 | 482,93 | 58.537 | | | 02 | 482,93 | 58.537 |
03 | 724,39 | 87.805 | | | 03 | 724,39 | 87.805 |
04 | 965,85 | 117.073 | | | 04 | 965,85 | 117.073 |
05 | 1207,32 | 146.341 | | | 05· | 1207,32 | 146.341 |
06 | 1448,78 | 175.61 | | | 06· | 1448,78 | 175.61 |
07 | 1690,24 | 204.878 | | | 07 | 1690,24 | 204.878 |
08· | 1931,71 | 234.146 | | | 08 | 1931,71 | 234.146 |
09 | 2173,17 | 263.415 | | | 09 | 2173,17 | 263.415 |
10 | 2414,63 | 292.683 | | | 10 | 2414,63 | 292.683 |
11 | 2656,1 | 321.951 | | | 11· | 2656,1 | 321.951 |
12 | 2897,56 | 351.22 | | | 12· | 2897,56 | 351.22 |
13· | 3139,02 | 380.488 | | | 13 | 3139,02 | 380.488 |
14 | 3380,49 | 409.756 | | | 14 | 3380,49 | 409.756 |
15 | 3621,95 | 439.024 | | | 15 | 3621,95 | 439.024 |
16 | 3863,41 | 468.293 | | | 16 | 3863,41 | 468.293 |
17 | 4104,88 | 497.561 | | | 17· | 4104,88 | 497.561 |
18· | 4346,34 | 526.829 | | | 18· | 4346,34 | 526.829 |
19 | 4587,8 | 556.098 | | | 19 | 4587,8 | 556.098 |
20 | 4829,27 | 585.366 | | | 20 | 4829,27 | 585.366 |
21 | 5070,73 | 614.634 | | | 21 | 5070,73 | 614.634 |
22 | 5312,2 | 643.902 | | | 22 | 5312,2 | 643.902 |
23· | 5553,66 | 673.171 | | | 23· | 5553,66 | 673.171 |
24 | 5795,12 | 702.439 | | | 24· | 5795,12 | 702.439 |
25 | 6036,59 | 731.707 | | | 25 | 6036,59 | 731.707 |
26 | 6278,05 | 760.976 | | | 26 | 6278,05 | 760.976 |
27 | 6519,51 | 790.244 | | | 27 | 6519,51 | 790.244 |
28· | 6760,98 | 819.512 | | | 28 | 6760,98 | 819.512 |
29 | 7002,44 | 848.78 | | | 29· | 7002,44 | 848.78 |
30 | 7243,9 | 878.049 | | | 30· | 7243,9 | 878.049 |
31 | 7485,37 | 907.317 | | | 31 | 7485,37 | 907.317 |
32 | 7726,83 | 936.585 | | | 32 | 7726,83 | 936.585 |
33· | 7968,29 | 965.854 | | | 33 | 7968,29 | 965.854 |
34 | 8209,76 | 995.122 | | | 34 | 8209,76 | 995.122 |
35 | 8451,22 | 1024.39 | | | 35· | 8451,22 | 1024.39 |
36 | 8692,68 | 1053.659 | | | 36· | 8692,68 | 1053.659 |
37 | 8934,15 | 1082.927 | | | 37 | 8934,15 | 1082.927 |
38 | 9175,61 | 1112.195 | | | 38 | 9175,61 | 1112.195 |
39 | 9417,07 | 1141.463 | | | 39 | 9417,07 | 1141.463 |
40 | 9658,54 | 1170.732 | | | 40 | 9658,54 | 1170.732 |
41\0: | 9900\0 | 1200\0 | | | 41\0: | 9900\0 | 1200\0 |
And, for last, 'The Classic Regular' dot-guide (heheh..) :The dots are in the places 10· 17· 24· 31· 41: 51· 58· & 65· denoting a scale of 2L3s 10;7 Relation, 10 7 7 7 10.
Step | Purdal size | Cent size |
01 | 241,46 | 29.268 |
02 | 482,93 | 58.537 |
03 | 724,39 | 87.805 |
04 | 965,85 | 117.073 |
05 | 1207,32 | 146.341 |
06 | 1448,78 | 175.61 |
07 | 1690,24 | 204.878 |
08 | 1931,71 | 234.146 |
09 | 2173,17 | 263.415 |
10· | 2414,63 | 292.683 |
11 | 2656,1 | 321.951 |
12 | 2897,56 | 351.22 |
13 | 3139,02 | 380.488 |
14 | 3380,49 | 409.756 |
15 | 3621,95 | 439.024 |
16 | 3863,41 | 468.293 |
17· | 4104,88 | 497.561 |
18 | 4346,34 | 526.829 |
19 | 4587,8 | 556.098 |
20 | 4829,27 | 585.366 |
21 | 5070,73 | 614.634 |
22 | 5312,2 | 643.902 |
23 | 5553,66 | 673.171 |
24· | 5795,12 | 702.439 |
25 | 6036,59 | 731.707 |
26 | 6278,05 | 760.976 |
27 | 6519,51 | 790.244 |
28 | 6760,98 | 819.512 |
29 | 7002,44 | 848.78 |
30 | 7243,9 | 878.049 |
31· | 7485,37 | 907.317 |
32 | 7726,83 | 936.585 |
33 | 7968,29 | 965.854 |
34 | 8209,76 | 995.122 |
35 | 8451,22 | 1024.39 |
36 | 8692,68 | 1053.659 |
37 | 8934,15 | 1082.927 |
38 | 9175,61 | 1112.195 |
39 | 9417,07 | 1141.463 |
40 | 9658,54 | 1170.732 |
41\0: | 9900\0 | 1200\0 |