Ed12
Ed12 means Division of the Twelfth Harmonic (12/1) into n equal parts.
Division of the twelfth harmonic into n equal parts
The twelfth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.1 dodecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hendecatave equivalence, this fact shapes one's musical approach dramatically. Also, the ed12-edo correspondences fall particularly close to the harmonic series of the NTSC or PAL-M color subcarrier:
| edo | ed12 | NTSC*n | PAL-M*n |
|---|---|---|---|
| 1 | 3.5849625 | 3.579545 MHz | 3.575611 MHz |
| 2 | 7.169925 | 7.158909 | 7.151222 |
| 3 | 10.7548875 | 10.7383635 | 10.726833 |
| 4 | 14.33985 | 14.317818 | 14.302444 |
| 5 | 17.9248125 | 17.8972725 | 17.878055 |
| 6 | 21.509775 | 21.476727 | 21.453666 |
| 7 | 25.0947375 | 25.0561815 | 25.029277 |
| 8 | 28.6797 | 28.635636 | 28.604888 |
| 9 | 32.2646625 | 32.2150905 | 32.180299 |
| 10 | 35.849625 | 35.79545 | 35.75611 |
| 11 | 39.4345875 | 39.3739995 | 39.331521 |
| 12 | 43.01955 | 42.953454 | 42.907332 |
| 13 | 46.6045125 | 46.5329085 | 46.482743 |
| 14 | 50.189475 | 50.112363 | 50.058554 |
| 15 | 53.7744375 | 53.6918175 | 53.634265 |
| 16 | 57.3594 | 57.271272 | 57.209776 |
| 17 | 60.9443625 | 60.8507265 | 60.785487 |
| 18 | 64.529325 | 64.430181 | 64.360598 |
| 19 | 68.1142875 | 68.0096355 | 67.936709 |
| 20 | 71.69925 | 71.58909 | 71.51222 |
| 21 | 75.2842125 | 75.1685445 | 75.087931 |
| 22 | 78.869175 | 78.747999 | 78.663442 |
| 23 | 82.4541375 | 82.3274535 | 82.239153 |
| 24 | 86.0391 | 85.906908 | 85.814664 |
| 25 | 89.6240625 | 89.4863625 | 89.390375 |
| 26 | 93.209025 | 93.065817 | 92.965886 |
| 27 | 96.7939875 | 96.6452715 | 96.541597 |
| 28 | 100.37895 | 100.2274726 | 100.117108 |
| 29 | 103.9639125 | 103.8041805 | 103.692819 |
| 30 | 107.548875 | 107.38365 | 107.28633 |
| 31 | 111.1338375 | 110.9630895 | 110.894041 |
| 32 | 114.7188 | 114.542544 | 114.437552 |
| 33 | 118.3037625 | 118.1219985 | 118.045263 |
| 34 | 121.888725 | 121.701453 | 121.588774 |
| 35 | 125.4736875 | 125.2809075 | 125.096485 |
| 36 | 129.05865 | 128.860362 | 128.739296 |
| 37 | 132.6436125 | 132.4398165 | 132.247707 |
| 38 | 136.228575 | 136.019271 | 135.860518 |
| 39 | 139.8135375 | 139.5987255 | 135.398929 |
| 40 | 143.3985 | 143.17818 | 143.02444 |