31-EDD
Dot-Guide for 31-EDD instruments
31-EDD Fretboard is based on the formula (Scale_Length/(2^(x/31))). Christiaan Huygens is with certain the first person in advocate to the Ditave into 31 parts, promoved by Adriaan Fokker starting in 1942 within studies about physics and arithmetic before of his dedication to the music innovation for our present. In the beginning, this system corresponds to 1/5-tone 5;3 Relation of the Diatonic scale, denoting a mesotonic mood in it. By the way, here is the classic 2L3s Dot-Guide for 31-EDD :
The dots are in the places 8· 13· 18· 23· 31: 39· 44· 49· 54· & 62: denoting its 8;5 Relation, 8 5 5 5 8.
Incredible, but another way for dot-guiding a 31-EDD fretboard is valid too with it :
The dots are in the places 5· 9· 13· 18· 22· 26· 31: 36· 40· 44· 49· 53· 57· & 62: denoting a scale of 3L4s 5;4 Relation, 5 4 4 5 4 4 5.
| Step (form 1) | Purdal size | Cent size | | | Step (form 2) | Purdal size | Cent size |
| 01 | 319,4 | 38.71 | | | 01 | 319,4 | 38.71 |
| 02 | 638,7 | 77.42 | | | 02 | 638,7 | 77.42 |
| 03 | 958,1 | 116.13 | | | 03 | 958,1 | 116.13 |
| 04 | 1277,4 | 154.84 | | | 04 | 1277,4 | 154.84 |
| 05 | 1596,8 | 193.55 | | | 05· | 1596,8 | 193.55 |
| 06 | 1916,1 | 232.26 | | | 06 | 1916,1 | 232.26 |
| 07 | 2235,5 | 270.97 | | | 07 | 2235,5 | 270.97 |
| 08· | 2554,8 | 309.68 | | | 08 | 2554,8 | 309.68 |
| 09 | 2874,2 | 348.39 | | | 09· | 2874,2 | 348.39 |
| 10 | 3193,5 | 387.1 | | | 10 | 3193,5 | 387.1 |
| 11 | 3512,9 | 425.81 | | | 11 | 3512,9 | 425.81 |
| 12 | 3832,3 | 464.52 | | | 12 | 3832,3 | 464.52 |
| 13· | 4151,6 | 503.23 | | | 13· | 4151,6 | 503.23 |
| 14 | 4471 | 541.94 | | | 14 | 4471 | 541.94 |
| 15 | 4790,3 | 580.65 | | | 15 | 4790,3 | 580.65 |
| 16 | 5109,7 | 619.35 | | | 16 | 5109,7 | 619.35 |
| 17 | 5429 | 658.06 | | | 17 | 5429 | 658.06 |
| 18· | 5748,4 | 696.77 | | | 18· | 5748,4 | 696.77 |
| 19 | 6067,7 | 735.48 | | | 19 | 6067,7 | 735.48 |
| 20 | 6387,1 | 774.19 | | | 20 | 6387,1 | 774.19 |
| 21 | 6706,5 | 812.9 | | | 21 | 6706,5 | 812.9 |
| 22 | 7025,8 | 851.61 | | | 22· | 7025,8 | 851.61 |
| 23· | 7345,2 | 890.32 | | | 23 | 7345,2 | 890.32 |
| 24 | 7664,5 | 929.03 | | | 24 | 7664,5 | 929.03 |
| 25 | 7983,9 | 967.74 | | | 25 | 7983,9 | 967.74 |
| 26 | 8303,2 | 1006.45 | | | 26· | 8303,2 | 1006.45 |
| 27 | 8622,6 | 1045.16 | | | 27 | 8622,6 | 1045.16 |
| 28 | 8941,9 | 1083.87 | | | 28 | 8941,9 | 1083.87 |
| 29 | 9261,3 | 1122.58 | | | 29 | 9261,3 | 1122.58 |
| 30 | 9580,6 | 1161.29 | | | 30 | 9580,6 | 1161.29 |
| 31\0: | 9900\0 | 1200\0 | | | 31\0: | 9900\0 | 1200\0 |