Ed12

From Xenharmonic Wiki
Jump to: navigation, search

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